File: ctomax21.tbl

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#############################################################################
##
#W  ctomax21.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of some subgroups of
##  (central extensions of) O7(3) and 2E6(2).
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctomax21.tbl,v $
#H  Revision 4.7  2012/04/23 16:16:10  gap
#H  next step of consolidation:
#H
#H  - removed a few unnecessary duplicate tables,
#H    and changed some related fusions, names of maxes, table constructions
#H  - make sure that duplicate tables arise only via `ConstructPermuted'
#H    constructions
#H  - added some relative names
#H  - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H    L2(41) -> M, (A5xA12):2 -> A17,
#H  - added maxes of A12.2, L6(2), 2.M22.2
#H  - added table of QD16.2,
#H  - fixed the syntax of two `ALN' calls
#H      TB
#H
#H  Revision 4.6  2012/01/26 11:18:40  gap
#H  added missing table automorphisms
#H      TB
#H
#H  Revision 4.5  2011/09/28 13:02:18  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added tables of 3^6:(L4(3)x2), 3^6:2U4(3).2_1 2^8:O8+(2):2,
#H    2^8:O8-(2):2, 2.2^5.S6, 2^(1+6)_-.3^3.S4, 2.3^4.2^3.S4
#H      TB
#H
#H  Revision 4.4  2011/02/09 16:00:05  gap
#H  added fusion 2.J2.2M2 = Isoclinic(2xU3(3).2) -> 2.J2.2
#H      TB
#H
#H  Revision 4.3  2010/12/02 08:46:20  gap
#H  - corrected the permutations in the construction data for
#H    "(A4x2(A4xA4).2).2",
#H  - changed texts for the fusions 3.2E6(2)M4 -> 3.2E6(2),
#H    3.2E6(2)M5 -> 3.2E6(2), 3.2E6(2)M8 -> 3.2E6(2),
#H    6xF4(2) -> 6.2E6(2), 3x2.F4(2) -> 6.2E6(2), 6.2E6(2)M5 -> 6.2E6(2),
#H    6x2.F4(2) -> (2^2x3).2E6(2), (2^2x3).2E6(2)M4 -> (2^2x3).2E6(2),
#H    (2^2x3).2E6(2)M5 -> 2E6(2)M5, (2^2x3).2E6(2)M5 -> (2^2x3).2E6(2),
#H    2x3.Fi22 -> 6.2E6(2), 6.2E6(2)M9 -> 6.2E6(2),
#H    2x6.Fi22 -> (2^2x3).2E6(2), (2^2x3).2E6(2)M8 -> (2^2x3).2E6(2),
#H    (2^2x3).2E6(2)M9 -> (2^2x3).2E6(2)
#H    (in some cases, the relativity of the maps w.r.t. other fusions
#H    cannot be stored because I do not have the tables of 3.2E6(2).3
#H    and its downward extensions)
#H      TB
#H
#H  Revision 4.2  2010/05/05 13:20:05  gap
#H  - added many class fusions,
#H  - changed several class fusions according to consistency conditions,
#H    after systematic checks of consistency
#H    - with Brauer tables w.r.t. the restriction of characters,
#H    - of subgroup fusions with the corresponding subgroup fusions between
#H      proper factors where the factor fusions are stored,
#H    - of subgroup fusions from maximal subgroups with subgroup fusions of
#H      extensions inside automorphic extensions
#H
#H      TB
#H
#H  Revision 4.1  2010/01/19 17:05:33  gap
#H  added several tables of maximal subgroups of central extensions of
#H  simple groups (many of them were contributed by S. Dany)
#H      TB
#H
##

MOT("3^5:U4(2):2",
0,
[12597120,139968,157464,174960,36,72,1458,1458,324,5832,432,648,864,5184,108,
108,162,324,5832,3888,3888,116640,3456,1728,108,108,108,162,2916,1458,1458,
2916,1458,2916,216,216,216,729,17496,17496,17496,36,36,36,288,144,48,24,432,
216,432,864,54,324,324,324,10,15,30,12,96,54,108,27,27,27,8,54,54,108,54,108,
108,72,72,288],
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33,34,40,39,41,38,39,40,41,37,36,35,23,24,14,11,4,3,2,1,28,34,29,32,59,58,59,6
,14,8,10,64,65,66,45,31,33,34,30,32,29,11,13,14],[1,1,1,1,12,14,1,1,3,1,14,14,
14,14,19,19,22,22,22,22,22,22,23,23,23,23,23,3,1,1,1,1,1,1,23,23,23,1,1,1,1,45
,45,45,45,45,47,47,52,52,52,52,19,22,22,22,57,59,59,61,61,23,23,40,41,39,67,52
,52,52,52,52,52,76,76,76],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,15,17,18,19,20
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,47,48,49,50,51,52,53,54,55,56,22,4,1,60,61,62,63,64,65,66,67,68,69,70,71,72,
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,-54,54,0,0,0,0,0,0,0,0,6,-6,-12,0,0,0,0
,0,0,0,0,12,-6,0,0,0,0,0,0,0,0,0,0,-3,-3,6,0,-27,-27,54,-2,1,1,4,-2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,-54,54,0,0,0,0,0,0,0,0
,6,-6,-12,0,0,0,0,0,0,0,0,12,-6,0,0,0,0,0,0,0,0,0,0,6,-3,-3,0,-27,54,-27,1,1,
-2,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[640,64,
-8,-80,0,0,-8,-8,4,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,28,10,10,-8,-8,-8,0
,0,0,1,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-2,1,0,0,0,0,0,0
,0,0,0,0],[640,64,-8,-80,0,0,-8,-8,4,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
-8,-8,10,-8,10,28,0,0,0,1,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,-2,1,1,0,0,0,0,0,0,0,0,0,0],[640,64,-8,-80,0,0,-8,-8,4,-8,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,-2,-8,10,-8,28,10,-8,0,0,0,1,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,1,1,-2,0,0,0,0,0,0,0,0,0,0],[648,0,-81,81,0,0,0,0,0,0,-3,3,
0,12,0,0,0,0,-9,18,-9,-90,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1
,3,3,-6,-6,0,0,0,0,0,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-2,4],
[TENSOR,[65,2]],[720,0,-90,90,0,0,3,-6,0,12,6,-6,0,-24,0,0,-3,6,-6,12,-6,-60,
0,0,0,0,0,0,6,-3,-3,6,-3,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,4,4,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,1,1,-2,1,-2,-2,0,0,0],
[TENSOR,[67,2]],[720,-72,72,0,0,0,6,-3,0,-12,0,0,0,0,0,0,0,0,0,0,0,0,-16,8,-4
,2,2,0,12,-6,-6,-6,12,-6,2,2,-4,0,-18,-18,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0],[720,-72,72,0,0,0,6,-3,0,-12,0,0,0,0,0,
0,0,0,0,0,0,0,-16,8,2,-4,2,0,-6,12,-6,-6,-6,12,-4,2,2,0,-18,36,-18,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0],[720,-72,72,0,0,0
,6,-3,0,-12,0,0,0,0,0,0,0,0,0,0,0,0,-16,8,2,2,-4,0,-6,-6,12,12,-6,-6,2,-4,2,0,
36,-18,-18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,2,0,0,0,0,0,0,0,0,0,0,0,
0,0],[810,-81,81,0,0,0,0,0,0,0,0,-3,3,6,0,0,0,0,-9,-9,18,-90,18,-9,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,0,0,-6,3,3,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-2,1,4],
[TENSOR,[72,2]],[960,96,-12,-120,0,0,0,0,0,0,0,0,0,0,-2,-2,4,4,28,-8,-8,-80,0
,0,0,0,0,3,-6,-6,-6,-6,-6,-6,0,0,0,-3,24,24,24,0,0,0,0,0,0,0,0,0,0,0,1,-2,-2,
-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[74,2]],[1152,0,-144,144,0,0,-6,12,0,-24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-12,6,6,-12,6,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,2,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(15,16),
(26,27)(30,31)(32,34)(35,36)(39,40)(43,44)(54,56)(64,66)(68,71)(70,72),
(25,27)(29,32)(31,33)(36,37)(39,41)(42,43)(55,56)(65,66)(68,69)(72,73)]);
ALF("3^5:U4(2):2","U4(2).2",[1,1,1,1,13,13,5,5,5,5,3,3,3,3,20,20,20,20,16,
16,16,16,2,2,12,12,12,6,6,6,6,6,6,6,10,10,10,4,4,4,4,15,15,15,7,7,8,8,17,
17,17,17,21,21,21,21,24,9,9,25,18,11,11,14,14,14,23,22,22,22,22,22,22,19,
19,19]);
ALF("3^5:U4(2):2","O7(3)",[1,7,5,6,57,24,10,11,36,6,24,20,22,3,54,55,27,
18,17,19,18,2,4,21,26,30,31,37,7,9,8,10,11,10,28,29,23,11,9,8,5,43,48,47,
13,42,15,49,25,23,26,4,56,27,19,27,41,53,16,49,15,32,25,38,37,39,34,28,32,
31,29,30,21,45,44,12]);
ALF("3^5:U4(2):2","Fi22",[1,7,6,5,58,18,7,8,31,5,18,17,23,3,55,56,19,15,
16,19,15,2,4,22,22,24,24,32,7,8,8,7,6,7,21,21,25,8,6,6,8,48,42,43,12,44,
13,46,20,21,24,4,57,19,19,19,34,52,14,46,13,25,20,32,33,32,30,25,21,22,25,
22,24,41,47,10],[
"fusion map is unique up to table aut."
]);
ALF("3^5:U4(2):2","3^5:(2xU4(2).2)",[1,4,3,2,61,60,25,24,26,23,15,14,13,
12,99,99,98,97,74,76,75,73,6,7,55,56,56,32,28,31,31,30,29,30,47,47,46,21,
20,20,19,68,69,69,34,35,37,38,83,84,82,81,104,103,102,103,116,44,43,119,
89,51,50,66,65,66,113,110,108,109,110,109,107,93,94,92],[
"fusion map is unique up to table aut."
]);

MOT("O7(3)M5",
[
"5th maximal subgroup of O7(3),\n",
"differs from O7(3)M4 = G2(3) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["G2(3)"]]);
ALF("O7(3)M5","O7(3)",[1,4,5,9,9,11,10,14,13,23,29,32,30,33,35,34,39,39,
39,46,48,51,50],[
"fusion G2(3) -> O7(3) mapped under O7(3).2"
]);

MOT("3^(3+3):L3(3)",
[
"origin: Dixon's Algorithm"
],
[4094064,157464,17496,17496,17496,13,13,13,13,27,27,81,81,81,729,4374,4374,
4374,81,1458,1458,1458,1458,1458,1458,54,54,54,54,54,54,54,54,54,216,216,216,
216,432,8,8,36,72,36,36,36],
[,[1,2,3,4,5,7,8,9,6,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,16,18,17,
23,24,25,21,22,20,5,4,3,2,1,43,43,38,39,35,36,37],[1,1,1,1,1,6,7,8,9,5,4,2,1,2
,1,1,1,1,2,1,1,1,1,1,1,39,39,39,39,39,39,39,39,39,39,39,39,39,39,40,41,43,43,
43,43,43],,,,,,,,,,[1,2,3,4,5,1,1,1,1,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,41,40,42,43,44,45,46]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1],[12,12,12,12,12,-1,-1,-1,-1,0,0,0,0,0,3,3,3,3,3,3,3,3,3,3,3,1
,1,1,1,1,1,1,1,1,4,4,4,4,4,0,0,0,0,0,0,0],[13,13,13,13,13,0,0,0,0,1,1,1,1,1,4,
4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,-3,-3,-3,-3,-3,-1,-1,1,1,1,1,1],[16,16,
16,16,16,E(13)^2+E(13)^5+E(13)^6,E(13)^4+E(13)^10+E(13)^12,
E(13)^7+E(13)^8+E(13)^11,E(13)+E(13)^3+E(13)^9,1,1,1,1,1,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[4,4]],
[GALOIS,[4,7]],
[GALOIS,[4,2]],[26,26,-1,-1,-1,0,0,0,0,-1,-1,2,2,2,8,8,8,8,-1,-1,-1,-1,-1,-1,
-1,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,0,0,2,2,-1,-1,-1],[26,26,26,26,26,0,0,
0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,2,2,2,2,2,0,0,2,2,2,2,2],[26,26,-1,-1,-1,0,0,0,0,-1,2,-1,-1,-1,-1,-1,-1,-1,-1
,8,8,8,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,-1,-1,-1,2,2,0,0,2,2,-1,-1,-1],[26,26,
-1,-1,-1,0,0,0,0,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,8,8,8,-1,-1,-1,2,2,2,-1
,-1,-1,-1,-1,-1,2,2,0,0,2,2,-1,-1,-1],[26,26,26,26,26,0,0,0,0,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,-E(8)-E(8)^3
,E(8)+E(8)^3,0,0,0,0,0],
[GALOIS,[12,5]],[27,27,27,27,27,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1],[39,39,39,39,39,0,0,0,0,0,0,0,0,0
,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,
-1,-1],[52,52,-2,-2,-2,0,0,0,0,-2,1,1,1,1,7,7,7,7,-2,7,7,7,-2,-2,-2,-1,-1,-1,2
,2,2,-1,-1,-1,2,2,2,-4,-4,0,0,0,0,0,0,0],[52,52,-2,-2,-2,0,0,0,0,1,-2,1,1,1,7,
7,7,7,-2,-2,-2,-2,7,7,7,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,-4,-4,0,0,0,0,0,0,0],[52
,52,-2,-2,-2,0,0,0,0,1,1,-2,-2,-2,-2,-2,-2,-2,-2,7,7,7,7,7,7,2,2,2,-1,-1,-1,-1
,-1,-1,2,2,2,-4,-4,0,0,0,0,0,0,0],[78,-3,6,-3,-3,0,0,0,0,0,0,-3,3,0,-3,6,-3,15
,0,-3,-3,6,-3,6,-3,-2,1,1,1,-2,1,1,-2,1,1,1,-2,1,-2,0,0,-1,2,-1,-1,2],[78,78,
-3,-3,-3,0,0,0,0,0,0,0,0,0,6,6,6,6,-3,6,6,6,6,6,6,0,0,0,0,0,0,0,0,0,-3,-3,-3,6
,6,0,0,-2,-2,1,1,1],[78,-3,6,-3,-3,0,0,0,0,0,0,0,-3,3,-3,15,6,-3,0,-3,6,-3,6,
-3,-3,1,1,-2,-2,1,1,-2,1,1,1,1,-2,1,-2,0,0,-1,2,-1,-1,2],[78,-3,6,-3,-3,0,0,0,
0,0,0,3,0,-3,-3,-3,15,6,0,6,-3,-3,-3,-3,6,1,-2,1,1,1,-2,1,1,-2,1,1,-2,1,-2,0,0
,-1,2,-1,-1,2],[156,-6,12,-6,-6,0,0,0,0,0,0,0,3,-3,-6,3,12,21,0,3,-6,3,-6,3,3,
1,1,-2,-2,1,1,-2,1,1,-2,-2,4,-2,4,0,0,0,0,0,0,0],[156,-6,12,-6,-6,0,0,0,0,0,0,
3,-3,0,-6,12,21,3,0,3,3,-6,3,-6,3,-2,1,1,1,-2,1,1,-2,1,-2,-2,4,-2,4,0,0,0,0,0,
0,0],[156,-6,12,-6,-6,0,0,0,0,0,0,-3,0,3,-6,21,3,12,0,-6,3,3,3,3,-6,1,-2,1,1,1
,-2,1,1,-2,-2,-2,4,-2,4,0,0,0,0,0,0,0],[208,208,-8,-8,-8,0,0,0,0,1,1,-2,-2,-2,
10,10,10,10,1,-8,-8,-8,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
208,208,-8,-8,-8,0,0,0,0,1,-2,1,1,1,-8,-8,-8,-8,1,10,10,10,-8,-8,-8,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[208,208,-8,-8,-8,0,0,0,0,-2,1,1,1,1,-8,-8,-8
,-8,1,-8,-8,-8,10,10,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[234,-9,-9,
-9,18,0,0,0,0,0,0,0,0,0,0,-9,-9,18,0,-9,9,0,0,-9,9,-1,2,-1,2,-1,-1,-1,2,-1,2,
-1,-1,-1,2,0,0,-1,2,2,-1,-1],[234,-9,-9,18,-9,0,0,0,0,0,0,0,0,0,0,-9,-9,18,0,9
,0,-9,9,0,-9,-1,2,-1,-1,2,-1,2,-1,-1,-1,2,-1,-1,2,0,0,-1,2,-1,2,-1],[234,-9,-9
,-9,18,0,0,0,0,0,0,0,0,0,0,-9,18,-9,0,0,-9,9,9,0,-9,-1,-1,2,-1,2,-1,-1,-1,2,2,
-1,-1,-1,2,0,0,-1,2,2,-1,-1],[234,-9,-9,-9,18,0,0,0,0,0,0,0,0,0,0,18,-9,-9,0,9
,0,-9,-9,9,0,2,-1,-1,-1,-1,2,2,-1,-1,2,-1,-1,-1,2,0,0,-1,2,2,-1,-1],[234,-9,-9
,18,-9,0,0,0,0,0,0,0,0,0,0,-9,18,-9,0,-9,9,0,-9,9,0,-1,-1,2,-1,-1,2,-1,2,-1,-1
,2,-1,-1,2,0,0,-1,2,-1,2,-1],[234,-9,-9,18,-9,0,0,0,0,0,0,0,0,0,0,18,-9,-9,0,0
,-9,9,0,-9,9,2,-1,-1,2,-1,-1,-1,-1,2,-1,2,-1,-1,2,0,0,-1,2,-1,2,-1],[234,-9,18
,-9,-9,0,0,0,0,0,0,0,0,0,-9,18,18,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,-6,3,
-6,0,0,1,-2,1,1,-2],[468,-18,-18,-18,36,0,0,0,0,0,0,0,0,0,0,-18,9,9,0,-9,0,9,9
,-9,0,2,-1,-1,-1,-1,2,2,-1,-1,-4,2,2,2,-4,0,0,0,0,0,0,0],[468,-18,-18,-18,36,0
,0,0,0,0,0,0,0,0,0,9,-18,9,0,0,9,-9,-9,0,9,-1,-1,2,-1,2,-1,-1,-1,2,-4,2,2,2,-4
,0,0,0,0,0,0,0],[468,-18,-18,36,-18,0,0,0,0,0,0,0,0,0,0,-18,9,9,0,0,9,-9,0,9,
-9,2,-1,-1,2,-1,-1,-1,-1,2,2,-4,2,2,-4,0,0,0,0,0,0,0],[468,-18,-18,36,-18,0,0,
0,0,0,0,0,0,0,0,9,-18,9,0,9,-9,0,9,-9,0,-1,-1,2,-1,-1,2,-1,2,-1,2,-4,2,2,-4,0,
0,0,0,0,0,0],[468,-18,-18,-18,36,0,0,0,0,0,0,0,0,0,0,9,9,-18,0,9,-9,0,0,9,-9,
-1,2,-1,2,-1,-1,-1,2,-1,-4,2,2,2,-4,0,0,0,0,0,0,0],[468,-18,-18,36,-18,0,0,0,0
,0,0,0,0,0,0,9,9,-18,0,-9,0,9,-9,0,9,-1,2,-1,-1,2,-1,2,-1,-1,2,-4,2,2,-4,0,0,0
,0,0,0,0],[624,-24,48,-24,-24,0,0,0,0,0,0,-3,0,3,3,-24,12,-6,0,12,-6,-6,-6,-6,
12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[624,-24,48,-24,-24,0,0,0,0,0,0,
0,3,-3,3,12,-6,-24,0,-6,12,-6,12,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0],[624,-24,48,-24,-24,0,0,0,0,0,0,3,-3,0,3,-6,-24,12,0,-6,-6,12,-6,12,-6,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[702,-27,-27,-27,54,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,-3,-3,-3,6,0,0,1,-2,-2,1,1],[702,-27
,-27,54,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,6,-3,
-3,6,0,0,1,-2,1,-2,1]],
[(40,41),(6,7,8,9),
( 4, 5)(10,11)(20,25)(21,23)(22,24)(29,32)(30,33)(31,34)(35,36)(44,45)]);
ALF("3^(3+3):L3(3)","O7(3)",[1,5,7,8,9,50,51,50,51,39,38,37,11,36,11,6,7,5,37,
8,10,11,10,11,9,25,23,26,30,32,29,31,32,28,29,28,21,23,4,34,34,43,13,48,
47,42]);
ALF("3^(3+3):L3(3)","Fi22",[1,6,7,8,6,49,50,49,50,32,33,32,8,31,8,5,7,6,
32,8,7,8,7,8,6,20,21,24,22,25,21,24,25,25,21,25,22,21,4,30,30,42,12,43,48,
44]);

MOT("3^(3+3)b:L3(3)",
0,
0,
0,
0,
0,
["ConstructPermuted",["3^(3+3):L3(3)"]]);
ALF("3^(3+3)b:L3(3)","Fi22M3",[1,5,7,8,9,50,51,50,51,39,38,37,11,36,11,6,
7,5,37,8,10,11,10,11,9,25,23,26,30,32,29,31,32,28,29,28,21,23,4,34,34,43,
13,48,47,42]);
ALF("3^(3+3)b:L3(3)","Fi22",[1,6,7,8,6,50,49,50,49,32,33,32,8,31,8,5,7,6,
32,8,7,8,7,8,6,20,21,24,22,25,21,24,25,25,21,25,22,21,4,30,30,43,12,42,48,
44],[
"fusion 3^(3+3):L3(3) -> Fi22 mapped under Fi22.2"
]);

MOT("O7(3)M8",
[
"8th maximal subgroup of O7(3),\n",
"differs from O7(3)M7 = S6(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["S6(2)"]]);
ALF("O7(3)M8","O7(3)",[1,2,4,3,4,6,9,10,13,15,12,14,15,16,18,25,29,24,27,
31,30,33,34,35,39,41,49,45,48,53],[
"fusion S6(2) -> O7(3) mapped under O7(3).2"
]);

MOT("O7(3)M11",
[
"11th maximal subgroup of O7(3),\n",
"differs from O7(3)M10 = A9.2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A9.2"]]);
ALF("O7(3)M11","O7(3)", [1,3,4,6,9,10,15,14,16,24,30,33,39,40,49,53,2,4,12,
15,18,25,27,31,29,35,41,45,52,58], [
"fusion A9.2 -> O7(3) mapped under O7(3).2"
]);

MOT("(2^2xU4(2)):2",
0,
[207360,207360,103680,48,96,96,864,864,432,768,768,384,2304,4608,4608,24,24,
192,192,64,64,64,64,32,2880,2880,72,72,72,72,216,432,432,288,288,288,288,2592,
2592,2592,2592,144,144,144,144,20,20,20,40,40,48,48,48,48,384,384,192,192,192,
72,144,144,16,16,24,24,36,36,36,36],
[,[1,1,1,8,8,8,8,8,8,1,1,1,1,1,1,5,6,10,11,10,11,11,11,11,2,1,7,8,33,32,32,32,
32,38,38,38,38,38,38,38,38,8,8,8,8,50,49,50,50,50,34,34,34,34,14,14,14,2,1,32,
32,32,56,55,32,33,68,68,68,68],[1,2,3,12,10,11,2,1,3,10,11,12,13,14,15,18,19,
18,19,20,21,22,23,24,25,26,25,26,25,26,3,1,2,14,15,13,13,1,2,3,3,14,15,13,13,
46,47,48,49,50,57,57,55,56,55,56,57,58,59,13,14,15,63,64,59,58,39,38,41,40],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,33,34,35,37,36,38,39,41,40,42,43,45,44,26,25,3,2,1,52,51,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68,70,69]],
0,
[(36,37)(40,41)(44,45)(51,52)(69,70)],
["ConstructIndexTwoSubdirectProduct","V4","D8","U4(2)","U4(2).2",[66,67,68,69,
70,71,72,73,74,75,116,117,118,119,120,121,122,123,124,125],(2,14,68,64,21,33,
12,61,26,43,45,60,16)(3,11,42,36,9,50,51,25,35,41,37,31)(4,38,57,66,30,54,20,
7,55,27,62,59,47,70,17,15,53,18,10,34,40,48,69,46)(5,8,23,22,56,29,67,65,28)
(6,32,13)(19,39,24,49,52,58,63),(2,4,9,22,55,29,7,20,49,61,45,47,53,13,34,16,
40,37,26,3,10,21,48,52,12,28,11,27)(5,8,19,65,58,36,25,62,50,60,42,44,64,59,
41,38,32,18,57,35,15,39,31,24,63,51)(6,23,54,14,33,17,43,56,30)]);
ALF("(2^2xU4(2)):2","O7(3)",[1,3,2,26,21,22,22,7,19,4,3,4,3,4,2,42,44,13,
12,14,15,12,15,15,12,3,44,22,45,24,18,6,24,23,17,20,20,5,20,17,17,26,19,
22,22,40,58,41,40,16,46,46,43,46,13,14,14,15,4,24,25,18,35,34,25,49,57,36,
54,55]);

MOT("(A4x2(A4xA4).2).2",
0,
[13824,13824,256,384,1152,4608,4608,768,108,108,54,54,36,216,216,48,864,864,
144,288,288,432,432,144,144,36,216,216,96,1728,1728,144,108,108,144,144,432,
432,64,64,16,32,16,64,64,32,192,192,192,192,32,32,24,24,24,24,36,36,384,384,64
,192,1152,1152,48,48,144,144,24,144,144,36,36],
[,[1,1,1,2,2,1,1,1,9,9,11,11,14,15,15,17,18,18,17,18,18,22,22,22,22,27,28,28,
30,30,30,31,33,33,37,37,37,37,3,3,4,1,5,8,8,6,1,1,6,6,3,8,22,22,25,25,9,9,1,1,
8,8,1,1,37,37,37,37,29,30,30,33,33],[1,2,3,4,5,6,7,8,1,2,1,2,5,2,1,4,2,1,5,7,6
,1,2,7,6,5,2,1,8,1,2,5,1,2,6,7,1,2,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
48,47,49,50,64,63,59,60,61,62,63,64,60,59,63,64,62,63,64,64,63]],
0,
[( 9,33)(10,34)(13,26)(14,27)(15,28)(57,72)(58,73),
(39,40)(44,45)(47,48)(49,50)(53,54)(55,56),
(39,40)(44,45)(57,58)(59,60)(63,64)(65,66)(67,68)(70,71)(72,73)],
[ "ConstructIndexTwoSubdirectProduct", "a4", "Symm(4)", "b33141", "w(f4)", 
  [ 87, 88, 89, 90, 91, 92, 95, 97, 98, 112, 113, 114, 115, 116, 117, 120, 
      122, 123 ], (3,8,38,28,59,43,34,31,66,39,14,62,52,58,45,11,19)(4,5,18,7,
    37,15,67,40,27,16,68,41,33,30,61,48,26,24,36,32,65,46,12,63,53,73,56,42,9,
    22,20)(6,17)(10,23,35,29,60,47,13,64,54,57,44)(49,70)(50,71,51,69)(55,72),
  (3,5)(7,12,21,35,40,38,39,37,41,54,27,10,34,25,43,52,18,32,23,45,58,65,62,
    49,17,31,9,24,46,57,51,28)(8,11,33,26)(13,20,36,42,55,29,14,22,44,59,64,
    72,70,68,66,63,48,61,47,60,50,16,53,15,19,56,30)(67,73,69) ]);
ALF("(A4x2(A4xA4).2).2","O7(3)",[1,4,4,14,13,3,2,3,10,30,11,32,48,29,9,46,23,
5,43,17,20,6,25,18,24,47,28,8,22,7,21,42,10,31,22,19,7,26,13,14,35,4,34,
15,12,15,4,3,15,12,14,15,24,25,49,45,31,27,4,3,15,12,2,4,22,26,19,21,44,
19,26,30,27]);

MOT("(2x3^5).U4(2).2",
[
"origin: Dixon's Algorithm"
],
[25194240,25194240,279936,279936,314928,314928,349920,349920,36,72,2916,2916,
2916,2916,648,648,11664,11664,432,648,864,5184,108,108,324,324,324,5832,3888,
3888,116640,3456,1728,108,108,108,324,324,5832,5832,2916,2916,2916,2916,5832,
5832,2916,2916,5832,5832,432,432,432,432,432,432,1458,1458,34992,34992,34992,
34992,34992,34992,72,72,72,72,72,72,576,576,288,288,48,24,432,432,432,432,864,
108,108,324,324,324,20,20,30,30,60,60,24,24,192,192,108,108,108,54,54,54,54,54
,54,16,16,108,108,108,108,108,108,108,108,108,72,72,288],
[,[1,1,3,3,5,5,7,7,16,18,11,11,13,13,15,15,17,17,8,6,4,2,16,16,12,12,18,6,4,8,
2,1,3,40,50,46,38,38,40,40,42,42,44,44,46,46,48,48,50,50,62,62,60,60,64,64,58,
58,60,60,62,62,64,64,55,55,53,53,51,51,32,32,33,33,22,19,7,5,5,3,1,37,37,49,39
,45,92,92,89,89,91,91,10,10,22,22,13,13,17,101,101,103,103,105,105,71,71,44,44
,48,48,50,42,42,46,40,19,21,22],[1,2,1,2,1,2,1,2,20,22,1,2,1,2,5,6,1,2,22,22,
22,22,28,28,31,31,31,31,31,31,31,32,32,32,32,32,6,5,2,1,2,1,2,1,2,1,2,1,2,1,32
,32,32,32,32,32,2,1,2,1,2,1,2,1,72,71,72,71,72,71,71,72,71,72,75,75,81,81,81,
81,81,28,28,31,31,31,87,88,91,92,91,92,96,95,95,96,32,32,32,61,62,63,64,59,60,
106,107,81,81,81,81,81,81,81,81,81,119,119,119],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,24,23,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,83,82,84,85,86,31,31,7,8,1,
2,94,93,96,95,97,98,99,100,101,102,103,104,105,107,106,108,109,110,111,112,113
,114,115,116,117,118,119]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1
,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[6,6,6,6,6,6,6,6,-1,-1,3,3
,3,3,3,3,3,3,2,2,2,2,-1,-1,-1,-1,-1,-4,-4,-4,-4,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,1,1,1,1,1,1,-3,-3,-3,-3,-3,-3,-3,-3,-1,-1,-1,-1,-1,-1,2,2,2,2,0,0
,0,0,0,0,0,2,2,2,2,2,1,1,1,1,1,1,-1,-1,2,2,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,-2,-2,-2],
[TENSOR,[3,2]],[8,-8,8,-8,8,-8,8,-8,0,0,-4,4,-4,4,-4,4,-4,4,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,3,-3,3,-3,3,-3,1,-1,1,-1
,1,-1,1,-1,-1,1,-1,1,-1,1,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,0,0,
0,0,0,0,0,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,10,10,10,10,10,10,10
,2,2,-2,-2,-2,-2,-2,-2,-2,-2,2,2,2,2,0,0,0,0,0,0,0,0,0,-6,-6,0,0,0,4,4,4,4,4,4
,4,4,4,4,4,4,4,4,-3,-3,-3,-3,-3,-3,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,2,2,2,2,
-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[15,15,15,15,15,15,15,15,0,0,0,0,0,0,0,0,0,0,3,3,3,3,2,2,2,2,2,
5,5,5,5,7,7,1,1,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,-3,-3,-3,-3,-3,-3,-3
,-3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0
,3,3,-2,-2,-2,0,0,0,0,0,0,-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,-1],
[TENSOR,[7,2]],[15,15,15,15,15,15,15,15,-1,-1,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,
-1,-1,-1,-1,5,5,5,5,-1,-1,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,6,6,6,
6,6,6,6,6,0,0,0,0,0,0,3,3,3,3,-1,-1,-3,-3,-3,-3,-3,2,2,2,2,2,0,0,0,0,0,0,1,1,1
,1,-1,-1,-1,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,1,1,1],
[TENSOR,[9,2]],[20,20,20,20,20,20,20,20,1,1,5,5,5,5,5,5,5,5,4,4,4,4,-1,-1,-1,
-1,-1,-10,-10,-10,-10,4,4,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-2,
-2,-2,-2,-2,-2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-1,-1,-1
,-1,-1,0,0,0,0,0,0,1,1,-2,-2,1,1,1,-1,-1,-1,-1,-1,-1,0,0,1,1,1,1,1,1,1,1,1,-2,
-2,-2],
[TENSOR,[11,2]],[20,20,20,20,20,20,20,20,2,2,2,2,2,2,2,2,2,2,-4,-4,-4,-4,0,0,
0,0,0,0,0,0,0,4,4,-2,-2,-2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,-7,-7,-7,-7
,-7,-7,-7,-7,1,1,1,1,1,1,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-2,-2,-2,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,-20,20,-20,20,-20,
20,-20,0,0,2,-2,2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,
-2,2,-2,2,-2,2,-2,2,-2,2,-3,3,-3,3,-3,3,7,-7,7,-7,7,-7,7,-7,1,-1,1,-1,1,-1,2,
-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,
-2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,0,0,1,-1,1,-1,1,-1,E(8)+E(8)^3,-E(8)-E(8)^3
,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[14,2]],[24,24,24,24,24,24,24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2
,-2,-2,4,4,4,4,8,8,-1,-1,-1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,6,6,6,6,6,
6,6,6,0,0,0,0,0,0,0,0,0,0,0,0,4,4,4,4,4,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,2,
2,2,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0],
[TENSOR,[16,2]],[30,30,30,30,30,30,30,30,-1,-1,3,3,3,3,3,3,3,3,2,2,2,2,1,1,1,
1,1,10,10,10,10,-10,-10,-1,-1,-1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1
,3,3,3,3,3,3,3,3,1,1,1,1,1,1,-2,-2,-2,-2,0,0,-2,-2,-2,-2,-2,1,1,1,1,1,0,0,0,0,
0,0,-1,-1,-4,-4,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0],
[TENSOR,[18,2]],[40,-40,40,-40,40,-40,40,-40,0,0,4,-4,4,-4,4,-4,4,-4,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-3,3,-3,3,-3,3,
-13,13,-13,13,-13,13,-13,13,-1,1,-1,1,-1,1,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[40,-40,
40,-40,40,-40,40,-40,0,0,-8,8,-8,8,-8,8,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,0,0,0,0,0,0,-4,4,-4,4,-4,4,-4,4,2,-2,2,
-2,2,-2,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,
-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[60,60,60,60,60,60,60,60,1,1,-3,-3,-3,-3,-3,
-3,-3,-3,4,4,4,4,-1,-1,-1,-1,-1,-10,-10,-10,-10,-4,-4,-1,-1,-1,-3,-3,-3,-3,-3,
-3,-3,-3,-3,-3,-3,-3,-3,-3,2,2,2,2,2,2,6,6,6,6,6,6,6,6,0,0,0,0,0,0,0,0,0,0,0,0
,-2,-2,-2,-2,-2,-1,-1,-1,-1,-1,0,0,0,0,0,0,-1,-1,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,
1,1,1,1,1,1,1,1,1,2,2,2],
[TENSOR,[22,2]],[60,60,60,60,60,60,60,60,-2,-2,-6,-6,-6,-6,-6,-6,-6,-6,4,4,4,
4,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,-3,-3,-3,
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,0,0,-24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,-12,-6,6,-6,6,12,-12,-6
,6,12,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-1,1,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1440
,-1440,0,0,-180,180,180,-180,0,0,6,-6,-12,12,0,0,24,-24,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-12,12,6,-6,6,-6,-12,12,6,-6,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 93, 94)( 95, 96)(106,107),(87,88),(82,83),(25,26),(23,24),
( 78, 79)(108,109)(110,111)(113,114),
( 35, 36)( 41, 43)( 42, 44)( 45, 49)( 46, 50)( 51, 53)( 52, 54)( 59, 61)( 60,
 62)( 67, 69)
( 68, 70)( 84, 86)( 97, 98)(100,104)(101,105)(108,113)(109,114)(110,111)(112,
115)
,
( 34, 35)( 39, 49)( 40, 50)( 41, 47)( 42, 48)( 51, 55)( 52, 56)( 61, 63)( 62,
 64)( 65, 69)
( 66, 70)( 84, 85)( 97, 98)(100,102)(101,103)(108,109)(110,114)(111,113)(112,
116)
]);
ALF("(2x3^5).U4(2).2","2.O7(3)",[1,2,10,11,6,7,8,9,86,35,16,17,18,19,52,
53,8,9,35,30,32,4,82,83,38,38,28,27,29,28,3,5,31,37,43,44,55,54,11,10,15,
14,13,12,17,16,19,18,17,16,39,40,41,42,34,33,19,18,15,14,13,12,7,6,65,64,
72,71,70,69,21,22,62,63,24,73,36,33,34,37,5,84,85,38,29,38,61,61,80,81,25,
26,73,73,24,24,45,46,36,57,56,55,54,59,58,49,49,40,39,46,45,44,42,41,43,
31,67,66,20],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(2x3^5).U4(2).2","3^5:U4(2):2",[1,1,2,2,3,3,4,4,5,6,7,7,8,8,9,9,10,
10,11,12,13,14,15,16,17,17,18,19,20,21,22,23,24,25,26,27,28,28,29,29,30,
30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,
42,43,43,44,44,45,45,46,46,47,48,49,50,50,51,52,53,53,54,55,56,57,57,58,
58,59,59,60,60,61,61,62,62,63,64,64,65,65,66,66,67,67,68,68,69,69,70,71,
71,72,73,74,75,76]);

MOT("2xG2(3)",
0,
0,
0,
0,
[(22,23)(45,46),(18,19)(41,42),
( 3, 4)( 8, 9)(10,11)(15,16)(20,21)(26,27)(31,32)(33,34)(38,39)(43,44)],
["ConstructDirectProduct",[["Cyclic",2],["G2(3)"]]]);
ALF("2xG2(3)","2.O7(3)",[1,5,6,12,12,18,16,23,21,33,39,45,44,47,50,49,56,
56,56,68,69,76,74,2,5,7,13,13,19,17,23,22,34,40,46,44,48,51,49,57,57,57,
68,70,77,75],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("2.O7(3)M5",
0,
0,
0,
0,
0,
["ConstructPermuted",["2xG2(3)"]]);
ALF("2.O7(3)M5","O7(3)M5",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23]);
ALF("2.O7(3)M5","2.O7(3)",[1,5,6,14,14,18,16,23,21,33,41,46,43,47,50,49,
58,58,58,68,71,74,76,2,5,7,15,15,19,17,23,22,34,42,45,43,48,51,49,59,59,
59,68,72,75,77],[
"equals the map from 2.O7(3)M4, mapped under an outer autom."
]);

MOT("2x3^(3+3):L3(3)",
0,
0,
0,
0,
[(40,41)(86,87),( 6, 7, 8, 9)(52,53,54,55),
( 4, 5)(10,11)(20,25)(21,23)(22,24)(29,32)(30,33)(31,34)(35,36)(44,45)(50,51)
(56,57)(66,71)(67,69)(68,70)(75,78)(76,79)(77,80)(81,82)(90,91)
],
["ConstructDirectProduct",[["Cyclic",2],["3^(3+3):L3(3)"]]]);
ALF("2x3^(3+3):L3(3)","2.O7(3)",[1,6,10,12,14,74,76,74,76,58,56,54,18,52,
18,8,10,6,54,12,16,18,16,18,14,36,33,37,43,45,42,44,46,40,41,39,31,34,5,
49,49,64,21,71,69,62,2,7,11,13,15,75,77,75,77,59,57,55,19,53,19,9,11,7,55,
13,17,19,17,19,15,36,34,37,43,46,41,44,45,39,42,40,31,33,5,49,49,65,22,72,
70,63],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2x3^(3+3):L3(3)","2xO7(3)",[1,5,7,8,9,50,51,50,51,39,38,37,11,36,11,
6,7,5,37,8,10,11,10,11,9,25,23,26,30,32,29,31,32,28,29,28,21,23,4,34,34,
43,13,48,47,42,59,63,65,66,67,108,109,108,109,97,96,95,69,94,69,64,65,63,
95,66,68,69,68,69,67,83,81,84,88,90,87,89,90,86,87,86,79,81,62,92,92,101,
71,106,105,100],[
"fusion map is unique up to table autom.",
]);
ALF("2x3^(3+3):L3(3)","2.Fi22",[1,10,12,14,10,85,87,85,87,55,57,55,14,53,
14,8,12,10,55,14,12,14,12,14,10,35,36,42,39,44,37,43,44,45,37,45,38,36,7,
52,52,74,20,76,83,77,2,11,13,15,11,86,88,86,88,56,58,56,15,54,15,9,13,11,
56,15,13,15,13,15,11,35,37,43,38,45,36,42,45,44,36,44,39,37,7,51,51,73,21,
75,84,78],[
"fusion map determined using the factorization through 2xO7(3)"
]);

MOT("2x3^(3+3)b:L3(3)",
0,
0,
0,
0,
0,
["ConstructPermuted",["2x3^(3+3):L3(3)"]]);
ALF("2x3^(3+3)b:L3(3)","3^(3+3)b:L3(3)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46]);
ALF("2x3^(3+3)b:L3(3)","2.Fi22",[1,10,12,14,10,87,85,87,85,55,57,55,14,53,
14,8,12,10,55,14,12,14,12,14,10,35,37,43,39,44,36,42,44,45,36,45,38,37,7,
51,51,76,20,74,83,77,2,11,13,15,11,88,86,88,86,56,58,56,15,54,15,9,13,11,
56,15,13,15,13,15,11,35,36,42,38,45,37,43,45,44,37,44,39,36,7,52,52,75,21,
73,84,78],[
"fusion 2x3^(3+3):L3(3) -> 2.Fi22 mapped under 2.Fi22.2"
]);

MOT("2.O7(3)M8",
[
"8th maximal subgroup of 2.O7(3),\n",
"differs from 2.O7(3)M7 = 2.S6(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2.S6(2)"]]);
ALF("2.O7(3)M8","2.O7(3)",[1,2,3,5,4,5,8,9,14,15,16,17,21,22,24,20,23,
24,25,26,28,36,41,42,35,38,44,43,47,48,49,50,51,58,59,61,61,73,67,71,
72,80,81],[
"fusion 2.S6(2) -> 2.O7(3) mapped under 2.O7(3).2"
]);
ALF("2.O7(3)M8","O7(3)M8",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,
14,15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30]);

MOT("2.O7(3)M9",
[
"origin: Dixon's Algorithm"
],
[2519424,2519424,1259712,1259712,26244,26244,2916,2916,17496,17496,34992,34992
,8748,8748,5832,5832,8748,8748,3456,3456,1728,1728,576,576,288,288,96,48,324,
972,972,23328,46656,216,2592,5184,972,972,972,972,972,972,54,54,162,162,108,
108,108,108,108,108,11664,11664,11664,11664,11664,11664,486,486,324,324,648,
648,432,432,432,432,432,432,36,216,216,216,108,108,108,108,648,648,648,108,108
,108,108,108,108,972,972,972,972,972,972,54,54,162,162,72,72,72,72,72,72,3888,
3888,3888,3888,3888,3888,162,162,432,432,432,432,432,432,108,108,216,108,108,
108,108,108,108,108,108,108,108,108,16,16,24,24,48,48,32,32,32,32],
[,[1,1,3,3,5,5,7,7,9,9,11,11,13,13,15,15,17,17,1,1,3,3,19,19,21,21,20,22,16,10
,12,4,2,12,4,2,37,37,39,39,41,41,43,43,45,45,37,37,39,39,41,41,53,53,55,55,57,
57,59,59,61,61,63,63,53,53,55,55,57,57,64,56,58,54,62,62,64,64,56,58,54,92,92,
88,88,90,90,88,88,90,90,92,92,94,94,96,96,112,112,114,114,116,116,104,104,106,
106,108,108,110,110,104,104,106,106,108,108,5,5,1,15,7,7,17,17,9,13,13,9,11,15
,23,23,34,34,36,36,27,27,27,27],[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,19,20,19,
20,23,24,23,24,27,27,33,33,33,33,33,36,36,36,1,2,1,2,1,2,17,18,5,6,19,20,19,20
,19,20,1,2,1,2,1,2,1,2,3,4,3,4,19,20,19,20,19,20,35,36,36,36,32,32,32,32,33,33
,33,19,20,19,20,19,20,1,2,1,2,1,2,13,14,5,6,23,24,23,24,23,24,1,2,1,2,1,2,5,6,
19,20,19,20,19,20,120,120,120,120,120,120,120,120,120,120,120,120,120,120,132,
133,136,137,136,137,138,139,140,141]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2
,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2
,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,2,-2,2,
-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,
1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[7,2]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,
-2,-2,-2,-2,-2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,-E(8)-E(8)^3,-E(8)-E(8)^3
,E(8)+E(8)^3,E(8)+E(8)^3],
[TENSOR,[9,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,3,3,3,3,3,3,3,3
,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,1,1,1,1,1,1,1,1],
[TENSOR,[11,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,
-1,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,
-1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,
-1,-1,-1,-1,1,1,1,1],
[TENSOR,[13,2]],[4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,
4,-4,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,4,-4,4,-4,4,
-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,-1,1,
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[(134,135)(136,137)(138,139)(140,141),(132,133)(138,140)(139,141),
(118,119)(122,123)(124,125)(127,128),(77,78),(75,76),
( 53, 55, 57)( 54, 56, 58)( 65, 67, 69)( 66, 68, 70)( 72, 73, 74)( 79, 80, 81)
( 82, 84, 86)( 83, 85, 87)( 88, 90, 92)( 89, 91, 93)( 98,100,102)( 99,101,103)
(104,106,108)(105,107,109)(112,114,116)(113,115,117),
( 37, 39, 41)( 38, 40, 42)( 47, 49, 51)( 48, 50, 52)( 82, 84, 86)( 83, 85, 87)
( 88, 90, 92)( 89, 91, 93)( 98,102,100)( 99,103,101)(104,108,106)(105,109,107)
(112,116,114)(113,117,115),
( 13, 17)( 14, 18)( 37, 88)( 38, 89)( 39, 92)( 40, 93)( 41, 90)( 42, 91)( 43,
 94)( 44, 95)( 45, 96)( 46, 97)( 47, 84)( 48, 85)( 49, 82)( 50, 83)( 51, 86)
( 52, 87)( 98,102)( 99,103)
(104,108)(105,109)(112,116)(113,117)(121,131)(122,123)(124,128)(125,127)]);
ALF("2.O7(3)M9","O7(3)N3A",[1,1,2,2,4,4,9,9,5,5,3,3,6,6,8,8,7,7,10,10,11,
11,12,12,13,13,25,38,33,29,28,26,23,34,27,24,47,47,48,48,46,46,64,64,62,
62,56,56,57,57,55,55,14,14,15,15,16,16,17,17,22,22,21,21,19,19,20,20,18,
18,42,37,35,36,41,41,39,40,30,31,32,59,59,58,58,60,60,49,49,51,51,50,50,
65,65,63,63,66,66,67,67,68,68,43,43,44,44,45,45,61,61,52,52,53,53,54,54,
78,78,69,74,76,76,77,77,71,79,79,73,75,72,83,82,84,84,70,70,80,80,81,81]);
ALF("2.O7(3)M9","2.O7(3)",[1,2,6,7,6,7,18,19,10,11,8,9,12,13,16,17,14,15,
5,5,34,33,21,22,64,65,23,68,38,29,28,27,3,35,30,4,14,15,16,17,18,19,58,59,
54,55,42,41,43,43,45,46,6,7,10,11,8,9,18,19,54,55,52,53,33,34,37,37,36,36,
86,32,35,30,84,85,82,83,29,28,27,40,39,46,45,44,44,18,19,16,17,12,13,56,
57,54,55,62,63,69,70,71,72,10,11,12,13,14,15,54,55,31,31,39,40,41,42,33,
34,5,43,46,45,41,42,31,40,39,37,36,44,49,49,73,73,24,24,50,51,51,50],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2.O7(3)M11",
0,
0,
0,
0,
0,
["ConstructPermuted",["Isoclinic(2.A9.2)"]]);
ALF("2.O7(3)M11","O7(3)M11",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,13,
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ALF("2.O7(3)M11","2.O7(3)",[1,2,4,5,8,9,14,15,16,17,24,23,25,26,35,43,47,
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"equals the map from 2.O7(3)M10, mapped under an outer autom."
]);

MOT("2.(2^2xU4(2)).2",
[
"origin: Dixon's Algorithm"
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-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,
E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,0,0,-2,
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0],
[TENSOR,[77,2]],[144,-144,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,-160,0,0,0,0,0,0,4,-4,0,0,0,0,0,
0,0,-2,2,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,8,-8,0,0,0,0,0,0,16,-16,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0],
[TENSOR,[80,2]],[162,162,-162,0,0,0,0,0,0,0,0,6,-6,0,0,18,-18,0,0,0,0,0,0,0,0
,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,0,0,0,0
,0,-6,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[240,-240,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-12,12,0,-6,6,0,0,0,6,-6,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,-2,2,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(54,55),(18,19)(21,22)(74,75),(42,43)(47,48)(51,52)(60,61)(82,83)]);
ALF("2.(2^2xU4(2)).2","(2^2xU4(2)):2",[1,1,2,3,4,5,6,7,8,8,9,10,11,12,13,
14,15,16,16,17,18,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,32,33,34,
34,35,36,37,38,38,39,40,41,42,43,44,45,46,47,47,48,49,50,50,51,52,53,53,
54,55,55,56,57,58,59,60,61,62,63,63,64,65,66,67,68,68,69,70]);
ALF("2.(2^2xU4(2)).2","2.O7(3)",[1,2,4,3,37,31,32,32,10,11,29,5,4,5,4,5,3,
62,63,66,22,21,20,23,24,20,24,24,20,4,66,32,67,35,28,9,8,35,33,34,27,30,
30,6,7,30,27,27,37,29,32,32,60,87,88,61,60,25,26,68,68,64,65,68,22,21,23,
23,24,5,35,36,28,51,50,49,36,73,86,53,52,82,83],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2^(1+6)_+:A7",
[
"origin: Dixon's Algorithm"
],
[322560,322560,7680,4608,23040,14,14,14,14,16,16,32,32,16,128,192,128,64,768,
768,384,24,96,96,48,144,96,576,144,1152,1152,20,40,40,20,20,36,72,72,36,36],
[,[1,1,2,1,2,7,7,8,8,20,21,15,15,17,4,3,1,3,4,4,2,27,28,28,30,30,30,31,31,31,
31,33,34,34,33,33,38,38,38,39,38],[1,2,3,4,5,9,8,7,6,10,11,12,13,14,15,16,17,
18,19,20,21,16,20,19,21,5,3,4,4,2,1,35,33,34,32,36,4,1,2,5,4],,[1,2,3,4,5,9,8,
7,6,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,5,2,1,5,
3,37,38,39,40,41],,[1,2,3,4,5,2,1,1,2,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,35,33,34,32,36,37,38,39,40,41]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1],[6,6,6,6,6,-1,-1,-1,-1,0,0,0,0,0,2,2,2,2,2,2,2,-1,-1,-1,-1,3,3,3,3,3,3,
1,1,1,1,1,0,0,0,0,0],[7,7,3,-1,-5,0,0,0,0,-1,1,1,1,-1,-1,-3,-1,1,3,3,3,0,0,0,0
,-2,0,-4,2,4,4,0,2,2,0,-2,-1,1,1,1,-1],[8,-8,0,0,0,-1,1,1,-1,0,0,-2,2,0,0,0,0,
0,-4,4,0,0,-2,2,0,0,0,0,0,4,-4,0,2,-2,0,0,0,2,-2,0,0],[10,10,10,10,10,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,
E(7)+E(7)^2+E(7)^4,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,0,0,0,0,
0,1,1,1,1,1],
[GALOIS,[5,3]],[14,14,14,14,14,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2],[14,14,14,14,14,0,0,0,0,0,0,0,0,0,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[15,15,15,15,15
,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,3,3,0,0,0,0,0
,0,0,0,0,0],[21,21,21,21,21,0,0,0,0,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,-3,-3
,-3,-3,-3,-3,1,1,1,1,1,0,0,0,0,0],[21,21,1,-3,9,0,0,0,0,-1,-1,1,1,1,1,3,-3,-1,
5,5,1,0,2,2,-2,0,-2,6,0,6,6,-1,1,1,-1,1,0,0,0,0,0],[21,21,1,-3,9,0,0,0,0,1,1,
-1,-1,-1,-3,3,1,-1,1,1,5,0,-2,-2,2,0,-2,6,0,6,6,-1,1,1,-1,1,0,0,0,0,0],[35,35,
35,35,35,0,0,0,0,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
0,0,0,0,0,-1,-1,-1,-1,-1],[35,35,15,-5,-25,0,0,0,0,1,-1,-1,-1,1,-1,-3,-1,1,3,3
,3,0,0,0,0,-4,0,-8,4,8,8,0,0,0,0,0,1,-1,-1,-1,1],[35,35,15,-5,-25,0,0,0,0,1,-1
,-1,-1,1,-1,-3,-1,1,3,3,3,0,0,0,0,2,0,4,-2,-4,-4,0,0,0,0,0,-2,2,2,2,-2],[35,35
,-5,3,-5,0,0,0,0,-1,1,-1,-1,1,3,-1,-1,-1,-5,-5,7,-1,1,1,1,1,1,-3,-3,5,5,0,0,0,
0,0,0,2,2,-2,0],[35,35,-5,3,-5,0,0,0,0,1,-1,1,1,-1,-1,-1,3,-1,7,7,-5,-1,1,1,1,
1,1,-3,-3,5,5,0,0,0,0,0,0,2,2,-2,0],[48,-48,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,
-8,8,0,0,2,-2,0,0,0,0,0,12,-12,0,2,-2,0,0,0,0,0,0,0],[56,56,24,-8,-40,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,4,-2,-4,-4,-E(5)+E(5)^2+E(5)^3-E(5)^4,1,1,
E(5)-E(5)^2-E(5)^3+E(5)^4,-1,1,-1,-1,-1,1],
[GALOIS,[19,2]],[63,63,27,-9,-45,0,0,0,0,-1,1,1,1,-1,-1,-3,-1,1,3,3,3,0,0,0,0
,0,0,0,0,0,0,0,-2,-2,0,2,0,0,0,0,0],[70,70,-10,6,-10,0,0,0,0,0,0,0,0,0,2,-2,2,
-2,2,2,2,-2,2,2,2,-4,2,6,0,-2,-2,0,0,0,0,0,0,-2,-2,2,0],[70,70,-10,6,-10,0,0,0
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[70,70,30,-10,-50,0,0,0,0,0,0,0,0,0,2,6,2,-2,-6,-6,-6,0,0,0,0,-2,0,-4,2,4,4,0,
0,0,0,0,-1,1,1,1,-1],[70,70,-10,6,-10,0,0,0,0,0,0,0,0,0,2,-2,2,-2,2,2,2,1,-1,
-1,-1,-1,-1,3,3,-5,-5,0,0,0,0,0,-3,1,1,-1,3],[70,70,-10,6,-10,0,0,0,0,0,0,0,0,
0,2,-2,2,-2,2,2,2,1,-1,-1,-1,-1,-1,3,3,-5,-5,0,0,0,0,0,3,1,1,-1,-3],[80,-80,0,
0,0,-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0,0,0,0,8,-8,0,0,-2,2,0,0,0,0,0,4,-4,0,0,0,0,0
,0,2,-2,0,0],
[GALOIS,[27,3]],[84,84,4,-12,36,0,0,0,0,0,0,0,0,0,-4,0,4,0,-4,-4,4,0,2,2,-2,0
,-2,6,0,6,6,1,-1,-1,1,-1,0,0,0,0,0],[84,84,4,-12,36,0,0,0,0,0,0,0,0,0,4,0,-4,0
,4,4,-4,0,-2,-2,2,0,-2,6,0,6,6,1,-1,-1,1,-1,0,0,0,0,0],[105,105,-15,9,-15,0,0,
0,0,-1,1,-1,-1,1,-3,1,1,1,5,5,-7,1,-1,-1,-1,-3,3,3,-3,3,3,0,0,0,0,0,0,0,0,0,0]
,[105,105,-15,9,-15,0,0,0,0,1,-1,1,1,-1,1,1,-3,1,-7,-7,5,1,-1,-1,-1,-3,3,3,-3,
3,3,0,0,0,0,0,0,0,0,0,0],[105,105,5,-15,45,0,0,0,0,-1,-1,1,1,1,-3,3,1,-1,1,1,5
,0,-2,-2,2,0,2,-6,0,-6,-6,0,0,0,0,0,0,0,0,0,0],[105,105,5,-15,45,0,0,0,0,1,1,
-1,-1,-1,1,3,-3,-1,5,5,1,0,2,2,-2,0,2,-6,0,-6,-6,0,0,0,0,0,0,0,0,0,0],[112,
-112,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,8,0,0,-4,4,0,0,0,0,0,8,-8,0,-2,2,0,0,0
,-2,2,0,0],[112,-112,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,8,0,0,2,-2,0,0,0,0,0,
-4,4,0,-2,2,0,0,0,4,-4,0,0],[120,-120,0,0,0,-1,1,1,-1,0,0,2,-2,0,0,0,0,0,4,-4,
0,0,2,-2,0,0,0,0,0,12,-12,0,0,0,0,0,0,0,0,0,0],[126,126,6,-18,54,0,0,0,0,0,0,0
,0,0,2,-6,2,2,-6,-6,-6,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,0,0,0,0,0],[168,-168,0,
0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,-4,4,0,0,-2,2,0,0,0,0,0,-12,12,0,2,-2,0,0,0,0,0
,0,0],[210,210,-30,18,-30,0,0,0,0,0,0,0,0,0,-2,2,-2,2,-2,-2,-2,-1,1,1,1,3,-3,
-3,3,-3,-3,0,0,0,0,0,0,0,0,0,0],[280,-280,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,4,
-4,0,0,2,-2,0,0,0,0,0,-4,4,0,0,0,0,0,0,-2,2,0,0]],
[(37,41),(32,35),(6,9)(7,8)]);
ALF("2^(1+6)_+:A7","2.O7(3)",[1,2,4,5,3,48,47,47,48,49,24,51,50,23,23,20,
5,24,22,21,4,66,62,63,32,29,32,31,37,11,10,61,26,25,61,60,43,16,17,38,44],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^(1+6)_+:A7","2^6:A7",[1,1,3,4,2,32,32,31,31,23,21,22,22,20,9,8,6,10,
7,7,5,30,29,29,28,13,15,12,14,11,11,26,24,24,27,25,17,16,16,18,19]);

MOT("2.(S6xS4)",
[
"origin: Dixon's Algorithm"
],
[34560,34560,5760,4320,4320,2880,2880,144,1152,384,192,192,72,72,144,864,864,
108,108,36,36,144,48,24,24,864,864,144,108,108,72,72,48,128,384,64,64,192,192,
384,1152,144,64,64,32,24,64,192,32,32,64,192,24,40,40,20,30,30,40,240,240,24,
24,144,48,36,36],
[,[1,1,2,4,4,2,3,4,1,2,1,3,15,17,17,16,16,19,19,19,19,16,17,16,15,26,26,27,29,
29,27,28,5,1,2,3,1,2,3,1,2,5,34,34,35,33,35,35,34,35,35,35,33,59,59,61,57,57,
61,60,60,27,28,27,26,30,30],[1,2,3,1,2,6,7,9,9,10,11,12,7,6,3,1,2,2,1,9,9,9,10
,11,12,1,2,3,1,2,6,7,35,34,35,36,37,38,39,40,41,41,43,44,45,48,47,48,49,50,51,
52,52,54,55,56,60,61,59,60,61,38,39,41,40,41,41],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,7,7,6,4,5,3,1,2,62,63,64,65,66,67
]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,-1,-1,-1
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-1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1],[1,1,1,1
,1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,-1,-1,1,1,1,-1,-1
,-1,-1,1,1,1,-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,1,1,1,1],
[TENSOR,[2,3]],[2,2,2,-1,-1,0,0,1,-2,-2,0,0,0,0,2,2,2,-1,-1,1,1,-2,-2,0,0,2,2
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,0,0,-2,-2,1,1],
[TENSOR,[5,2]],[3,3,-1,0,0,-1,1,0,-3,1,1,-1,1,-1,-1,3,3,0,0,0,0,-3,1,1,-1,3,3
,-1,0,0,-1,1,0,-1,3,1,-1,1,-1,1,-3,0,1,1,-1,0,-1,3,-1,1,1,-3,0,1,1,-1,0,0,-1,3
,3,1,-1,-3,1,0,0],
[TENSOR,[7,3]],
[TENSOR,[7,4]],
[TENSOR,[7,2]],[5,5,5,5,5,5,5,-3,-3,-3,-3,-3,2,2,2,2,2,2,2,0,0,0,0,0,0,-1,-1,
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0,0,0,1,1,1,1,1,1],
[TENSOR,[11,3]],
[TENSOR,[11,4]],
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,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[15,4]],
[TENSOR,[15,3]],
[TENSOR,[15,2]],[9,9,9,9,9,9,9,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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-1,0,0,0,0,0,0],
[TENSOR,[19,3]],
[TENSOR,[19,4]],
[TENSOR,[19,2]],[10,10,10,-5,-5,0,0,3,-6,-6,0,0,0,0,4,4,4,-2,-2,0,0,0,0,0,0,
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,0,0,0,2,2,-1,-1],
[TENSOR,[23,2]],[10,10,10,-5,-5,0,0,-1,2,2,0,0,0,0,-2,-2,-2,1,1,-1,-1,2,2,0,0
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0,0,0,0,0,0,0,0],
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,0,0,0,1,1,-1,-1,-1,-1],
[TENSOR,[27,4]],
[TENSOR,[27,3]],
[TENSOR,[27,2]],[15,15,-5,0,0,-5,5,0,-9,3,3,-3,2,-2,-2,6,6,0,0,0,0,0,0,0,0,-3
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0,0,-1,1,3,-1,0,0],
[TENSOR,[31,3]],
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,
[(66,67),(54,55),(43,44),(20,21)]);
ALF("2.(S6xS4)","2.O7(3)",[1,2,4,8,9,3,20,36,5,4,5,20,66,29,32,10,11,19,18,
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ALF("2.(S6xS4)","S6xS4",[1,1,2,3,3,4,5,33,31,32,34,35,15,14,12,11,11,13,13,
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MOT("2.(A4x2(A4xA4).2).2",
[
"origin: Dixon's Algorithm"
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[(58,59)(61,62),
(11,51)(12,50)(13,52)(16,17)(18,39)(19,38)(20,40)(21,41)(22,43)(23,42)(78,93)
(79,94)
]);
ALF("2.(A4x2(A4xA4).2).2","2.O7(3)",[1,2,5,5,23,21,22,4,3,4,16,17,43,18,
19,46,45,71,72,41,42,14,15,68,33,34,6,7,65,64,27,30,9,8,36,28,35,70,69,39,
40,13,12,32,11,10,31,63,62,17,16,44,32,29,11,10,37,21,22,23,50,51,5,49,24,
20,24,5,4,24,20,23,24,35,36,73,67,44,38,5,4,24,20,3,5,32,37,29,31,66,29,
37,43,38],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(A4x2(A4xA4).2).2","(A4x2(A4xA4).2).2",[1,1,2,3,4,5,5,6,7,8,9,9,10,11,
11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,21,22,22,23,24,25,26,26,
27,27,28,28,29,30,30,31,32,32,33,33,34,35,36,37,37,38,39,39,40,41,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73]);

MOT("3.3^5:U4(2):2",
[
"origin: Dixon's Algorithm"
],
[37791360,37791360,37791360,524880,524880,524880,139968,157464,30,30,30,45,45,
45,90,90,90,3888,11664,11664,11664,349920,349920,349920,17496,17496,17496,162,
2916,1458,1458,1458,2916,2916,216,2592,2592,2592,432,1296,1296,1296,288,288,
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0,0,0,0,0,0,0,0,0,0,0,-6,0,0,0,-24,-24,-24,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[1296,1296*E(3)^2,1296*E(3),-54*E(3)^2,-54*E(3),-54,0,0
,-1,-E(3)^2,-E(3),E(3)^2,E(3),1,1,E(3)^2,E(3),0,-18*E(3),-18,-18*E(3)^2,
-36*E(3),-36,-36*E(3)^2,18,18*E(3)^2,18*E(3),0,0,0,0,0,0,0,0,12,12*E(3)^2,
12*E(3),0,-6,-6*E(3)^2,-6*E(3),0,0,0,6*E(3)^2,6*E(3),6,-6*E(3),-6,-6*E(3)^2,0,
0,0,-24,-24*E(3)^2,-24*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[137,2]],
[TENSOR,[137,2]],
[TENSOR,[138,2]]],
[
(  2,  3)(  4,  5)( 10, 11)( 12, 13)( 16, 17)( 19, 21)( 22, 24)( 26, 27)( 37,
 38)( 41, 42)
( 43, 45)( 46, 47)( 49, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 64, 66)( 69,
 70)( 71, 72)
( 89, 90)( 92, 94)( 95,100)( 96, 99)( 97, 98)(113,114)(117,118)(120,121)(123,
124)(126,127)
(129,130)(131,132)(135,136)
,
( 30, 31)( 33, 34)( 75, 78)( 79, 81)( 83, 84)( 85, 87)(102,104)(106,107)(109,
110)(139,140)
,
( 29, 33)( 31, 32)( 75, 77)( 80, 83)( 81, 82)( 86, 87)(103,104)(105,107)(109,
111)(138,139)
]);
ALF("3.3^5:U4(2):2","3^5:U4(2):2",[1,1,1,4,4,4,2,3,57,57,57,58,58,58,59,
59,59,20,21,21,21,22,22,22,19,19,19,28,29,30,31,33,32,34,50,52,52,52,51,
49,49,49,61,61,61,11,11,11,12,12,12,13,13,13,14,14,14,60,60,60,5,5,5,6,6,
6,7,9,9,9,10,10,10,8,56,53,55,54,71,73,68,69,72,70,26,25,27,24,23,23,23,
18,18,18,15,15,15,16,16,16,17,44,42,43,37,35,36,38,39,40,41,46,45,45,45,
74,74,74,75,75,75,76,76,76,48,48,48,47,47,47,67,67,67,62,63,63,63,65,66,
64]);
ALF("3.3^5:U4(2):2","3.O7(3)",[1,3,2,16,15,14,17,13,83,85,84,113,112,111,
34,36,35,43,41,40,42,5,4,6,37,39,38,77,17,19,18,21,20,20,51,10,12,11,58,
55,57,56,32,31,33,54,53,52,45,44,46,48,50,49,7,9,8,99,101,100,121,123,122,
53,52,54,20,74,76,75,16,15,14,21,59,120,43,59,61,47,60,64,62,63,62,58,63,
47,12,11,10,41,40,42,115,114,116,118,117,119,59,97,87,98,51,60,61,21,19,
18,13,86,27,26,25,91,93,92,88,90,89,22,24,23,99,101,100,31,33,32,70,69,68,
64,57,56,55,77,79,78],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3xL4(3).2_2",
0,
0,
0,
0,
[
( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)( 57,106)
( 58,107)( 59,108)( 60,109)( 61,110)( 62,111)( 63,112)( 64,113)( 65,114)
( 66,115)( 67,116)( 68,117)( 69,118)( 70,119)( 71,120)( 72,121)( 73,122)
( 74,123)( 75,124)( 76,125)( 77,126)( 78,127)( 79,128)( 80,129)( 81,130)
( 82,131)( 83,132)( 84,133)( 85,134)( 86,135)( 87,136)( 88,137)( 89,138)
( 90,139)( 91,140)( 92,141)( 93,142)( 94,143)( 95,144)( 96,145)( 97,146)
( 98,147)
,( 24, 25)( 73, 74)(122,123),
(  5,  6)( 12, 13)( 15, 16)( 18, 19)( 21, 22)( 27, 28)( 31, 32)( 33, 34)
( 35, 36)( 37, 38)( 39, 40)( 43, 44)( 46, 47)( 48, 49)( 54, 55)( 61, 62)
( 64, 65)( 67, 68)( 70, 71)( 76, 77)( 80, 81)( 82, 83)( 84, 85)( 86, 87)
( 88, 89)( 92, 93)( 95, 96)( 97, 98)(103,104)(110,111)(113,114)(116,117)
(119,120)(125,126)(129,130)(131,132)(133,134)(135,136)(137,138)(141,142)
(144,145)(146,147)
],
["ConstructDirectProduct",[["Cyclic",3],["L4(3).2_2"]]]);
ALF("3xL4(3).2_2","3.O7(3)",[1,7,10,13,14,17,21,22,25,31,34,52,48,51,55,
58,68,77,74,80,91,88,87,105,102,124,7,4,10,28,31,22,44,37,48,40,52,43,55,
47,64,68,80,83,94,99,88,121,120,2,8,11,13,15,17,21,23,26,32,35,53,49,51,
56,58,69,77,75,81,92,89,87,106,103,125,8,5,11,29,32,23,45,38,49,41,53,43,
56,47,64,69,81,84,95,100,89,122,120,3,9,12,13,16,17,21,24,27,33,36,54,50,
51,57,58,70,77,76,82,93,90,87,107,104,126,9,6,12,30,33,24,46,39,50,42,54,
43,57,47,64,70,82,85,96,101,90,123,120],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3.O7(3)M5",
[
"5th maximal subgroup of 3.O7(3),\n",
"differs from 3.O7(3)M4 = 3.G2(3) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.G2(3)"]]);
ALF("3.O7(3)M5","3.O7(3)", [1,3,2,10,12,11,13,19,19,21,20,28,30,29,25,27,26,
51,61,64,62,65,67,66,71,73,72,68,70,69,79,79,79,94,96,95,98,98,98,102,104,
103,105,107,106],[
"fusion map is unique up to table automorphisms,\n",
"equals the map from 3.O7(3)M4, mapped under an outer autom. of order 2"
]);
ALF("3.O7(3)M5","O7(3)M5",[1,1,1,2,2,2,3,4,5,6,7,8,8,8,9,9,9,10,11,12,13,
14,14,14,15,15,15,16,16,16,17,18,19,20,20,20,21,21,21,22,22,22,23,23,23]);

MOT("3.(3^(3+3):L3(3))",
[
"origin: Dixon's Algorithm"
],
[12282192,12282192,12282192,157464,17496,17496,17496,54,54,162,162,162,54,54,
54,54,54,54,13122,13122,13122,729,4374,4374,81,1458,1458,1458,1458,1458,1458,
1296,1296,1296,216,216,216,216,24,24,24,24,24,24,36,216,216,216,36,36,36,39,39
,39,39,39,39,39,39,39,39,39,39,81,243,243,243,81,27,27],
[,[1,3,2,4,5,6,7,24,23,19,21,20,31,29,30,28,27,26,19,21,20,22,23,24,25,26,27,
28,29,30,31,1,3,2,4,6,5,7,46,48,47,46,48,47,35,32,34,33,38,37,36,55,57,56,58,
60,59,61,63,62,52,54,53,64,65,67,66,68,69,70],[1,1,1,1,1,1,1,32,32,32,32,32,32
,32,32,32,32,32,1,1,1,1,1,1,4,1,1,1,1,1,1,32,32,32,32,32,32,32,39,39,39,42,42,
42,46,46,46,46,46,46,46,52,52,52,55,55,55,58,58,58,61,61,61,1,4,4,4,4,7,6],,,,
,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27
,28,29,30,31,32,33,34,35,36,37,38,42,43,44,39,40,41,45,46,47,48,49,50,51,1,2,3
,1,2,3,1,2,3,1,2,3,64,65,66,67,68,69,70]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[12,12,12,12,
12,12,12,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,0,0,0,0
,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0],[13,13,
13,13,13,13,13,0,0,0,0,0,0,0,0,0,0,0,4,4,4,4,4,4,4,4,4,4,4,4,4,-3,-3,-3,-3,-3,
-3,-3,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[
16,16,16,16,16,16,16,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2
,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(13)^2+E(13)^5+E(13)^6,
E(13)^2+E(13)^5+E(13)^6,E(13)^2+E(13)^5+E(13)^6,E(13)^4+E(13)^10+E(13)^12,
E(13)^4+E(13)^10+E(13)^12,E(13)^4+E(13)^10+E(13)^12,E(13)^7+E(13)^8+E(13)^11,
E(13)^7+E(13)^8+E(13)^11,E(13)^7+E(13)^8+E(13)^11,E(13)+E(13)^3+E(13)^9,
E(13)+E(13)^3+E(13)^9,E(13)+E(13)^3+E(13)^9,1,1,1,1,1,1,1],
[GALOIS,[4,4]],
[GALOIS,[4,7]],
[GALOIS,[4,2]],[26,26,26,26,-1,-1,-1,2,2,2,2,2,-1,-1,-1,-1,-1,-1,8,8,8,8,8,8,
-1,-1,-1,-1,-1,-1,-1,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,2,2,2,2,-1,-1,-1,0,0,0,0,0,0
,0,0,0,0,0,0,2,2,2,2,2,-1,-1],[26,26,26,26,26,26,26,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,0,0,0,0,0,0,2,2,2,
2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1],[26,26,26,26,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,2,2,2,-1,-1,-1,-1,-1,-1,-1,8,8,8,-1,-1,-1,2,2,2,2,-1,-1,
-1,0,0,0,0,0,0,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,2,-1],[
26,26,26,26,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,8,8,8,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0
,-1,-1,-1,-1,-1,-1,2],[26,26,26,26,26,26,26,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-2,-2,-2,-2,-2,-2,-2,-E(8)-E(8)^3,-E(8)-E(8)^3,
-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,-1,-1,-1,-1,-1,-1,-1],
[GALOIS,[12,5]],[27,27,27,27,27,27,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,
1,1,1,1,0,0,0,0,0,0,0],[27,27*E(3)^2,27*E(3),0,0,0,0,0,0,3,3*E(3)^2,3*E(3),0,0
,0,0,0,0,9,9*E(3)^2,9*E(3),0,0,0,0,0,0,0,0,0,0,3,3*E(3)^2,3*E(3),0,0,0,0,1,
E(3)^2,E(3),1,E(3)^2,E(3),0,3,3*E(3)^2,3*E(3),0,0,0,1,E(3)^2,E(3),1,E(3)^2,
E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),0,3,3*E(3)^2,3*E(3),0,0,0],
[GALOIS,[15,2]],[39,39,39,39,39,39,39,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,
3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[52,52,52,52,-2,-2,-2,-1,-1,-1,-1,-1,-1,-1,
-1,2,2,2,7,7,7,7,7,7,-2,-2,-2,-2,7,7,7,-4,-4,-4,-4,2,2,2,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,-2,1],[52,52,52,52,-2,-2,-2,-1,-1,-1,-1
,-1,2,2,2,-1,-1,-1,7,7,7,7,7,7,-2,7,7,7,-2,-2,-2,-4,-4,-4,-4,2,2,2,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,-2],[52,52,52,52,-2,-2,-2,2
,2,2,2,2,-1,-1,-1,-1,-1,-1,-2,-2,-2,-2,-2,-2,-2,7,7,7,7,7,7,-4,-4,-4,-4,2,2,2,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,1,1],[78,78,
78,-3,6,-3,-3,-2,1,1,1,1,-2,1,1,1,-2,1,15,15,15,-3,-3,6,0,-3,6,-3,-3,-3,6,-2,
-2,-2,1,1,-2,1,0,0,0,0,0,0,-1,2,2,2,-1,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,3,3,0
,0,0],[78,78,78,78,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,6,6,6,6,6,6,-3,6,6,6,6,6,6,6
,6,6,6,-3,-3,-3,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[78,78,78,-3,6,-3,-3,1,-2,1,1,1,1,-2,1,1,1,-2,-3,-3,-3,-3,6,15,0,6,-3,
-3,6,-3,-3,-2,-2,-2,1,1,-2,1,0,0,0,0,0,0,-1,2,2,2,-1,2,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,-3,-3,-3,3,0,0],[78,78,78,-3,6,-3,-3,1,1,-2,-2,-2,1,1,-2,-2,1,1,6,6,6,-3
,15,-3,0,-3,-3,6,-3,6,-3,-2,-2,-2,1,1,-2,1,0,0,0,0,0,0,-1,2,2,2,-1,2,-1,0,0,0,
0,0,0,0,0,0,0,0,0,3,0,0,0,-3,0,0],[156,156,156,-6,12,-6,-6,1,-2,1,1,1,1,-2,1,1
,1,-2,21,21,21,-6,12,3,0,-6,3,3,-6,3,3,4,4,4,-2,-2,4,-2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,-3,0,0],[156,156,156,-6,12,-6,-6,-2,1,1,1,
1,-2,1,1,1,-2,1,3,3,3,-6,21,12,0,3,-6,3,3,3,-6,4,4,4,-2,-2,4,-2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,-3,-3,-3,0,0,0],[156,156,156,-6,12,-6,-6
,1,1,-2,-2,-2,1,1,-2,-2,1,1,12,12,12,-6,3,21,0,3,3,-6,3,-6,3,4,4,4,-2,-2,4,-2,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,3,0,0],[208,208,208
,208,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,10,10,10,10,10,10,1,-8,-8,-8,-8,-8,-8,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,1,1
],[208,208,208,208,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,-8,-8,-8,-8,-8,-8,1,10,10,10
,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,
1,1,1,-2,1],[208,208,208,208,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,-8,-8,-8,-8,-8,-8,
1,-8,-8,-8,10,10,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,1,1,1,1,1,-2],[234,234,234,-9,-9,-9,18,-1,-1,2,2,2,2,-1,-1,-1,-1,2,18,
18,18,0,-9,-9,0,0,-9,9,9,-9,0,2,2,2,-1,-1,-1,2,0,0,0,0,0,0,-1,2,2,2,2,-1,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[234,234,234,-9,-9,18,-9,-1,-1,2,2,2,-1,2
,-1,-1,2,-1,18,18,18,0,-9,-9,0,9,0,-9,0,9,-9,2,2,2,-1,2,-1,-1,0,0,0,0,0,0,-1,2
,2,2,-1,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[234,234,234,-9,-9,18,-9,2
,-1,-1,-1,-1,-1,-1,2,-1,-1,2,-9,-9,-9,0,-9,18,0,0,-9,9,-9,0,9,2,2,2,-1,2,-1,-1
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234,-9,-9,18,-9,-1,2,-1,-1,-1,2,-1,-1,2,-1,-1,-9,-9,-9,0,18,-9,0,-9,9,0,9,-9,0
,2,2,2,-1,2,-1,-1,0,0,0,0,0,0,-1,2,2,2,-1,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0],[234,234,234,-9,-9,-9,18,2,-1,-1,-1,-1,-1,2,-1,2,-1,-1,-9,-9,-9,0,-9,
18,0,-9,9,0,0,9,-9,2,2,2,-1,-1,-1,2,0,0,0,0,0,0,-1,2,2,2,2,-1,-1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0],[234,234,234,-9,-9,-9,18,-1,2,-1,-1,-1,-1,-1,2,-1,2,
-1,-9,-9,-9,0,18,-9,0,9,0,-9,-9,0,9,2,2,2,-1,-1,-1,2,0,0,0,0,0,0,-1,2,2,2,2,-1
,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[234,234,234,-9,18,-9,-9,0,0,0,0,0,
0,0,0,0,0,0,18,18,18,-9,18,18,0,0,0,0,0,0,0,-6,-6,-6,3,3,-6,3,0,0,0,0,0,0,1,-2
,-2,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[324,324*E(3)^2,324*E(3),
0,0,0,0,0,0,3,3*E(3)^2,3*E(3),0,0,0,0,0,0,27,27*E(3)^2,27*E(3),0,0,0,0,0,0,0,0
,0,0,12,12*E(3)^2,12*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3)^2,-E(3),
-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),0,0,0,0,0,0,0],
[GALOIS,[38,2]],[351,351*E(3)^2,351*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,36,
36*E(3)^2,36*E(3),0,0,0,0,0,0,0,0,0,0,-9,-9*E(3)^2,-9*E(3),0,0,0,0,-1,-E(3)^2,
-E(3),-1,-E(3)^2,-E(3),0,3,3*E(3)^2,3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,
3*E(3)^2,3*E(3),0,0,0],
[GALOIS,[40,2]],[432,432*E(3)^2,432*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-18,
-18*E(3)^2,-18*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,E(13)^2+E(13)^5+E(13)^6,E(39)^2+E(39)^5+E(39)^32,E(39)^19+E(39)^28+E(39)^31,
E(13)^4+E(13)^10+E(13)^12,E(39)^17+E(39)^23+E(39)^38,E(39)^4+E(39)^10+E(39)^25
,E(13)^7+E(13)^8+E(13)^11,E(39)^8+E(39)^11+E(39)^20,E(39)^7+E(39)^34+E(39)^37,
E(13)+E(13)^3+E(13)^9,E(39)^14+E(39)^29+E(39)^35,E(39)+E(39)^16+E(39)^22,0,3,
3*E(3)^2,3*E(3),0,0,0],
[GALOIS,[42,4]],
[GALOIS,[42,7]],
[GALOIS,[42,19]],
[GALOIS,[42,14]],
[GALOIS,[42,17]],
[GALOIS,[42,8]],
[GALOIS,[42,2]],[468,468,468,-18,-18,-18,36,-1,2,-1,-1,-1,-1,-1,2,-1,2,-1,9,9
,9,0,-18,9,0,-9,0,9,9,0,-9,-4,-4,-4,2,2,2,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[468,468,468,-18,-18,-18,36,2,-1,-1,-1,-1,-1,2
,-1,2,-1,-1,9,9,9,0,9,-18,0,9,-9,0,0,-9,9,-4,-4,-4,2,2,2,-4,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[468,468,468,-18,-18,36,-18,-1,
2,-1,-1,-1,2,-1,-1,2,-1,-1,9,9,9,0,-18,9,0,9,-9,0,-9,9,0,-4,-4,-4,2,-4,2,2,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[468,468,468,-18
,-18,36,-18,2,-1,-1,-1,-1,-1,-1,2,-1,-1,2,9,9,9,0,9,-18,0,0,9,-9,9,0,-9,-4,-4,
-4,2,-4,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
468,468,468,-18,-18,36,-18,-1,-1,2,2,2,-1,2,-1,-1,2,-1,-18,-18,-18,0,9,9,0,-9,
0,9,0,-9,9,-4,-4,-4,2,-4,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0],[468,468,468,-18,-18,-18,36,-1,-1,2,2,2,2,-1,-1,-1,-1,2,-18,
-18,-18,0,9,9,0,0,9,-9,-9,9,0,-4,-4,-4,2,2,2,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[624,624,624,-24,48,-24,-24,0,0,0,0,0,0,0,0
,0,0,0,-6,-6,-6,3,12,-24,0,-6,-6,12,-6,12,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,3,0,0],[624,624,624,-24,48,-24,-24,0,0
,0,0,0,0,0,0,0,0,0,-24,-24,-24,3,-6,12,0,12,-6,-6,12,-6,-6,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,-3,0,0],[624,624,624,-24,
48,-24,-24,0,0,0,0,0,0,0,0,0,0,0,12,12,12,3,-24,-6,0,-6,12,-6,-6,-6,12,0,0,0,0
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702,702,702,-27,-27,-27,54,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6
,6,-3,-3,-3,6,0,0,0,0,0,0,1,-2,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[702,702,702,-27,-27,54,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,6,6,6,-3,6,-3,-3,0,0,0,0,0,0,1,-2,-2,-2,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[702,702*E(3)^2,702*E(3),0,0,0,0,0,0,-3,-3*E(3)^2,-3*E(3),0,0,0,0,0
,0,-9,-9*E(3)^2,-9*E(3),0,0,0,0,0,0,0,0,0,0,6,6*E(3)^2,6*E(3),0,0,0,0,0,0,0,0,
0,0,0,6,6*E(3)^2,6*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3*E(3)^2,-3*E(3),0
,0,0],
[GALOIS,[61,2]],[702,702*E(3)^2,702*E(3),0,0,0,0,0,0,3,3*E(3)^2,3*E(3),0,0,0,
0,0,0,-9,-9*E(3)^2,-9*E(3),0,0,0,0,0,0,0,0,0,0,-6,-6*E(3)^2,-6*E(3),0,0,0,0,
-E(8)-E(8)^3,-E(24)-E(24)^19,-E(24)^11-E(24)^17,E(8)+E(8)^3,E(24)+E(24)^19,
E(24)^11+E(24)^17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3*E(3)^2,-3*E(3)
,0,0,0],
[GALOIS,[63,7]],
[GALOIS,[63,11]],
[GALOIS,[63,5]],[729,729*E(3)^2,729*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,9,9*E(3)^2,9*E(3),0,0,0,0,-1,-E(3)^2,-E(3),-1,-E(3)^2,
-E(3),0,-3,-3*E(3)^2,-3*E(3),0,0,0,1,E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),1
,E(3)^2,E(3),0,0,0,0,0,0,0],
[GALOIS,[67,2]],[1053,1053*E(3)^2,1053*E(3),0,0,0,0,0,0,-3,-3*E(3)^2,-3*E(3),
0,0,0,0,0,0,27,27*E(3)^2,27*E(3),0,0,0,0,0,0,0,0,0,0,-3,-3*E(3)^2,-3*E(3),0,0,
0,0,1,E(3)^2,E(3),1,E(3)^2,E(3),0,-3,-3*E(3)^2,-3*E(3),0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[69,2]]],
[(39,42)(40,43)(41,44),
( 6, 7)(13,17)(14,18)(15,16)(26,29)(27,31)(28,30)(36,38)(49,51)(69,70),
(52,55,58,61)(53,56,59,62)(54,57,60,63),
( 2, 3)(11,12)(20,21)(33,34)(40,41)(43,44)(47,48)(53,54)(56,57)(59,60)(62,63)
(66,67)
]);
ALF("3.(3^(3+3):L3(3))","3^(3+3):L3(3)",[1,1,1,2,3,4,5,28,27,26,26,26,32,
34,33,30,29,31,16,16,16,15,18,17,19,25,23,24,20,22,21,39,39,39,38,36,37,
35,41,41,41,40,40,40,42,43,43,43,44,46,45,6,6,6,7,7,7,8,8,8,9,9,9,13,14,
14,14,12,10,11]);
ALF("3.(3^(3+3):L3(3))","3.O7(3)",[1,2,3,13,17,18,19,58,51,55,56,57,63,60,
64,64,62,61,14,15,16,21,13,17,77,19,20,21,18,21,20,10,11,12,51,60,47,61,
68,69,70,68,69,70,87,25,26,27,98,86,97,102,103,104,105,106,107,102,103,
104,105,106,107,21,74,75,76,77,79,78],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3.O7(3)M8",
0,
0,
0,
0,
0,
["ConstructPermuted",["3xS6(2)"]]);
ALF("3.O7(3)M8","O7(3)M8",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]);
ALF("3.O7(3)M8","3.O7(3)",[1,4,10,7,10,14,19,20,25,31,22,28,31,34,40,55,
61,52,59,63,62,65,68,71,79,83,99,91,98,111,3,6,12,9,12,16,19,20,27,33,24,
30,33,36,42,57,61,54,59,63,62,67,70,73,79,85,101,93,98,113,2,5,11,8,11,15,
19,20,26,32,23,29,32,35,41,56,61,53,59,63,62,66,69,72,79,84,100,92,98,112],[
"fusion 3xS6(2) -> 3.O7(3) mapped under 3.O7(3).2"
]);

MOT("3.O7(3)M9",
[
"origin: Dixon's Algorithm"
],
[3779136,3779136,3779136,629856,52488,52488,52488,8748,13122,2916,1458,4374,
4374,139968,139968,139968,69984,69984,69984,2916,2916,2916,972,324,15552,15552
,15552,7776,7776,7776,648,648,648,5184,5184,5184,864,864,864,864,144,144,144,
144,288,288,288,17496,17496,17496,5832,5832,972,972,972,162,243,1944,1944,1944
,1944,1944,1944,1944,1944,1944,324,324,324,324,324,324,54,648,648,648,648,648,
648,648,648,648,108,108,108,648,648,648,216,216,81,486,486,486,27,54,54,54,486
,486,486,81,27,54,54,54,81,1944,1944,1944,216,216,216,36,36,36,324,324,324,54,
54,54,54,648,648,648,108,108,108,108,36,36,36,72,72,72,48,48,48,48,48,48,48,48
,48,48,48,48],
[,[1,3,2,4,5,7,6,8,9,10,11,12,13,1,3,2,4,4,4,5,7,6,8,10,1,3,2,4,4,4,5,7,6,1,3,
2,4,34,36,35,37,37,37,37,34,36,35,48,50,49,51,52,53,55,54,56,57,51,51,51,52,52
,52,48,50,49,55,54,53,54,53,55,56,52,52,52,49,48,50,51,51,51,53,55,54,48,50,49
,51,52,91,92,93,94,95,92,93,94,99,100,101,102,103,99,100,101,107,108,109,110,
108,109,110,111,112,113,5,7,6,11,13,9,12,1,3,2,8,10,8,10,31,33,32,25,27,26,38,
40,39,38,40,39,46,45,47,46,45,47],[1,1,1,1,1,1,1,1,1,1,1,1,1,14,14,14,14,14,14
,14,14,14,14,14,25,25,25,25,25,25,25,25,25,34,34,34,34,38,38,38,38,45,45,45,45
,45,45,1,1,1,1,1,4,4,4,4,1,14,14,14,14,14,14,14,14,14,18,18,18,19,19,19,17,25,
25,25,25,25,25,25,25,25,29,29,29,34,34,34,34,34,9,1,1,1,13,34,34,34,1,1,1,9,12
,34,34,34,9,1,1,1,34,34,34,38,38,38,124,124,124,124,124,124,124,124,124,124,
124,124,124,124,134,134,134,134,134,134,137,137,137,140,140,140,144,144,144,
147,147,147]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,2,2,2,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2
,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,
2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,2,2,2,2,2,2,2,2,2,
-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,
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3*E(3)^2,3*E(3),0,0,6,6*E(3)^2,6*E(3),6,6*E(3)^2,6*E(3),-12,-12*E(3)^2,
-12*E(3),3*E(3)^2,3*E(3),3,3*E(3),3,3*E(3)^2,0,2,2*E(3)^2,2*E(3),2*E(3),2,
2*E(3)^2,2*E(3)^2,2*E(3),2,-1,-E(3)^2,-E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],
[GALOIS,[146,2]],[486,486,486,-243,0,0,0,0,0,0,0,0,0,54,54,54,-27,-27,-27,0,0
,0,0,0,-18,-18,-18,9,9,9,0,0,0,-18,-18,-18,9,-6,-6,-6,3,-1,-1,-1,2,2,2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[
( 92, 93, 94)( 96, 97, 98)( 99,100,101)(104,105,106)(108,109,110)(111,112,113)
(114,115,116),
( 12, 13)( 91,102)( 92, 99)( 93,101)( 94,100)( 95,103)( 96,104)( 97,106)( 98,
105)(109,110)(112,113)(115,116)(121,123)(128,130)
,(137,140)(138,141)(139,142)(143,146)(144,147)(145,148),
(  2,  3)(  6,  7)( 15, 16)( 18, 19)( 21, 22)( 26, 27)( 28, 30)( 32, 33)( 35,
 36)( 39, 40)
( 43, 44)( 46, 47)( 49, 50)( 54, 55)( 59, 60)( 62, 63)( 65, 66)( 67, 70)( 68,
 72)( 69, 71)
( 75, 76)( 77, 79)( 80, 81)( 84, 85)( 87, 88)(118,119)(125,126)(132,133)(135,
136)(138,139)(141,142)(143,145)(146,148)
]);
ALF("3.O7(3)M9","O7(3)N3A",[1,1,1,2,3,3,3,5,4,8,9,7,6,23,23,23,26,26,26,
28,28,28,29,33,24,24,24,27,27,27,34,34,34,10,10,10,11,12,12,12,13,38,38,
38,25,25,25,16,16,16,14,15,21,21,21,22,17,32,32,32,30,30,30,31,31,31,40,
40,40,39,39,39,41,37,37,37,35,35,35,36,36,36,42,42,42,18,18,18,19,20,63,
51,49,50,65,60,58,59,47,46,48,62,64,56,55,57,61,45,43,44,54,52,53,68,66,
67,75,75,75,76,79,78,77,69,69,69,71,74,73,72,84,84,84,70,70,70,82,82,82,
83,83,83,81,81,81,80,80,80]);
ALF("3.O7(3)M9","3.O7(3)",[1,3,2,13,14,16,15,17,13,20,21,19,18,4,6,5,37,
39,38,40,42,41,43,59,7,9,8,45,44,46,52,54,53,10,12,11,51,25,27,26,87,94,
96,95,28,30,29,14,16,15,13,17,74,76,75,77,21,37,39,38,43,43,43,40,42,41,
119,118,117,115,114,116,120,48,50,49,53,52,54,46,45,44,121,123,122,55,57,
56,51,58,77,20,21,18,78,63,64,60,19,21,20,77,79,61,64,62,77,19,17,18,61,
47,60,98,86,97,55,57,56,64,60,51,61,10,12,11,47,62,58,63,99,101,100,31,33,
32,68,70,69,68,70,69,72,71,73,72,71,73],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3xS9",
0,
0,
0,
0,
[
(31,61)(32,62)(33,63)(34,64)(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)
(42,72)(43,73)(44,74)(45,75)(46,76)(47,77)(48,78)(49,79)(50,80)(51,81)(52,82)
(53,83)(54,84)(55,85)(56,86)(57,87)(58,88)(59,89)(60,90)
],
["ConstructDirectProduct",[["Cyclic",3],["A9.2"]]]);
ALF("3xS9","3.O7(3)",[1,7,10,14,18,20,31,28,34,52,63,65,78,80,99,111,4,10,
22,31,40,55,59,62,60,71,83,91,108,124,2,8,11,15,18,20,32,29,35,53,63,66,
78,81,100,112,5,11,23,32,41,56,59,62,60,72,84,92,109,125,3,9,12,16,18,20,
33,30,36,54,63,67,78,82,101,113,6,12,24,33,42,57,59,62,60,73,85,93,110,
126],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3.O7(3)M11",
0,
0,
0,
0,
0,
["ConstructPermuted",["3xS9"]]);
ALF("3.O7(3)M11","O7(3)M11",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]);
ALF("3.O7(3)M11","3.O7(3)",[1,7,10,14,19,20,31,28,34,52,62,65,79,80,99,
111,4,10,22,31,40,55,59,63,61,71,83,91,108,124,3,9,12,16,19,20,33,30,36,
54,62,67,79,82,101,113,6,12,24,33,42,57,59,63,61,73,85,93,110,126,2,8,11,
15,19,20,32,29,35,53,62,66,79,81,100,112,5,11,23,32,41,56,59,63,61,72,84,
92,109,125],[
"fusion 3xS9 -> 3.O7(3) mapped under 3.O7(3).2"
]);

MOT("3x(2^2xU4(2)):2",
0,
0,
0,
0,
[
( 36, 37)( 40, 41)( 44, 45)( 51, 52)( 69, 70)( 71,141)( 72,142)( 73,143)
( 74,144)( 75,145)( 76,146)( 77,147)( 78,148)( 79,149)( 80,150)( 81,151)
( 82,152)( 83,153)( 84,154)( 85,155)( 86,156)( 87,157)( 88,158)( 89,159)
( 90,160)( 91,161)( 92,162)( 93,163)( 94,164)( 95,165)( 96,166)( 97,167)
( 98,168)( 99,169)(100,170)(101,171)(102,172)(103,173)(104,174)(105,175)
(106,177)(107,176)(108,178)(109,179)(110,181)(111,180)(112,182)(113,183)
(114,185)(115,184)(116,186)(117,187)(118,188)(119,189)(120,190)(121,192)
(122,191)(123,193)(124,194)(125,195)(126,196)(127,197)(128,198)(129,199)
(130,200)(131,201)(132,202)(133,203)(134,204)(135,205)(136,206)(137,207)
(138,208)(139,210)(140,209)
,
( 71,141)( 72,142)( 73,143)( 74,144)( 75,145)( 76,146)( 77,147)( 78,148)
( 79,149)( 80,150)( 81,151)( 82,152)( 83,153)( 84,154)( 85,155)( 86,156)
( 87,157)( 88,158)( 89,159)( 90,160)( 91,161)( 92,162)( 93,163)( 94,164)
( 95,165)( 96,166)( 97,167)( 98,168)( 99,169)(100,170)(101,171)(102,172)
(103,173)(104,174)(105,175)(106,176)(107,177)(108,178)(109,179)(110,180)
(111,181)(112,182)(113,183)(114,184)(115,185)(116,186)(117,187)(118,188)
(119,189)(120,190)(121,191)(122,192)(123,193)(124,194)(125,195)(126,196)
(127,197)(128,198)(129,199)(130,200)(131,201)(132,202)(133,203)(134,204)
(135,205)(136,206)(137,207)(138,208)(139,209)(140,210)
],
["ConstructDirectProduct",[["Cyclic",3],["(2^2xU4(2)):2"]]]);
ALF("3x(2^2xU4(2)):2","3.O7(3)",[1,7,4,58,47,48,48,17,43,10,7,10,7,10,4,
86,88,25,22,28,31,22,31,31,22,7,88,48,91,52,40,14,52,51,37,45,46,13,44,39,
38,58,43,49,50,80,124,83,80,34,95,96,87,94,25,28,28,31,10,52,55,40,71,68,
55,99,121,74,114,117,2,8,5,58,47,49,49,17,43,11,8,11,8,11,5,86,89,26,23,
29,32,23,32,32,23,8,89,49,92,53,41,15,53,51,38,46,44,13,45,37,39,58,43,50,
48,81,125,84,81,35,96,94,87,95,26,29,29,32,11,53,56,41,72,69,56,100,122,
75,115,118,3,9,6,58,47,50,50,17,43,12,9,12,9,12,6,86,90,27,24,30,33,24,33,
33,24,9,90,50,93,54,42,16,54,51,39,44,45,13,46,38,37,58,43,48,49,82,126,
85,82,36,94,95,87,96,27,30,30,33,12,54,57,42,73,70,57,101,123,76,116,119],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2^6:3A7",
[
"origin: Dixon's Algorithm"
],
[483840,483840,483840,13824,13824,13824,23040,23040,23040,69120,69120,69120,
384,384,384,1152,1152,1152,192,192,192,384,384,384,576,576,576,1152,1152,1152,
48,48,48,48,48,48,48,48,48,48,48,48,21,21,21,21,21,21,60,60,60,60,60,60,60,60,
60,60,60,60,72,72,72,144,144,144,144,144,144,144,288,288,288,144,576,576,36,36
,36,36],
[,[1,3,2,1,3,2,1,3,2,2,1,3,1,3,2,4,6,5,8,7,9,4,6,5,8,7,9,2,1,3,17,16,18,23,22,
24,28,30,29,15,14,13,43,45,44,48,47,46,60,59,58,60,59,58,60,59,58,60,59,58,73,
72,71,75,75,75,76,76,76,75,75,75,75,75,75,75,77,77,77,77],[1,1,1,4,4,4,7,7,7,
11,11,11,13,13,13,16,16,16,20,20,20,22,22,22,26,26,26,29,29,29,32,32,32,35,35,
35,39,39,39,42,42,42,47,47,47,43,43,43,53,53,53,50,50,50,56,56,56,59,59,59,26,
26,26,29,29,29,16,16,16,11,7,7,7,4,1,4,1,4,4,11],,[1,3,2,4,6,5,7,9,8,12,11,10,
13,15,14,16,18,17,21,20,19,22,24,23,27,26,25,30,29,28,33,32,31,36,35,34,38,37,
39,41,40,42,47,46,48,44,43,45,12,11,10,12,11,10,8,7,9,2,1,3,63,62,61,66,65,64,
69,68,67,70,73,72,71,74,75,76,77,78,79,80],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,1,2,3,3,1,2,52,53,54,49,50,51,55,56,57,58,59,60,61,62,63,64,65,66,67,68,
69,70,71,72,73,74,75,76,77,78,79,80]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1],[6,6,6,6,6,6,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,
0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,3,3,3,3,3,3,3,0,0,0,0],[6,6*E(3)^2,6*E(3),6,6*E(3)^2,6*E(3),6,6*E(3)^2,
6*E(3),6*E(3),6,6*E(3)^2,2,2*E(3)^2,2*E(3),2,2*E(3)^2,2*E(3),2*E(3),2,2*E(3)^2
,2,2*E(3)^2,2*E(3),2*E(3),2,2*E(3)^2,2*E(3),2,2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0
,-1,-E(3)^2,-E(3),-E(3),-1,-E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,
E(3),1,E(3)^2,2*E(3),2,2*E(3)^2,2*E(3),2,2*E(3)^2,2*E(3),2,2*E(3)^2,0,0,0,0,0,
0,0,0,0,0,0],
[GALOIS,[3,2]],[7,7,7,-1,-1,-1,3,3,3,-5,-5,-5,-1,-1,-1,3,3,3,1,1,1,-1,-1,-1,
-3,-3,-3,3,3,3,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,
2,2,2,0,0,0,0,0,0,0,0,0,-2,0,0,0,2,4,-4,1,-1,-1,1],[10,10,10,10,10,10,10,10,10
,10,10,10,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,
0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,0,0,0,0,0,0,0,0,0,0,0
,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[GALOIS,[6,3]],[14,14,14,14,14,14,14,14,14,14,14,14,2,2,2,2,2,2,2,2,2,2,2,2,2
,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2],[14,14,14,14,14
,14,14,14,14,14,14,14,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,-1,-1,-1,-1],[15,15,15,15,15,15,15,15,15,15,15,15,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1
,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,3,3,3,0,0,0,0],[
15,15*E(3)^2,15*E(3),15,15*E(3)^2,15*E(3),15,15*E(3)^2,15*E(3),15*E(3),15,
15*E(3)^2,-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),-E(3),-1,-E(3)^2,-1,-E(3)^2,-E(3),
-E(3),-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3)^2,
-E(3),-1,-E(3)^2,-E(3),-1,1,E(3)^2,E(3),E(3),1,E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,
2*E(3),2,2*E(3)^2,2*E(3),2,2*E(3)^2,2*E(3),2,2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,2]],[15,15*E(3)^2,15*E(3),15,15*E(3)^2,15*E(3),15,15*E(3)^2,
15*E(3),15*E(3),15,15*E(3)^2,3,3*E(3)^2,3*E(3),3,3*E(3)^2,3*E(3),3*E(3),3,
3*E(3)^2,3,3*E(3)^2,3*E(3),3*E(3),3,3*E(3)^2,3*E(3),3,3*E(3)^2,E(3),1,E(3)^2,
E(3),1,E(3)^2,E(3)^2,E(3),1,E(3)^2,E(3),1,1,E(3)^2,E(3),E(3),1,E(3)^2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[13,2]],[21,21,21,21,21,21,21,21,21,21,21,21,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,-3,-3,-3,-3,-3,-3,-3,0,0,0,0],[21,21,21,-3,-3,-3,1,1,1
,9,9,9,1,1,1,1,1,1,-1,-1,-1,-3,-3,-3,3,3,3,5,5,5,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1
,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,0,0,0,2,2,2,-2,-2,-2,0,-2,-2,-2,0,6
,6,0,0,0,0],[21,21,21,-3,-3,-3,1,1,1,9,9,9,-3,-3,-3,5,5,5,-1,-1,-1,1,1,1,3,3,3
,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,1,1,1,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1
,0,0,0,-2,-2,-2,2,2,2,0,-2,-2,-2,0,6,6,0,0,0,0],[21,21*E(3)^2,21*E(3),21,
21*E(3)^2,21*E(3),21,21*E(3)^2,21*E(3),21*E(3),21,21*E(3)^2,1,E(3)^2,E(3),1,
E(3)^2,E(3),E(3),1,E(3)^2,1,E(3)^2,E(3),E(3),1,E(3)^2,E(3),1,E(3)^2,-E(3),-1,
-E(3)^2,-E(3),-1,-E(3)^2,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),-1,0,0,0,0,0,0,E(3),1,
E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),
-2,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[18,2]],[21,21*E(3)^2,21*E(3),21,21*E(3)^2,21*E(3),21,21*E(3)^2,
21*E(3),21*E(3),21,21*E(3)^2,-3,-3*E(3)^2,-3*E(3),-3,-3*E(3)^2,-3*E(3),-3*E(3)
,-3,-3*E(3)^2,-3,-3*E(3)^2,-3*E(3),-3*E(3),-3,-3*E(3)^2,-3*E(3),-3,-3*E(3)^2,
E(3),1,E(3)^2,E(3),1,E(3)^2,E(3)^2,E(3),1,E(3)^2,E(3),1,0,0,0,0,0,0,E(3),1,
E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0],
[GALOIS,[20,2]],[21,21*E(3)^2,21*E(3),-3,-3*E(3)^2,-3*E(3),1,E(3)^2,E(3),
9*E(3),9,9*E(3)^2,1,E(3)^2,E(3),1,E(3)^2,E(3),-E(3),-1,-E(3)^2,-3,-3*E(3)^2,
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,
[GALOIS,[73,2]],[126,126,126,-18,-18,-18,6,6,6,54,54,54,2,2,2,-6,-6,-6,2,2,2,
2,2,2,-6,-6,-6,-6,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,
1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[126,126*E(3)^2,126*E(3),
-18,-18*E(3)^2,-18*E(3),6,6*E(3)^2,6*E(3),54*E(3),54,54*E(3)^2,2,2*E(3)^2,
2*E(3),-6,-6*E(3)^2,-6*E(3),2*E(3),2,2*E(3)^2,2,2*E(3)^2,2*E(3),-6*E(3),-6,
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,0,0,0,0,0,0,0],
[GALOIS,[76,2]],[210,210,210,18,18,18,-30,-30,-30,-30,-30,-30,-2,-2,-2,-2,-2,
-2,2,2,2,-2,-2,-2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,1,1,3,-3,-3,-3,3,-3,-3,0,0,0,0],[210,
210*E(3)^2,210*E(3),18,18*E(3)^2,18*E(3),-30,-30*E(3)^2,-30*E(3),-30*E(3),-30,
-30*E(3)^2,-2,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),2*E(3),2,2*E(3)^2,-2,
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-2*E(3),-2,-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[79,2]]],
[(78,79),(49,52)(50,53)(51,54),
( 2, 3)( 5, 6)( 8, 9)(10,12)(14,15)(17,18)(19,21)(23,24)(25,27)(28,30)(31,33)
(34,36)(37,38)
(40,41)(44,45)(46,48)(49,51)(52,54)(55,57)(58,60)(61,63)(64,66)(67,69)(71,73)
,(43,47)(44,48)(45,46)]);
ALF("2^6:3A7","2^6:A7",[1,1,1,4,4,4,3,3,3,2,2,2,6,6,6,7,7,7,10,10,10,9,
9,9,8,8,8,5,5,5,23,23,23,22,22,22,21,21,21,20,20,20,32,32,32,31,31,31,26,
26,26,27,27,27,25,25,25,24,24,24,30,30,30,28,28,28,29,29,29,13,15,15,15,
14,11,12,16,17,19,18]);
ALF("2^6:3A7","3.O7(3)",[1,2,3,10,11,12,7,8,9,6,4,5,10,11,12,25,26,27,33,
31,32,28,29,30,24,22,23,9,7,8,70,68,69,73,71,72,32,33,31,29,30,28,65,66,
67,67,65,66,85,83,84,85,83,84,82,80,81,36,34,35,90,88,89,50,48,49,86,86,
86,43,50,48,49,58,17,47,20,62,63,59],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3xS6xS4",
0,
0,
0,
0,
[
( 56,111)( 57,112)( 58,113)( 59,114)( 60,115)( 61,116)( 62,117)( 63,118)
( 64,119)( 65,120)( 66,121)( 67,122)( 68,123)( 69,124)( 70,125)( 71,126)
( 72,127)( 73,128)( 74,129)( 75,130)( 76,131)( 77,132)( 78,133)( 79,134)
( 80,135)( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)
( 88,143)( 89,144)( 90,145)( 91,146)( 92,147)( 93,148)( 94,149)( 95,150)
( 96,151)( 97,152)( 98,153)( 99,154)(100,155)(101,156)(102,157)(103,158)
(104,159)(105,160)(106,161)(107,162)(108,163)(109,164)(110,165)
,
( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 36)( 32, 37)( 33, 38)
( 34, 39)( 35, 40)( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 66, 71)
( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(101,106)(102,107)(103,108)(104,109)(105,110)(121,126)(122,127)
(123,128)(124,129)(125,130)(141,146)(142,147)(143,148)(144,149)(145,150)
(156,161)(157,162)(158,163)(159,164)(160,165)
],
["ConstructDirectProduct",[["Cyclic",3],["S6xS4"]]]);
ALF("3xS6xS4","3.O7(3)",[1,7,14,4,22,7,10,52,10,31,17,48,21,43,88,14,52,
20,40,91,31,22,99,31,25,34,80,111,83,124,10,7,55,10,22,4,10,40,7,31,22,31,
91,31,28,47,48,64,58,88,40,55,59,52,99,2,8,15,5,23,8,11,53,11,32,17,49,21,
43,89,15,53,20,41,92,32,23,100,32,26,35,81,112,84,125,11,8,56,11,23,5,11,
41,8,32,23,32,92,32,29,47,49,64,58,89,41,56,59,53,100,3,9,16,6,24,9,12,54,
12,33,17,50,21,43,90,16,54,20,42,93,33,24,101,33,27,36,82,113,85,126,12,9,
57,12,24,6,12,42,9,33,24,33,93,33,30,47,50,64,58,90,42,57,59,54,101],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3.(A4x2(A4xA4).2).2",
[
"origin: Dixon's Algorithm"
],
[41472,41472,41472,41472,41472,41472,13824,13824,13824,13824,13824,13824,3456,
3456,3456,1152,1152,1152,2304,2304,2304,768,768,768,432,432,432,432,432,432,
432,432,108,108,1728,1728,144,288,288,288,108,108,576,576,576,576,576,576,576,
576,576,576,576,576,96,96,96,96,96,96,1296,1296,1296,1296,1296,1296,432,432,
432,432,432,432,864,864,864,864,864,864,864,864,144,144,144,144,54,54,216,216,
36,216,216,36,72,72,72,72,72,72,72,72,72,72,72,72,3456,3456,3456,3456,3456,
3456,1152,1152,1152,1152,1152,1152,576,576,576,192,192,192,144,144,144,144,144
,144,144,144,144,144,72,72,72,36,36,36,36,96,96,96,96,96,96,48,48,48,48,48,48,
192,192,192,192,192,192,192,192,192,192,192,192],
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33,35,35,36,35,35,35,41,41,1,3,2,1,3,2,10,12,11,10,12,11,19,21,20,22,24,23,61,
63,62,61,63,62,61,63,62,61,63,62,73,73,73,73,73,73,73,73,74,74,74,74,85,85,87,
87,88,90,90,91,61,63,62,61,63,62,70,72,71,70,72,71,1,3,2,1,3,2,1,3,2,1,3,2,19,
21,20,19,21,20,25,25,25,25,25,25,25,25,35,35,40,39,38,41,41,33,33,1,3,2,10,12,
11,13,15,14,16,18,17,19,21,20,19,21,20,22,24,23,22,24,23],[1,1,1,4,4,4,7,7,7,
10,10,10,13,13,13,16,16,16,19,19,19,22,22,22,1,4,7,7,7,10,10,10,1,4,1,4,13,19,
19,19,1,4,43,43,43,46,46,46,49,49,49,52,52,52,55,55,55,58,58,58,1,1,1,4,4,4,7,
7,7,10,10,10,1,4,7,7,7,10,10,10,13,16,16,16,1,4,1,4,13,1,4,13,43,43,43,46,46,
46,49,49,49,52,52,52,105,105,105,108,108,108,111,111,111,114,114,114,117,117,
117,120,120,120,105,108,111,111,111,114,114,114,105,108,117,117,117,105,108,
105,108,140,140,140,143,143,143,146,146,146,149,149,149,152,152,152,155,155,
155,158,158,158,161,161,161]],
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1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[TENSOR,[5,2]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
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[TENSOR,[7,2]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,
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[TENSOR,[9,2]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,
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[TENSOR,[11,2]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,
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[TENSOR,[13,2]],[3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,3,3,3,-1,-1,-1,3,3,3,-1,-1,-1,
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[TENSOR,[15,4]],
[TENSOR,[15,3]],
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[GALOIS,[19,2]],
[TENSOR,[19,4]],
[TENSOR,[20,4]],
[TENSOR,[19,3]],
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[GALOIS,[27,2]],
[TENSOR,[27,4]],
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E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3)],
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[TENSOR,[150,3]],
[TENSOR,[151,3]],
[TENSOR,[150,2]],
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[GALOIS,[162,2]]],
[( 33, 41)( 34, 42)( 87, 90)( 88, 91)( 89, 92)(136,138)(137,139),
(105,108)(106,109)(107,110)(111,114)(112,115)(113,116)(123,124)(125,128)(126,
129)(127,130)
(131,132)(136,137)(138,139)(152,155)(153,156)(154,157)(158,161)(159,162)(160,
163)
,
( 43, 46)( 44, 47)( 45, 48)( 49, 52)( 50, 53)( 51, 54)( 93, 96)( 94, 97)( 95,
 98)( 99,102)
(100,103)(101,104)(152,155)(153,156)(154,157)(158,161)(159,162)(160,163)
,
(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)( 28,
 29)( 31, 32)
( 38, 39)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65,
 66)( 68, 69)
( 71, 72)( 75, 76)( 78, 79)( 82, 83)( 94, 95)( 97, 98)(100,101)(103,104)(106,
107)(109,110)
(112,113)(115,116)(118,119)(121,122)(125,126)(128,129)(134,135)(141,142)(144,
145)(147,148)
(150,151)(153,154)(156,157)(159,160)(162,163)
]);
ALF("3.(A4x2(A4xA4).2).2","(A4x2(A4xA4).2).2",[1,1,1,2,2,2,7,7,7,6,6,6,5,5,5,
4,4,4,8,8,8,3,3,3,37,38,36,36,36,35,35,35,9,10,30,31,32,29,29,29,33,34,47,
47,47,48,48,48,49,49,49,50,50,50,52,52,52,51,51,51,22,22,22,23,23,23,24,
24,24,25,25,25,18,17,20,20,20,21,21,21,19,16,16,16,11,12,15,14,13,28,27,
26,54,54,54,53,53,53,55,55,55,56,56,56,63,63,63,64,64,64,60,60,60,59,59,
59,62,62,62,61,61,61,67,68,65,65,65,66,66,66,70,71,69,69,69,73,72,58,57,
42,42,42,46,46,46,43,43,43,41,41,41,44,44,44,45,45,45,40,40,40,39,39,39]);
ALF("3.(A4x2(A4xA4).2).2","3.O7(3)",[1,2,3,10,11,12,4,5,6,7,8,9,25,26,27,
28,29,30,7,8,9,10,11,12,17,58,43,43,43,48,49,50,20,62,17,47,86,49,50,48,
20,63,10,11,12,7,8,9,31,32,33,22,23,24,31,32,33,28,29,30,14,15,16,55,56,
57,40,41,42,52,53,54,13,51,38,39,37,45,46,44,87,95,96,94,21,64,19,61,98,
18,60,97,55,56,57,52,53,54,99,100,101,91,92,93,4,5,6,10,11,12,7,8,9,10,11,
12,22,23,24,31,32,33,43,47,49,50,48,58,58,58,43,58,88,89,90,59,62,59,63,
10,11,12,31,32,33,68,69,70,71,72,73,31,32,33,22,23,24,28,29,30,25,26,27],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("6.(3^5:U4(2):2)",
0,
[75582720,75582720,75582720,75582720,75582720,75582720,279936,279936,314928,
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34992,34992,1296,1296,1296,1944,1944,1944,2592,2592,2592,15552,15552,15552,324
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1728,1728,1728,1728,288,288,144,144,144,72,72,72,1296,1296,1296,432,432,432,
2592,2592,2592,108,108,324,324,324,60,60,60,60,60,60,90,90,90,90,90,90,180,180
,180,180,180,180,72,72,72,72,72,72,576,576,576,576,576,576,108,108,324,324,324
,54,54,54,54,54,54,48,48,48,48,48,48,108,108,108,108,108,108,108,108,108,216,
216,216,216,216,216,864,864,864],
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24,24,36,38,34,10,10,10,8,14,16,12,2,4,6,3,5,1,7,82,92,88,80,80,82,82,84,84,86
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97,97,95,95,93,93,73,72,74,73,72,74,75,75,48,50,49,41,40,39,13,15,11,9,9,7,1,3
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153,155,157,21,20,22,21,20,22,49,48,50,49,48,50,25,25,37,33,35,177,177,179,179
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48,50,49],[1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,43,43,43,48,48,48,1,4,1,4,9,10,9,10
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70,70,70,70,70,70,70,70,70,70,70,70,70,74,74,74,74,74,74,74,10,9,4,1,4,1,4,1,4
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115,118,115,118,115,118,121,121,121,121,121,121,133,133,133,133,133,133,133,
133,133,62,62,70,70,70,141,144,141,144,141,144,153,156,153,156,153,156,153,156
,153,156,153,156,166,169,166,169,166,169,169,166,169,166,169,166,74,74,74,74,
74,103,104,105,106,101,102,184,187,184,187,184,187,133,133,133,133,133,133,133
,133,133,203,203,203,203,203,203,203,203,203],,[1,6,5,4,3,2,7,8,9,10,15,14,13,
12,11,16,17,19,18,22,21,20,23,24,25,26,27,32,31,30,29,28,37,36,35,34,33,38,40,
39,41,44,43,42,45,47,46,48,50,49,56,55,54,53,52,51,57,58,61,60,59,62,64,63,65,
68,67,66,71,70,69,73,72,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
117,116,115,114,113,118,119,120,121,123,122,124,126,125,127,129,128,130,131,
132,133,135,134,137,136,138,139,140,70,69,71,70,69,71,15,14,13,12,11,16,1,6,5,
4,3,2,162,161,160,159,164,163,170,169,168,167,166,165,171,172,174,173,175,176,
177,178,179,180,181,183,182,187,186,185,184,188,189,190,191,192,193,194,195,
196,197,199,198,200,202,201,203,205,204]],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(3)^2,-E(3),1,-E(3)^2,E(3),-1,-2,2*E(3)^2,
-2*E(3),2,-2*E(3)^2,2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[188,2]],[108,-108*E(3)^2,108*E(3),-108,108*E(3)^2,-108*E(3),0,0,0,0,
36*E(3)^2,-36*E(3),36,-36*E(3)^2,36*E(3),-36,0,0,0,0,0,0,0,0,0,0,-6,6*E(3)^2,
-6*E(3),6,-6*E(3)^2,6*E(3),-18*E(3)^2,18*E(3),-18,18*E(3)^2,-18*E(3),18,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6*E(3)^2,
-6*E(3),6,-6*E(3)^2,6*E(3),-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,E(3)^2,-E(3),1,-E(3)^2,E(3),-1,-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),
-E(8)-E(8)^3,E(24)+E(24)^19,-E(24)^11-E(24)^17,E(8)+E(8)^3,-E(24)-E(24)^19,
E(24)^11+E(24)^17,-2*E(24)^11-2*E(24)^17,2*E(8)+2*E(8)^3,-2*E(24)-2*E(24)^19,
2*E(24)^11+2*E(24)^17,-2*E(8)-2*E(8)^3,2*E(24)+2*E(24)^19,0,0,0,0,0,0,0,0,0,0,
0,-E(24)-E(24)^19,E(24)^11+E(24)^17,-E(8)-E(8)^3,E(24)+E(24)^19,
-E(24)^11-E(24)^17,E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[190,11]],
[TENSOR,[190,2]],
[TENSOR,[191,2]],[432,-432*E(3)^2,432*E(3),-432,432*E(3)^2,-432*E(3),0,0,0,0,
144*E(3)^2,-144*E(3),144,-144*E(3)^2,144*E(3),-144,0,0,0,0,0,0,0,0,0,0,-6,
6*E(3)^2,-6*E(3),6,-6*E(3)^2,6*E(3),-18*E(3)^2,18*E(3),-18,18*E(3)^2,-18*E(3),
18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(3)^2,E(3),-1
,E(3)^2,-E(3),1,2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,-2*E(3),-E(8)-E(8)^3,
E(24)+E(24)^19,-E(24)^11-E(24)^17,E(8)+E(8)^3,-E(24)-E(24)^19,
E(24)^11+E(24)^17,4*E(24)^11+4*E(24)^17,-4*E(8)-4*E(8)^3,4*E(24)+4*E(24)^19,
-4*E(24)^11-4*E(24)^17,4*E(8)+4*E(8)^3,-4*E(24)-4*E(24)^19,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[194,11]],
[TENSOR,[194,2]],
[TENSOR,[195,2]],[2592,-2592*E(3)^2,2592*E(3),-2592,2592*E(3)^2,-2592*E(3),0,
0,0,0,-108*E(3)^2,108*E(3),-108,108*E(3)^2,-108*E(3),108,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),-2,2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,
-2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[198,2]],[1728,-1728*E(3)^2,1728*E(3),-1728,1728*E(3)^2,-1728*E(3),0,
0,0,0,-72*E(3)^2,72*E(3),-72,72*E(3)^2,-72*E(3),72,0,0,0,0,0,0,0,0,0,0,-6,
6*E(3)^2,-6*E(3),6,-6*E(3)^2,6*E(3),36*E(3)^2,-36*E(3),36,-36*E(3)^2,36*E(3),
-36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(3)^2,
2*E(3),-2,2*E(3)^2,-2*E(3),2,-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],
[GALOIS,[200,2]],[864,-864*E(3)^2,864*E(3),-864,864*E(3)^2,-864*E(3),0,0,0,0,
-36*E(3)^2,36*E(3),-36,36*E(3)^2,-36*E(3),36,0,0,0,0,0,0,0,0,0,0,6,-6*E(3)^2,
6*E(3),-6,6*E(3)^2,-6*E(3),-36*E(3)^2,36*E(3),-36,36*E(3)^2,-36*E(3),36,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(20)+E(20)^9-E(20)^13-E(20)^17,
-E(60)^7+E(60)^19+E(60)^31-E(60)^43,-E(60)^11+E(60)^23+E(60)^47-E(60)^59,
-E(20)-E(20)^9+E(20)^13+E(20)^17,E(60)^7-E(60)^19-E(60)^31+E(60)^43,
E(60)^11-E(60)^23-E(60)^47+E(60)^59,-E(3)^2,E(3),-1,E(3)^2,-E(3),1,-1,E(3)^2,
-E(3),1,-E(3)^2,E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[202,23]],
[TENSOR,[202,2]],
[TENSOR,[203,2]]],
[
(159,162)(160,163)(161,164)(165,168)(166,169)(167,170)(182,185)(183,186)
(184,187)
,(141,144)(142,145)(143,146),(136,137),
( 57, 58)(136,137)(141,144)(142,145)(143,146)(159,162)(160,163)(161,164)
(165,168)(166,169)(167,170)(182,185)(183,186)(184,187)
,
(  2,  6)(  3,  5)( 11, 15)( 12, 14)( 18, 19)( 20, 22)( 28, 32)( 29, 31)
( 33, 37)( 34, 36)( 39, 40)( 42, 44)( 46, 47)( 49, 50)( 51, 56)( 52, 55)
( 53, 54)( 59, 61)( 63, 64)( 66, 68)( 69, 71)( 72, 73)(113,117)(114,116)
(122,123)(125,126)(128,129)(134,135)(136,137)(142,146)(143,145)(147,151)
(148,150)(154,158)(155,157)(160,164)(161,163)(165,167)(168,170)(173,174)
(182,186)(183,185)(198,199)(201,202)(204,205)
,(130,131)(188,189)(190,191)(193,194),
( 77, 78)( 83, 85)( 84, 86)( 87, 91)( 88, 92)( 93, 95)( 94, 96)(101,103)
(102,104)(109,111)(110,112)(138,140)(171,172)(176,180)(177,181)(188,193)
(189,194)(190,191)(192,195)
,
( 76, 77)( 81, 91)( 82, 92)( 83, 89)( 84, 90)( 93, 97)( 94, 98)(103,105)
(104,106)(107,111)(108,112)(138,139)(171,172)(176,178)(177,179)(188,189)
(190,194)(191,193)(192,196)
]);
ALF("6.(3^5:U4(2):2)","3^5:U4(2):2",[1,1,1,1,1,1,2,2,3,3,4,4,4,4,4,4,5,5,
5,6,6,6,7,7,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,13,13,13,
14,14,14,15,15,15,16,16,16,17,17,18,18,18,19,19,19,20,21,21,21,22,22,22,
23,23,23,24,25,26,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,
36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,45,45,45,45,46,
46,47,47,47,48,48,48,49,49,49,50,50,51,52,52,52,53,53,54,55,56,57,57,57,
57,57,57,58,58,58,58,58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,
61,61,61,62,62,63,63,63,64,64,65,65,66,66,67,67,67,67,67,67,68,68,69,69,
70,71,71,72,73,74,74,74,75,75,75,76,76,76]);
ALF("6.(3^5:U4(2):2)","(2x3^5).U4(2).2",[1,2,1,2,1,2,3,4,5,6,7,8,7,8,7,8,
9,9,9,10,10,10,11,12,13,14,15,16,15,16,15,16,17,18,17,18,17,18,19,19,19,
20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,26,27,27,27,28,28,28,29,
30,30,30,31,31,31,32,32,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,71,72,71,72,73,74,75,75,75,76,76,76,77,77,77,78,79,80,81,81,81,82,83,
84,85,86,87,88,87,88,87,88,89,90,89,90,89,90,91,92,91,92,91,92,93,94,93,
94,93,94,95,96,95,96,95,96,97,98,99,99,99,100,101,102,103,104,105,106,107,
106,107,106,107,108,109,110,111,112,113,114,115,116,117,117,117,118,118,
118,119,119,119]);
ALF("6.(3^5:U4(2):2)","3.3^5:U4(2):2",[1,2,3,1,2,3,7,7,8,8,4,5,6,4,5,6,61,
62,63,64,65,66,67,67,74,74,68,69,70,68,69,70,71,72,73,71,72,73,46,47,48,
49,50,51,52,53,54,55,56,57,95,96,97,98,99,100,101,101,92,93,94,25,26,27,
18,19,20,21,22,23,24,89,90,91,88,86,85,87,28,28,29,29,30,30,31,31,33,33,
32,32,34,34,106,106,107,107,105,105,108,108,109,109,110,110,111,111,103,
103,104,104,102,102,113,114,115,113,114,115,112,112,128,129,130,125,126,
127,40,41,42,35,35,39,36,37,38,76,76,78,77,75,9,10,11,9,10,11,12,13,14,12,
13,14,15,16,17,15,16,17,58,59,60,58,59,60,43,44,45,43,44,45,134,134,135,
136,137,140,140,138,138,139,139,131,132,133,131,132,133,81,81,82,82,84,79,
79,83,80,116,117,118,119,120,121,122,123,124]);
ALF("6.(3^5:U4(2):2)","6.O7(3)",[1,6,5,4,3,2,24,25,16,17,20,19,18,23,22,
21,172,174,173,72,71,73,30,31,32,33,102,107,106,105,104,103,20,19,18,23,
22,21,73,72,71,63,62,64,66,68,67,10,12,11,165,164,166,168,167,169,78,78,
59,58,60,55,57,56,61,59,58,60,8,7,9,15,14,13,65,77,83,84,109,108,25,24,29,
28,27,26,31,30,33,32,31,30,79,80,81,82,70,69,33,32,29,28,27,26,17,16,123,
122,136,135,134,133,39,38,37,42,41,40,120,121,46,48,47,137,139,138,74,76,
75,69,70,77,13,15,14,170,171,78,61,78,117,119,118,117,119,118,160,159,158,
163,162,161,49,54,53,52,51,50,137,139,138,137,139,138,47,46,48,47,46,48,
85,86,76,75,74,111,110,109,108,113,112,95,94,93,95,94,93,80,79,86,85,84,
82,81,83,65,127,129,128,124,126,125,34,36,35],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3x2.L4(3).2_2",
0,
0,
0,
0,
[( 57, 58)(126,127)(195,196),
( 47, 48)( 49, 50)( 62, 63)( 66, 67)( 68, 69)(116,117)(118,119)(131,132)
(135,136)(137,138)(185,186)(187,188)(200,201)(204,205)(206,207)
,
( 47, 48)( 49, 50)( 62, 63)( 66, 67)( 68, 69)( 70,139)( 71,140)( 72,141)
( 73,142)( 74,143)( 75,144)( 76,145)( 77,146)( 78,147)( 79,148)( 80,149)
( 81,150)( 82,151)( 83,152)( 84,153)( 85,154)( 86,155)( 87,156)( 88,157)
( 89,158)( 90,159)( 91,160)( 92,161)( 93,162)( 94,163)( 95,164)( 96,165)
( 97,166)( 98,167)( 99,168)(100,169)(101,170)(102,171)(103,172)(104,173)
(105,174)(106,175)(107,176)(108,177)(109,178)(110,179)(111,180)(112,181)
(113,182)(114,183)(115,184)(116,186)(117,185)(118,188)(119,187)(120,189)
(121,190)(122,191)(123,192)(124,193)(125,194)(126,195)(127,196)(128,197)
(129,198)(130,199)(131,201)(132,200)(133,202)(134,203)(135,205)(136,204)
(137,207)(138,206)
,( 39, 40)(108,109)(177,178),
( 35, 37)( 36, 38)(104,106)(105,107)(173,175)(174,176),
( 70,139)( 71,140)( 72,141)( 73,142)( 74,143)( 75,144)( 76,145)( 77,146)
( 78,147)( 79,148)( 80,149)( 81,150)( 82,151)( 83,152)( 84,153)( 85,154)
( 86,155)( 87,156)( 88,157)( 89,158)( 90,159)( 91,160)( 92,161)( 93,162)
( 94,163)( 95,164)( 96,165)( 97,166)( 98,167)( 99,168)(100,169)(101,170)
(102,171)(103,172)(104,173)(105,174)(106,175)(107,176)(108,177)(109,178)
(110,179)(111,180)(112,181)(113,182)(114,183)(115,184)(116,185)(117,186)
(118,187)(119,188)(120,189)(121,190)(122,191)(123,192)(124,193)(125,194)
(126,195)(127,196)(128,197)(129,198)(130,199)(131,200)(132,201)(133,202)
(134,203)(135,204)(136,205)(137,206)(138,207)
,
(  7,  9)(  8, 10)( 19, 20)( 23, 24)( 26, 28)( 27, 29)( 31, 32)( 41, 42)
( 45, 46)( 47, 49)( 48, 50)( 51, 52)( 53, 54)( 55, 56)( 60, 61)( 64, 65)
( 66, 68)( 67, 69)( 76, 78)( 77, 79)( 88, 89)( 92, 93)( 95, 97)( 96, 98)
(100,101)(110,111)(114,115)(116,118)(117,119)(120,121)(122,123)(124,125)
(129,130)(133,134)(135,137)(136,138)(145,147)(146,148)(157,158)(161,162)
(164,166)(165,167)(169,170)(179,180)(183,184)(185,187)(186,188)(189,190)
(191,192)(193,194)(198,199)(202,203)(204,206)(205,207)
],
["ConstructDirectProduct",[["Cyclic",3],["2.L4(3).2_2"]]]);
ALF("3x2.L4(3).2_2","L4(3).2_2",[1,1,2,3,4,4,5,5,6,6,7,7,8,9,9,10,11,11,
12,13,14,14,15,16,17,18,18,19,19,20,21,22,23,23,24,24,25,25,26,26,27,28,
29,30,31,32,33,33,34,34,35,36,37,38,39,40,41,41,42,43,44,45,45,46,47,48,
48,49,49,1,1,2,3,4,4,5,5,6,6,7,7,8,9,9,10,11,11,12,13,14,14,15,16,17,18,
18,19,19,20,21,22,23,23,24,24,25,25,26,26,27,28,29,30,31,32,33,33,34,34,
35,36,37,38,39,40,41,41,42,43,44,45,45,46,47,48,48,49,49,1,1,2,3,4,4,5,5,
6,6,7,7,8,9,9,10,11,11,12,13,14,14,15,16,17,18,18,19,19,20,21,22,23,23,24,
24,25,25,26,26,27,28,29,30,31,32,33,33,34,34,35,36,37,38,39,40,41,41,42,
43,44,45,45,46,47,48,48,49,49]);
ALF("3x2.L4(3).2_2","3xL4(3).2_2",[1,1,2,3,4,4,5,5,6,6,7,7,8,9,9,10,11,11,
12,13,14,14,15,16,17,18,18,19,19,20,21,22,23,23,24,24,25,25,26,26,27,28,
29,30,31,32,33,33,34,34,35,36,37,38,39,40,41,41,42,43,44,45,45,46,47,48,
48,49,49,50,50,51,52,53,53,54,54,55,55,56,56,57,58,58,59,60,60,61,62,63,
63,64,65,66,67,67,68,68,69,70,71,72,72,73,73,74,74,75,75,76,77,78,79,80,
81,82,82,83,83,84,85,86,87,88,89,90,90,91,92,93,94,94,95,96,97,97,98,98,
99,99,100,101,102,102,103,103,104,104,105,105,106,107,107,108,109,109,110,
111,112,112,113,114,115,116,116,117,117,118,119,120,121,121,122,122,123,
123,124,124,125,126,127,128,129,130,131,131,132,132,133,134,135,136,137,
138,139,139,140,141,142,143,143,144,145,146,146,147,147]);
ALF("3x2.L4(3).2_2","6.O7(3)",[1,4,10,13,16,17,18,21,24,25,32,33,34,37,40,
46,49,52,71,66,70,69,74,77,93,108,109,102,105,114,127,124,122,123,146,149,
140,143,178,175,10,7,13,43,46,34,62,62,55,55,66,58,71,61,74,65,85,86,93,
114,117,130,130,137,124,172,172,171,170,5,2,11,14,16,17,22,19,24,25,32,33,
35,41,38,47,53,50,72,67,70,69,75,77,94,108,109,106,103,115,128,125,122,
123,150,147,144,141,176,179,11,8,14,44,47,35,63,63,56,56,67,59,72,61,75,
65,85,86,94,115,118,131,131,138,125,173,173,171,170,3,6,12,15,16,17,20,23,
24,25,32,33,36,39,42,48,51,54,73,68,70,69,76,77,95,108,109,104,107,116,
129,126,122,123,148,151,142,145,180,177,12,9,15,45,48,36,64,64,57,57,68,
60,73,61,76,65,85,86,95,116,119,132,132,139,126,174,174,171,170],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("2x3.G2(3)",
0,
0,
0,
0,
[(40,43)(41,44)(42,45)(85,88)(86,89)(87,90),
( 2, 3)( 5, 6)(13,14)(16,17)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)
(44,45)(47,48)(50,51)(58,59)(61,62)(68,69)(71,72)(74,75)(77,78)(80,81)(83,84)
(86,87)(89,90)
,
( 2, 3)( 5, 6)(13,14)(16,17)(23,24)(26,27)(29,30)(35,36)(38,39)(41,42)(44,45)
(47,48)(50,51)(58,59)(61,62)(68,69)(71,72)(74,75)(80,81)(83,84)(86,87)(89,90)
,
( 7, 8)(12,15)(13,16)(14,17)(18,19)(25,28)(26,29)(27,30)(34,37)(35,38)(36,39)
(52,53)(57,60)(58,61)(59,62)(63,64)(70,73)(71,74)(72,75)(79,82)(80,83)(81,84)
],
["ConstructDirectProduct",[["Cyclic",2],["3.G2(3)"]]]);
ALF("2x3.G2(3)","G2(3)",[1,1,1,2,2,2,3,4,5,6,7,8,8,8,9,9,9,10,11,12,13,14,
14,14,15,15,15,16,16,16,17,18,19,20,20,20,21,21,21,22,22,22,23,23,23,1,1,
1,2,2,2,3,4,5,6,7,8,8,8,9,9,9,10,11,12,13,14,14,14,15,15,15,16,16,16,17,
18,19,20,20,20,21,21,21,22,22,22,23,23,23]);
ALF("2x3.G2(3)","2xG2(3)",[1,1,1,2,2,2,3,4,5,6,7,8,8,8,9,9,9,10,11,12,13,
14,14,14,15,15,15,16,16,16,17,18,19,20,20,20,21,21,21,22,22,22,23,23,23,
24,24,24,25,25,25,26,27,28,29,30,31,31,31,32,32,32,33,34,35,36,37,37,37,
38,38,38,39,39,39,40,41,42,43,43,43,44,44,44,45,45,45,46,46,46]);
ALF("2x3.G2(3)","6.O7(3)",[1,5,3,13,14,15,16,26,26,32,30,43,44,45,37,41,
39,69,79,85,84,87,91,89,96,100,98,93,94,95,110,110,110,130,131,132,133,
133,133,146,150,148,140,144,142,4,2,6,13,14,15,17,27,27,33,31,43,44,45,40,
38,42,70,80,86,84,90,88,92,99,97,101,93,94,95,111,111,111,130,131,132,134,
134,134,149,147,151,143,141,145],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("6.O7(3)M5",
[
"5th maximal subgroup of 6.O7(3),\n",
"differs from 6.O7(3)M4 = 2x3.G2(3) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2x3.G2(3)"]]);
ALF("6.O7(3)M5","O7(3)M5",[1,1,1,2,2,2,3,4,5,6,7,8,8,8,9,9,9,10,11,12,13,
14,14,14,15,15,15,16,16,16,17,18,19,20,20,20,21,21,21,22,22,22,23,23,23,1,
1,1,2,2,2,3,4,5,6,7,8,8,8,9,9,9,10,11,12,13,14,14,14,15,15,15,16,16,16,17,
18,19,20,20,20,21,21,21,22,22,22,23,23,23]);
ALF("6.O7(3)M5","2.O7(3)M5",[1,1,1,2,2,2,3,4,5,6,7,8,8,8,9,9,9,10,11,12,
13,14,14,14,15,15,15,16,16,16,17,18,19,20,20,20,21,21,21,22,22,22,23,23,
23,24,24,24,25,25,25,26,27,28,29,30,31,31,31,32,32,32,33,34,35,36,37,37,
37,38,38,38,39,39,39,40,41,42,43,43,43,44,44,44,45,45,45,46,46,46]);
ALF("6.O7(3)M5","3.O7(3)M5",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]);
ALF("6.O7(3)M5","6.O7(3)",[1,3,5,13,15,14,16,28,28,32,30,43,45,44,37,39,
41,69,81,86,83,87,89,91,96,98,100,93,95,94,112,112,112,130,132,131,135,
135,135,140,142,144,146,148,150,4,6,2,13,15,14,17,29,29,33,31,43,45,44,40,
42,38,70,82,85,83,90,92,88,99,101,97,93,95,94,113,113,113,130,132,131,136,
136,136,143,145,141,149,151,147],[
"equals the map from 6.O7(3)M4, mapped under an outer autom."
]);

MOT("2x3.(3^(3+3):L3(3))",
0,
0,
0,
0,
[
( 52, 55, 58, 61)( 53, 56, 59, 62)( 54, 57, 60, 63)(122,125,128,131)
(123,126,129,132)(124,127,130,133)
,( 39, 42)( 40, 43)( 41, 44)(109,112)(110,113)(111,114),
(  6,  7)( 13, 17)( 14, 18)( 15, 16)( 26, 29)( 27, 31)( 28, 30)( 36, 38)
( 49, 51)( 69, 70)( 76, 77)( 83, 87)( 84, 88)( 85, 86)( 96, 99)( 97,101)
( 98,100)(106,108)(119,121)(139,140)
,
(  2,  3)( 11, 12)( 20, 21)( 33, 34)( 40, 41)( 43, 44)( 47, 48)( 53, 54)
( 56, 57)( 59, 60)( 62, 63)( 66, 67)( 72, 73)( 81, 82)( 90, 91)(103,104)
(110,111)(113,114)(117,118)(123,124)(126,127)(129,130)(132,133)(136,137)
],
["ConstructDirectProduct",[["Cyclic",2],["3.(3^(3+3):L3(3))"]]]);
ALF("2x3.(3^(3+3):L3(3))","3^(3+3):L3(3)",[1,1,1,2,3,4,5,28,27,26,26,26,
32,34,33,30,29,31,16,16,16,15,18,17,19,25,23,24,20,22,21,39,39,39,38,36,
37,35,41,41,41,40,40,40,42,43,43,43,44,46,45,6,6,6,7,7,7,8,8,8,9,9,9,13,
14,14,14,12,10,11,1,1,1,2,3,4,5,28,27,26,26,26,32,34,33,30,29,31,16,16,16,
15,18,17,19,25,23,24,20,22,21,39,39,39,38,36,37,35,41,41,41,40,40,40,42,
43,43,43,44,46,45,6,6,6,7,7,7,8,8,8,9,9,9,13,14,14,14,12,10,11]);
ALF("2x3.(3^(3+3):L3(3))","2x3^(3+3):L3(3)",[1,1,1,2,3,4,5,28,27,26,26,26,
32,34,33,30,29,31,16,16,16,15,18,17,19,25,23,24,20,22,21,39,39,39,38,36,
37,35,41,41,41,40,40,40,42,43,43,43,44,46,45,6,6,6,7,7,7,8,8,8,9,9,9,13,
14,14,14,12,10,11,47,47,47,48,49,50,51,74,73,72,72,72,78,80,79,76,75,77,
62,62,62,61,64,63,65,71,69,70,66,68,67,85,85,85,84,82,83,81,87,87,87,86,
86,86,88,89,89,89,90,92,91,52,52,52,53,53,53,54,54,54,55,55,55,59,60,60,
60,58,56,57]);
ALF("2x3.(3^(3+3):L3(3))","6.O7(3)",[1,5,3,16,24,26,28,77,69,74,75,76,84,
80,86,85,83,82,18,22,20,32,16,24,108,28,30,32,26,32,30,13,14,15,70,79,65,
81,93,94,95,93,94,95,122,37,41,39,135,120,133,140,144,142,146,150,148,140,
144,142,146,150,148,32,102,106,104,108,112,110,4,2,6,17,25,27,29,77,70,74,
75,76,84,79,85,86,83,81,21,19,23,33,17,25,109,29,31,33,27,33,31,13,14,15,
69,80,65,82,93,94,95,93,94,95,123,40,38,42,136,121,134,143,141,145,149,
147,151,143,141,145,149,147,151,33,105,103,107,109,113,111],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3x2.S6(2)",
0,
0,
0,
0,
[
( 44, 87)( 45, 88)( 46, 89)( 47, 90)( 48, 91)( 49, 92)( 50, 93)( 51, 94)
( 52, 95)( 53, 96)( 54, 97)( 55, 98)( 56, 99)( 57,100)( 58,101)( 59,102)
( 60,103)( 61,104)( 62,105)( 63,106)( 64,107)( 65,108)( 66,109)( 67,110)
( 68,111)( 69,112)( 70,113)( 71,114)( 72,115)( 73,116)( 74,117)( 75,118)
( 76,119)( 77,120)( 78,121)( 79,122)( 80,123)( 81,124)( 82,125)( 83,126)
( 84,127)( 85,128)( 86,129)
,( 36, 37)( 79, 80)(122,123)],
["ConstructDirectProduct",[["Cyclic",3],["2.S6(2)"]]]);
ALF("3x2.S6(2)","S6(2)",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,15,
16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30,1,1,2,3,
4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,15,16,17,17,18,19,20,21,22,22,23,24,
24,25,25,26,26,27,28,29,29,30,30,1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,
14,14,15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,
30]);
ALF("3x2.S6(2)","3xS6(2)",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,
15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30,31,
31,32,33,34,35,36,36,37,37,38,38,39,39,40,41,42,43,44,44,45,46,47,47,48,
49,50,51,52,52,53,54,54,55,55,56,56,57,58,59,59,60,60,61,61,62,63,64,65,
66,66,67,67,68,68,69,69,70,71,72,73,74,74,75,76,77,77,78,79,80,81,82,82,
83,84,84,85,85,86,86,87,88,89,89,90,90]);
ALF("3x2.S6(2)","6.O7(3)",[1,4,7,13,10,13,18,21,26,27,30,31,37,40,46,34,
43,46,49,52,58,74,79,80,71,78,83,84,87,90,93,96,99,110,111,117,117,137,
127,133,134,158,161,5,2,8,14,11,14,22,19,26,27,30,31,41,38,47,35,44,47,53,
50,59,75,79,80,72,78,83,84,91,88,94,100,97,110,111,118,118,138,128,133,
134,162,159,3,6,9,15,12,15,20,23,26,27,30,31,39,42,48,36,45,48,51,54,60,
76,79,80,73,78,83,84,89,92,95,98,101,110,111,119,119,139,129,133,134,160,
163],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("6.O7(3)M8",
[
"8th maximal subgroup of 6.O7(3),\n",
"differs from 6.O7(3)M7 = 3x2.S6(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3x2.S6(2)"]]);
ALF("6.O7(3)M8","3.O7(3)M8",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,
14,15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30,
31,31,32,33,34,35,36,36,37,37,38,38,39,39,40,41,42,43,44,44,45,46,47,47,
48,49,50,51,52,52,53,54,54,55,55,56,56,57,58,59,59,60,60,61,61,62,63,64,
65,66,66,67,67,68,68,69,69,70,71,72,73,74,74,75,76,77,77,78,79,80,81,82,
82,83,84,84,85,85,86,86,87,88,89,89,90,90]);
ALF("6.O7(3)M8","2.O7(3)M8",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36,37,38,39,40,41,42,43]);
ALF("6.O7(3)M8","O7(3)M8",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,
15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30,1,1,
2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,15,16,17,17,18,19,20,21,22,22,
23,24,24,25,25,26,26,27,28,29,29,30,30,1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,
12,13,14,14,15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,
29,30,30]);
ALF("6.O7(3)M8","6.O7(3)",[1,4,7,13,10,13,18,21,28,29,30,31,37,40,46,34,
43,46,49,52,58,74,81,82,71,78,84,83,87,90,93,96,99,112,113,117,117,137,
127,135,136,158,161,3,6,9,15,12,15,20,23,28,29,30,31,39,42,48,36,45,48,51,
54,60,76,81,82,73,78,84,83,89,92,95,98,101,112,113,119,119,139,129,135,
136,160,163,5,2,8,14,11,14,22,19,28,29,30,31,41,38,47,35,44,47,53,50,59,
75,81,82,72,78,84,83,91,88,94,100,97,112,113,118,118,138,128,135,136,162,
159],[
"fusion 3x2.S6(2) -> 6.O7(3) mapped under 6.O7(3).2"
]);

MOT("6.O7(3)M9",
0,
[7558272,7558272,7558272,7558272,7558272,7558272,1259712,1259712,104976,104976
,104976,104976,104976,104976,26244,26244,17496,17496,8748,8748,8748,8748,5832,
5832,2916,2916,10368,10368,10368,10368,10368,10368,1728,1728,1728,1728,1728,
1728,1728,1728,288,288,11664,11664,11664,11664,34992,34992,34992,34992,34992,
34992,486,486,1296,1296,1296,1296,1296,1296,432,432,432,432,1944,1944,1944,
1944,1944,1944,324,324,139968,139968,139968,15552,15552,15552,288,288,288,
69984,69984,69984,7776,7776,7776,2916,2916,2916,972,1944,1944,1944,1944,1944,
1944,1944,1944,1944,324,648,648,648,648,648,648,648,648,648,648,648,648,144,
144,144,324,324,324,324,324,324,108,108,108,108,108,3888,3888,3888,3888,3888,
3888,972,972,972,972,972,972,972,972,972,972,972,972,432,432,432,432,432,432,
108,108,108,108,108,108,108,108,108,108,108,108,162,162,162,162,162,162,54,54,
54,54,72,72,72,72,72,72,648,648,648,144,144,144,144,144,144,108,108,108,108,
324,324,324,108,108,108,108,108,108,108,108,96,96,96,96,96,96,96,96,96,96,96,
96,48,48,48,48,48,48,72,72,72,72,72,72],
[,[1,3,5,1,3,5,7,7,9,11,13,9,11,13,15,15,17,17,19,19,21,21,23,23,25,25,1,3,5,1
,3,5,7,7,27,29,31,27,29,31,33,33,43,43,45,45,47,49,51,47,49,51,53,53,47,49,51,
47,49,51,43,43,45,45,65,67,69,65,67,69,71,71,4,6,2,4,6,2,30,32,28,8,8,8,8,8,8,
12,14,10,18,46,46,46,50,52,48,44,44,44,24,12,14,10,48,50,52,44,44,44,46,46,46,
34,34,34,66,68,70,70,66,68,72,72,68,70,66,128,128,130,130,132,132,134,134,136,
136,138,138,140,140,142,142,144,144,128,128,130,130,132,132,134,134,136,136,
138,138,140,140,142,142,144,144,164,164,166,166,168,168,170,170,172,172,146,
146,148,148,150,150,1,3,5,76,78,77,76,78,77,17,23,17,23,9,11,13,25,25,21,21,15
,15,19,19,80,79,81,80,79,81,80,79,81,80,79,81,35,37,39,35,37,39,102,104,103,
102,104,103],[1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,27,30,27,30,
27,30,27,30,35,38,35,38,35,38,35,38,1,4,1,4,1,4,1,4,1,4,1,4,27,30,27,30,27,30,
27,30,27,30,7,8,7,8,7,8,7,8,73,73,73,76,76,76,79,79,79,73,73,73,76,76,76,73,73
,73,73,73,73,73,73,73,73,73,73,73,73,76,76,76,76,76,76,76,76,76,76,76,76,79,79
,79,84,84,84,83,83,83,82,82,86,86,86,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,27,30
,27,30,27,30,27,30,27,30,27,30,27,30,27,30,27,30,15,16,15,16,15,16,21,22,19,20
,35,38,35,38,35,38,180,180,180,183,186,183,186,183,186,180,180,180,180,180,180
,180,180,180,180,180,180,180,180,180,208,205,208,205,208,205,214,211,214,211,
214,211,216,216,216,219,219,219,183,186,183,186,183,186]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[TENSOR,[9,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
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[GALOIS,[216,11]],
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[
(204,210)(205,211)(206,212)(207,213)(208,214)(209,215)(216,219)(217,220)
(218,221)
,(196,197)(198,199)(200,201)(202,203),
(183,186)(184,187)(185,188)(204,213)(205,214)(206,215)(207,210)(208,211)
(209,212)(216,219)(217,220)(218,221)(222,225)(223,226)(224,227)
,
(123,124)(183,186)(184,187)(185,188)(204,213)(205,214)(206,215)(207,210)
(208,211)(209,212)(216,219)(217,220)(218,221)(222,225)(223,226)(224,227)
,
(  2,  6)(  3,  5)( 10, 14)( 11, 13)( 28, 32)( 29, 31)( 36, 40)( 37, 39)
( 48, 52)( 49, 51)( 56, 60)( 57, 59)( 66, 70)( 67, 69)( 74, 75)( 77, 78)
( 80, 81)( 83, 84)( 85, 87)( 89, 90)( 93, 94)( 96, 97)( 99,100)(103,104)
(105,107)(108,109)(112,113)(115,116)(117,120)(118,122)(119,121)(123,124)
(126,127)(181,182)(184,188)(185,187)(194,195)(204,206)(207,209)(210,212)
(213,215)(217,218)(220,221)(223,227)(224,226)
,
(128,130,132)(129,131,133)(134,138,136)(135,139,137)(140,142,144)(141,143,145)
(146,148,150)(147,149,151)(152,156,154)(153,157,155)(158,160,162)(159,161,163)
(174,176,178)(175,177,179)
,
( 19, 21)( 20, 22)(130,132)(131,133)(134,140)(135,141)(136,142)(137,143)
(138,144)(139,145)(148,150)(149,151)(152,158)(153,159)(154,160)(155,161)
(156,162)(157,163)(166,168)(167,169)(170,172)(171,173)(176,178)(177,179)
(190,192)(198,202)(199,203)(200,201)
]);
ALF("6.O7(3)M9","O7(3)N3A",[1,1,1,1,1,1,2,2,3,3,3,3,3,3,4,4,5,5,6,6,7,7,
8,8,9,9,10,10,10,10,10,10,11,11,12,12,12,12,12,12,13,13,14,14,15,15,16,16,
16,16,16,16,17,17,18,18,18,18,18,18,19,19,20,20,21,21,21,21,21,21,22,22,
23,23,23,24,24,24,25,25,25,26,26,26,27,27,27,28,28,28,29,30,30,30,31,31,
31,32,32,32,33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,
40,40,41,41,42,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50,50,51,
51,52,52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,
63,64,64,65,65,66,66,67,67,68,68,69,69,69,70,70,70,70,70,70,71,72,73,74,
75,75,75,76,76,77,77,78,78,79,79,80,80,80,80,80,80,81,81,81,81,81,81,82,
82,82,83,83,83,84,84,84,84,84,84]);
ALF("6.O7(3)M9","2.O7(3)M9",[1,2,1,2,1,2,3,4,11,12,11,12,11,12,5,6,9,10,
13,14,17,18,15,16,7,8,19,20,19,20,19,20,21,22,23,24,23,24,23,24,25,26,53,
54,55,56,57,58,57,58,57,58,59,60,69,70,69,70,69,70,65,66,67,68,63,64,63,
64,63,64,61,62,33,33,33,36,36,36,27,27,27,32,32,32,35,35,35,31,31,31,30,
79,79,79,80,80,80,81,81,81,29,34,34,34,73,73,73,74,74,74,72,72,72,28,28,
28,77,77,77,78,78,78,75,76,71,71,71,104,105,106,107,108,109,41,42,37,38,
39,40,88,89,92,93,90,91,112,113,114,115,116,117,51,52,47,48,49,50,84,85,
82,83,86,87,110,111,45,46,96,97,43,44,94,95,98,99,100,101,102,103,120,120,
120,136,137,136,137,136,137,126,131,129,121,130,130,130,122,123,124,125,
118,119,127,128,138,139,138,139,138,139,140,141,140,141,140,141,133,133,
133,132,132,132,134,135,134,135,134,135]);
ALF("6.O7(3)M9","3.O7(3)M9",[1,2,3,1,2,3,4,4,5,6,7,5,6,7,9,9,8,8,13,13,
12,12,10,10,11,11,34,35,36,34,35,36,37,37,38,39,40,38,39,40,41,41,51,51,
52,52,48,49,50,48,49,50,57,57,86,87,88,86,87,88,89,89,90,90,53,54,55,53,
54,55,56,56,14,15,16,25,26,27,45,46,47,17,18,19,28,29,30,20,21,22,23,61,
62,63,64,65,66,58,59,60,24,31,32,33,77,78,79,80,81,82,74,75,76,42,43,44,
70,71,72,67,68,69,73,73,83,84,85,109,109,110,110,108,108,100,100,99,99,
101,101,93,93,94,94,92,92,112,112,113,113,111,111,105,105,104,104,106,106,
97,97,98,98,96,96,107,107,102,102,91,91,103,103,95,95,115,115,116,116,114,
114,124,125,126,134,135,136,134,135,136,127,130,129,128,117,118,119,120,
120,123,123,122,122,121,121,146,147,148,146,147,148,143,144,145,143,144,
145,137,138,139,140,141,142,131,132,133,131,132,133]);
ALF("6.O7(3)M9","6.O7(3)",[1,6,5,4,3,2,16,17,18,23,22,21,20,19,16,17,24,
25,26,27,28,29,30,31,32,33,13,15,14,13,15,14,70,69,37,42,41,40,39,38,122,
123,16,17,24,25,18,23,22,21,20,19,32,33,74,76,75,74,76,75,69,70,77,77,102,
107,106,105,104,103,108,109,7,9,8,10,12,11,43,45,44,55,57,56,63,62,64,58,
60,59,61,61,61,61,58,60,59,55,57,56,78,71,73,72,72,71,73,64,63,62,66,68,
67,130,132,131,165,164,166,169,168,167,170,171,172,174,173,24,25,26,27,28,
29,32,33,28,29,30,31,32,33,26,27,30,31,65,65,79,80,81,82,85,86,82,81,83,
83,86,85,80,79,84,84,108,109,108,109,108,109,112,113,110,111,120,121,133,
134,135,136,13,15,14,46,48,47,46,48,47,65,84,77,83,74,76,75,86,85,81,82,
69,70,80,79,100,99,98,97,96,101,97,96,101,100,99,98,93,95,94,93,95,94,137,
139,138,137,139,138],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3xIsoclinic(2.A9.2)",
0,
0,
0,
0,
[
( 43, 85)( 44, 86)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)( 50, 92)
( 51, 93)( 52, 94)( 53, 95)( 54, 96)( 55, 97)( 56, 98)( 57, 99)( 58,100)
( 59,101)( 60,102)( 61,103)( 62,104)( 63,105)( 64,106)( 65,107)( 66,108)
( 67,109)( 68,110)( 69,111)( 70,112)( 71,113)( 72,114)( 73,115)( 74,116)
( 75,117)( 76,118)( 77,119)( 78,120)( 79,121)( 80,122)( 81,123)( 82,124)
( 83,125)( 84,126)
,( 41, 42)( 83, 84)(125,126),( 39, 40)( 81, 82)(123,124),
( 33, 34)( 75, 76)(117,118),( 35, 36)( 77, 78)(119,120)],
["ConstructDirectProduct",[["Cyclic",3],["Isoclinic(2.A9.2)"]]]);
ALF("3xIsoclinic(2.A9.2)","A9.2",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,
13,13,14,15,16,16,17,18,19,20,21,22,23,24,25,25,26,26,27,28,29,29,30,30,1,
1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,13,13,14,15,16,16,17,18,19,20,21,22,
23,24,25,25,26,26,27,28,29,29,30,30,1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,
12,13,13,14,15,16,16,17,18,19,20,21,22,23,24,25,25,26,26,27,28,29,29,30,
30]);
ALF("3xIsoclinic(2.A9.2)","3xS9",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,
13,13,14,15,16,16,17,18,19,20,21,22,23,24,25,25,26,26,27,28,29,29,30,30,
31,31,32,33,34,34,35,35,36,36,37,38,39,39,40,41,42,42,43,43,44,45,46,46,
47,48,49,50,51,52,53,54,55,55,56,56,57,58,59,59,60,60,61,61,62,63,64,64,
65,65,66,66,67,68,69,69,70,71,72,72,73,73,74,75,76,76,77,78,79,80,81,82,
83,84,85,85,86,86,87,88,89,89,90,90]);
ALF("3xIsoclinic(2.A9.2)","6.O7(3)",[1,4,10,13,18,21,26,27,30,31,46,43,49,
52,71,84,87,90,110,111,114,137,158,161,7,13,34,46,58,74,78,83,79,80,96,99,
117,127,155,152,178,175,5,2,11,14,22,19,26,27,30,31,47,44,53,50,72,84,91,
88,110,111,115,138,162,159,8,14,35,47,59,75,78,83,79,80,100,97,118,128,
153,156,176,179,3,6,12,15,20,23,26,27,30,31,48,45,51,54,73,84,89,92,110,
111,116,139,160,163,9,15,36,48,60,76,78,83,79,80,98,101,119,129,157,154,
180,177],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("6.O7(3)M11",
[
"11th maximal subgroup of 6.O7(3),\n",
"differs from 6.O7(3)M10 = 3xIsoclinic(2.A9.2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3xIsoclinic(2.A9.2)"]]);
ALF("6.O7(3)M11","3.O7(3)M11",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,13,
13,14,15,16,16,17,18,19,20,21,22,23,24,25,25,26,26,27,28,29,29,30,30,31,
31,32,33,34,34,35,35,36,36,37,38,39,39,40,41,42,42,43,43,44,45,46,46,47,
48,49,50,51,52,53,54,55,55,56,56,57,58,59,59,60,60,61,61,62,63,64,64,65,
65,66,66,67,68,69,69,70,71,72,72,73,73,74,75,76,76,77,78,79,80,81,82,83,
84,85,85,86,86,87,88,89,89,90,90]);
ALF("6.O7(3)M11","2.O7(3)M11",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42]);
ALF("6.O7(3)M11","O7(3)M11",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,13,
13,14,15,16,16,17,18,19,20,21,22,23,24,25,25,26,26,27,28,29,29,30,30,1,1,
2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,13,13,14,15,16,16,17,18,19,20,21,22,
23,24,25,25,26,26,27,28,29,29,30,30,1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,
12,13,13,14,15,16,16,17,18,19,20,21,22,23,24,25,25,26,26,27,28,29,29,30,
30]);
ALF("6.O7(3)M11","6.O7(3)",[1,4,10,13,18,21,28,29,30,31,46,43,49,52,71,83,
87,90,112,113,114,137,158,161,7,13,34,46,58,74,78,84,81,82,96,99,117,127,
152,155,175,178,3,6,12,15,20,23,28,29,30,31,48,45,51,54,73,83,89,92,112,
113,116,139,160,163,9,15,36,48,60,76,78,84,81,82,98,101,119,129,154,157,
177,180,5,2,11,14,22,19,28,29,30,31,47,44,53,50,72,83,91,88,112,113,115,
138,162,159,8,14,35,47,59,75,78,84,81,82,100,97,118,128,156,153,179,176],[
"fusion map is unique up to table automorphisms,\n",
"equals the map from 6.O7(3)M10, mapped under an outer autom. of order 2"
]);

MOT("3x2.(2^2xU4(2)).2",
0,
0,
0,
0,
[( 54, 55)(137,138)(220,221),
( 42, 43)( 47, 48)( 51, 52)( 60, 61)( 82, 83)( 84,167)( 85,168)( 86,169)
( 87,170)( 88,171)( 89,172)( 90,173)( 91,174)( 92,175)( 93,176)( 94,177)
( 95,178)( 96,179)( 97,180)( 98,181)( 99,182)(100,183)(101,184)(102,185)
(103,186)(104,187)(105,188)(106,189)(107,190)(108,191)(109,192)(110,193)
(111,194)(112,195)(113,196)(114,197)(115,198)(116,199)(117,200)(118,201)
(119,202)(120,203)(121,204)(122,205)(123,206)(124,207)(125,209)(126,208)
(127,210)(128,211)(129,212)(130,214)(131,213)(132,215)(133,216)(134,218)
(135,217)(136,219)(137,220)(138,221)(139,222)(140,223)(141,224)(142,225)
(143,227)(144,226)(145,228)(146,229)(147,230)(148,231)(149,232)(150,233)
(151,234)(152,235)(153,236)(154,237)(155,238)(156,239)(157,240)(158,241)
(159,242)(160,243)(161,244)(162,245)(163,246)(164,247)(165,249)(166,248)
,
( 18, 19)( 21, 22)( 74, 75)(101,102)(104,105)(157,158)(184,185)(187,188)
(240,241)
,
( 84,167)( 85,168)( 86,169)( 87,170)( 88,171)( 89,172)( 90,173)( 91,174)
( 92,175)( 93,176)( 94,177)( 95,178)( 96,179)( 97,180)( 98,181)( 99,182)
(100,183)(101,184)(102,185)(103,186)(104,187)(105,188)(106,189)(107,190)
(108,191)(109,192)(110,193)(111,194)(112,195)(113,196)(114,197)(115,198)
(116,199)(117,200)(118,201)(119,202)(120,203)(121,204)(122,205)(123,206)
(124,207)(125,208)(126,209)(127,210)(128,211)(129,212)(130,213)(131,214)
(132,215)(133,216)(134,217)(135,218)(136,219)(137,220)(138,221)(139,222)
(140,223)(141,224)(142,225)(143,226)(144,227)(145,228)(146,229)(147,230)
(148,231)(149,232)(150,233)(151,234)(152,235)(153,236)(154,237)(155,238)
(156,239)(157,240)(158,241)(159,242)(160,243)(161,244)(162,245)(163,246)
(164,247)(165,248)(166,249)
],
["ConstructDirectProduct",[["Cyclic",3],["2.(2^2xU4(2)).2"]]]);
ALF("3x2.(2^2xU4(2)).2","(2^2xU4(2)):2",[1,1,2,3,4,5,6,7,8,8,9,10,11,12,
13,14,15,16,16,17,18,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,32,33,
34,34,35,36,37,38,38,39,40,41,42,43,44,45,46,47,47,48,49,50,50,51,52,53,
53,54,55,55,56,57,58,59,60,61,62,63,63,64,65,66,67,68,68,69,70,1,1,2,3,4,
5,6,7,8,8,9,10,11,12,13,14,15,16,16,17,18,18,19,20,21,22,23,24,25,26,27,
28,29,30,31,32,32,33,34,34,35,36,37,38,38,39,40,41,42,43,44,45,46,47,47,
48,49,50,50,51,52,53,53,54,55,55,56,57,58,59,60,61,62,63,63,64,65,66,67,
68,68,69,70,1,1,2,3,4,5,6,7,8,8,9,10,11,12,13,14,15,16,16,17,18,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,32,33,34,34,35,36,37,38,38,39,40,41,
42,43,44,45,46,47,47,48,49,50,50,51,52,53,53,54,55,55,56,57,58,59,60,61,
62,63,63,64,65,66,67,68,68,69,70]);
ALF("3x2.(2^2xU4(2)).2","3x(2^2xU4(2)):2",[1,1,2,3,4,5,6,7,8,8,9,10,11,12,
13,14,15,16,16,17,18,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,32,33,
34,34,35,36,37,38,38,39,40,41,42,43,44,45,46,47,47,48,49,50,50,51,52,53,
53,54,55,55,56,57,58,59,60,61,62,63,63,64,65,66,67,68,68,69,70,71,71,72,
73,74,75,76,77,78,78,79,80,81,82,83,84,85,86,86,87,88,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,102,103,104,104,105,106,107,108,108,109,110,
111,112,113,114,115,116,117,117,118,119,120,120,121,122,123,123,124,125,
125,126,127,128,129,130,131,132,133,133,134,135,136,137,138,138,139,140,
141,141,142,143,144,145,146,147,148,148,149,150,151,152,153,154,155,156,
156,157,158,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,
172,173,174,174,175,176,177,178,178,179,180,181,182,183,184,185,186,187,
187,188,189,190,190,191,192,193,193,194,195,195,196,197,198,199,200,201,
202,203,203,204,205,206,207,208,208,209,210]);
ALF("3x2.(2^2xU4(2)).2","6.O7(3)",[1,4,10,7,77,65,66,66,24,25,61,13,10,13,
10,13,7,120,121,124,40,37,34,43,46,34,46,46,34,10,124,66,127,71,58,21,18,
71,69,70,55,63,64,16,17,62,57,56,77,61,67,68,114,175,178,117,114,49,52,
131,132,122,123,130,40,37,43,43,46,13,71,74,58,99,96,93,74,137,172,105,
102,164,167,5,2,11,8,77,65,67,67,24,25,61,14,11,14,11,14,8,120,121,125,38,
41,35,44,47,35,47,47,35,11,125,67,128,72,59,19,22,72,69,70,56,64,62,16,17,
63,55,57,77,61,68,66,115,179,176,118,115,53,50,132,130,122,123,131,38,41,
44,44,47,14,72,75,59,97,100,94,75,138,173,103,106,165,168,3,6,12,9,77,65,
68,68,24,25,61,15,12,15,12,15,9,120,121,126,42,39,36,45,48,36,48,48,36,12,
126,68,129,73,60,23,20,73,69,70,57,62,63,16,17,64,56,55,77,61,66,67,116,
177,180,119,116,51,54,130,131,122,123,132,42,39,45,45,48,15,73,76,60,101,
98,95,76,139,174,107,104,166,169],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2^(1+6)_+:3A7",
0,
[967680,967680,967680,967680,967680,967680,69120,69120,69120,23040,23040,23040
,13824,13824,13824,1152,1152,1152,384,384,384,2304,2304,2304,2304,2304,2304,
576,576,576,384,384,384,192,192,192,1152,1152,576,144,144,288,288,288,72,72,36
,36,36,48,48,48,48,48,48,96,96,96,96,96,96,48,48,48,120,120,120,120,120,120,60
,60,60,60,60,60,60,60,60,144,144,144,288,288,288,288,288,288,72,72,72,42,42,42
,42,42,42,42,42,42,42,42,42],
[,[1,3,5,1,3,5,2,4,6,4,6,2,1,3,5,2,4,6,1,3,5,13,15,14,13,15,14,11,10,12,13,15,
14,11,10,12,38,38,38,37,38,37,37,37,45,45,45,46,45,21,20,19,16,18,17,32,31,33,
32,31,33,23,25,27,70,66,68,70,66,68,67,69,65,67,69,65,67,69,65,37,37,37,39,39,
39,39,39,39,44,43,42,94,96,92,94,96,92,101,103,99,101,103,99],[1,4,1,4,1,4,8,8
,8,10,10,10,13,13,13,17,17,17,19,19,19,22,25,22,25,22,25,29,29,29,31,31,31,35,
35,35,4,1,13,8,13,10,10,10,1,4,13,8,13,52,52,52,55,55,55,60,57,60,57,60,57,63,
63,63,69,66,69,66,69,66,72,72,72,78,78,78,75,75,75,17,17,17,25,22,25,22,25,22,
29,29,29,101,98,101,98,101,98,93,96,93,96,93,96],,[1,6,5,4,3,2,9,8,7,10,12,11,
13,15,14,18,17,16,19,21,20,22,27,26,25,24,23,30,29,28,31,33,32,36,35,34,37,38,
39,40,41,44,43,42,45,46,47,48,49,51,50,52,54,53,55,58,57,56,61,60,59,64,63,62,
2,1,6,5,4,3,11,10,12,9,8,7,9,8,7,82,81,80,85,84,83,88,87,86,91,90,89,99,98,103
,102,101,100,93,92,97,96,95,94],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18
,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44
,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70
,71,72,73,77,78,79,74,75,76,80,81,82,83,84,85,86,87,88,89,90,91,3,4,5,6,1,2,4,
5,6,1,2,3]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[6,6,6,6,6,6,6,6,6,6,6,6,
6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[7,7,7,7,7,7,-5,-5,-5,3,3,
3,-1,-1,-1,3,3,3,-1,-1,-1,3,3,3,3,3,3,-3,-3,-3,-1,-1,-1,1,1,1,4,4,-4,-2,2,0,0,
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,-3*E(3),5,5*E(3)^2,5*E(3),5,5*E(3)^2,5*E(3),3*E(3),3,3*E(3)^2,1,E(3)^2,E(3),
-E(3),-1,-E(3)^2,0,0,0,0,0,-4*E(3),-4,-4*E(3)^2,0,0,0,0,0,-E(3)^2,-E(3),-1,
E(3)^2,E(3),1,-E(3),-1,-E(3)^2,-E(3),-1,-E(3)^2,E(3),1,E(3)^2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-2*E(3),-2,-2*E(3)^2,2*E(3),2,2*E(3)^2,2*E(3),2,2*E(3)^2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[82,2]],[105,105*E(3)^2,105*E(3),105,105*E(3)^2,105*E(3),45*E(3),45,
45*E(3)^2,5,5*E(3)^2,5*E(3),-15,-15*E(3)^2,-15*E(3),5*E(3),5,5*E(3)^2,1,E(3)^2
,E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),3*E(3),3,3*E(3)^2,-3,-3*E(3)^2,-3*E(3),-E(3)
,-1,-E(3)^2,0,0,0,0,0,-4*E(3),-4,-4*E(3)^2,0,0,0,0,0,E(3)^2,E(3),1,-E(3)^2,
-E(3),-1,E(3),1,E(3)^2,E(3),1,E(3)^2,-E(3),-1,-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,2*E(3),2,2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[84,2]],[126,126*E(3)^2,126*E(3),126,126*E(3)^2,126*E(3),54*E(3),54,
54*E(3)^2,6,6*E(3)^2,6*E(3),-18,-18*E(3)^2,-18*E(3),-6*E(3),-6,-6*E(3)^2,2,
2*E(3)^2,2*E(3),-6,-6*E(3)^2,-6*E(3),-6,-6*E(3)^2,-6*E(3),-6*E(3),-6,-6*E(3)^2
,2,2*E(3)^2,2*E(3),2*E(3),2,2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,-E(3),-1,-E(3)^2,
-E(3),-1,-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[86,2]],[210,210*E(3)^2,210*E(3),210,210*E(3)^2,210*E(3),-30*E(3),-30
,-30*E(3)^2,-30,-30*E(3)^2,-30*E(3),18,18*E(3)^2,18*E(3),-2*E(3),-2,-2*E(3)^2,
-2,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),2*E(3),2,
2*E(3)^2,-2,-2*E(3)^2,-2*E(3),2*E(3),2,2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(3),-2,-2*E(3)^2,
-2*E(3),-2,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,2*E(3),2,2*E(3)^2,0,0,0,0,0,0,0,0,0,
0,0,0],
[GALOIS,[88,2]],[48,-48*E(3)^2,48*E(3),-48,48*E(3)^2,-48*E(3),0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,-8,8*E(3)^2,-8*E(3),8,-8*E(3)^2,8*E(3),0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3),-2,2*E(3)^2,-2*E(3),2
,-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,-4*E(3),4,-4*E(3)^2,4*E(3),-4,4*E(3)^2,0,0,
0,-E(3),1,-E(3)^2,E(3),-1,E(3)^2,1,-E(3)^2,E(3),-1,E(3)^2,-E(3)],
[GALOIS,[90,2]],[120,-120*E(3)^2,120*E(3),-120,120*E(3)^2,-120*E(3),0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,4,-4*E(3)^2,4*E(3),-4,4*E(3)^2,-4*E(3),0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4*E(3),4,-4*E(3)^2,4*E(3),-4,
4*E(3)^2,0,0,0,E(3),-1,E(3)^2,-E(3),1,-E(3)^2,-1,E(3)^2,-E(3),1,-E(3)^2,E(3)],
[GALOIS,[92,2]],[120,-120*E(3)^2,120*E(3),-120,120*E(3)^2,-120*E(3),0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,-12,12*E(3)^2,-12*E(3),12,-12*E(3)^2,12*E(3),0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(3),2,-2*E(3)^2,2*E(3),-2,
2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(3),-1,
E(3)^2,-E(3),1,-E(3)^2,-1,E(3)^2,-E(3),1,-E(3)^2,E(3)],
[GALOIS,[94,2]],[168,-168*E(3)^2,168*E(3),-168,168*E(3)^2,-168*E(3),0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,-4,4*E(3)^2,-4*E(3),4,-4*E(3)^2,4*E(3),0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,0
,0,0,2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,4*E(3),-4,
4*E(3)^2,-4*E(3),4,-4*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[96,2]],[168,-168*E(3)^2,168*E(3),-168,168*E(3)^2,-168*E(3),0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,12,-12*E(3)^2,12*E(3),-12,12*E(3)^2,-12*E(3),0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(3),2,-2*E(3)^2,2*E(3),-2,
2*E(3)^2,0,0,0,2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[98,2]],[192,-192*E(3)^2,192*E(3),-192,192*E(3)^2,-192*E(3),0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(3),2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(21)^10+E(21)^13+E(21)^19,-E(7)-E(7)^2-E(7)^4
,E(21)^5+E(21)^17+E(21)^20,-E(21)^10-E(21)^13-E(21)^19,E(7)+E(7)^2+E(7)^4,
-E(21)^5-E(21)^17-E(21)^20,-E(7)^3-E(7)^5-E(7)^6,E(21)^2+E(21)^8+E(21)^11,
-E(21)-E(21)^4-E(21)^16,E(7)^3+E(7)^5+E(7)^6,-E(21)^2-E(21)^8-E(21)^11,
E(21)+E(21)^4+E(21)^16],
[GALOIS,[100,2]],
[GALOIS,[100,10]],
[GALOIS,[100,5]]],
[( 92,103)( 93, 98)( 94, 99)( 95,100)( 96,101)( 97,102),
( 74, 77)( 75, 78)( 76, 79),(47,49),
(  2,  6)(  3,  5)(  7,  9)( 11, 12)( 14, 15)( 16, 18)( 20, 21)( 23, 27)
( 24, 26)( 28, 30)( 32, 33)( 34, 36)( 42, 44)( 50, 51)( 53, 54)( 56, 58)
( 59, 61)( 62, 64)( 65, 67)( 68, 70)( 71, 73)( 74, 76)( 77, 79)( 80, 82)
( 83, 85)( 86, 88)( 89, 91)( 92, 94)( 95, 97)( 99,103)(100,102)
]);
ALF("2^(1+6)_+:3A7","2^6:A7",[1,1,1,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,
7,7,7,7,8,8,8,9,9,9,10,10,10,11,11,12,13,14,15,15,15,16,16,17,18,19,20,20,
20,21,21,21,22,22,22,22,22,22,23,23,23,24,24,24,24,24,24,25,25,25,26,26,
26,27,27,27,28,28,28,29,29,29,29,29,29,30,30,30,31,31,31,31,31,31,32,32,
32,32,32,32]);
ALF("2^(1+6)_+:3A7","2^(1+6)_+:A7",[1,2,1,2,1,2,5,5,5,3,3,3,4,4,4,21,21,21,17,
17,17,19,20,19,20,19,20,16,16,16,15,15,15,18,18,18,30,31,28,26,29,27,27,
27,38,39,37,40,41,14,14,14,11,11,11,12,13,12,13,12,13,10,10,10,33,34,33,
34,33,34,36,36,36,32,32,32,35,35,35,25,25,25,23,24,23,24,23,24,22,22,22,8,
9,8,9,8,9,6,7,6,7,6,7]);
ALF("2^(1+6)_+:3A7","2^6:3A7",[1,2,3,1,2,3,10,11,12,7,8,9,4,5,6,28,29,30,
13,14,15,16,17,18,16,17,18,25,26,27,22,23,24,19,20,21,75,75,76,70,74,71,
72,73,77,77,78,80,79,40,41,42,37,38,39,34,35,36,34,35,36,31,32,33,58,59,
60,58,59,60,55,56,57,49,50,51,52,53,54,64,65,66,67,68,69,67,68,69,61,62,
63,46,47,48,46,47,48,43,44,45,43,44,45]);
ALF("2^(1+6)_+:3A7","6.O7(3)",[1,2,3,4,5,6,9,7,8,10,11,12,13,14,15,12,10,
11,13,14,15,40,41,42,37,38,39,36,34,35,43,44,45,48,46,47,25,24,65,61,77,
68,66,67,30,31,83,78,84,44,45,43,47,48,46,101,96,97,98,99,100,95,93,94,54,
49,50,51,52,53,116,114,115,119,117,118,119,117,118,68,66,67,120,121,120,
121,120,121,126,124,125,89,90,91,92,87,88,90,91,92,87,88,89],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3x2.(S6xS4)",
0,
0,
0,
0,
[
( 68,135)( 69,136)( 70,137)( 71,138)( 72,139)( 73,140)( 74,141)( 75,142)
( 76,143)( 77,144)( 78,145)( 79,146)( 80,147)( 81,148)( 82,149)( 83,150)
( 84,151)( 85,152)( 86,153)( 87,154)( 88,155)( 89,156)( 90,157)( 91,158)
( 92,159)( 93,160)( 94,161)( 95,162)( 96,163)( 97,164)( 98,165)( 99,166)
(100,167)(101,168)(102,169)(103,170)(104,171)(105,172)(106,173)(107,174)
(108,175)(109,176)(110,177)(111,178)(112,179)(113,180)(114,181)(115,182)
(116,183)(117,184)(118,185)(119,186)(120,187)(121,188)(122,189)(123,190)
(124,191)(125,192)(126,193)(127,194)(128,195)(129,196)(130,197)(131,198)
(132,199)(133,200)(134,201)
,( 66, 67)(133,134)(200,201),( 54, 55)(121,122)(188,189),
( 43, 44)(110,111)(177,178),( 20, 21)( 87, 88)(154,155)],
["ConstructDirectProduct",[["Cyclic",3],["2.(S6xS4)"]]]);
ALF("3x2.(S6xS4)","S6xS4",[1,1,2,3,3,4,5,33,31,32,34,35,15,14,12,11,11,13,
13,48,48,46,47,49,50,16,16,17,18,18,19,20,8,7,6,10,9,39,40,37,36,38,25,25,
24,23,22,21,45,44,42,41,43,30,30,29,28,28,27,26,26,54,55,51,52,53,53,1,1,
2,3,3,4,5,33,31,32,34,35,15,14,12,11,11,13,13,48,48,46,47,49,50,16,16,17,
18,18,19,20,8,7,6,10,9,39,40,37,36,38,25,25,24,23,22,21,45,44,42,41,43,30,
30,29,28,28,27,26,26,54,55,51,52,53,53,1,1,2,3,3,4,5,33,31,32,34,35,15,14,
12,11,11,13,13,48,48,46,47,49,50,16,16,17,18,18,19,20,8,7,6,10,9,39,40,37,
36,38,25,25,24,23,22,21,45,44,42,41,43,30,30,29,28,28,27,26,26,54,55,51,
52,53,53]);
ALF("3x2.(S6xS4)","3xS6xS4",[1,1,2,3,3,4,5,33,31,32,34,35,15,14,12,11,11,
13,13,48,48,46,47,49,50,16,16,17,18,18,19,20,8,7,6,10,9,39,40,37,36,38,25,
25,24,23,22,21,45,44,42,41,43,30,30,29,28,28,27,26,26,54,55,51,52,53,53,
56,56,57,58,58,59,60,88,86,87,89,90,70,69,67,66,66,68,68,103,103,101,102,
104,105,71,71,72,73,73,74,75,63,62,61,65,64,94,95,92,91,93,80,80,79,78,77,
76,100,99,97,96,98,85,85,84,83,83,82,81,81,109,110,106,107,108,108,111,
111,112,113,113,114,115,143,141,142,144,145,125,124,122,121,121,123,123,
158,158,156,157,159,160,126,126,127,128,128,129,130,118,117,116,120,119,
149,150,147,146,148,135,135,134,133,132,131,155,154,152,151,153,140,140,
139,138,138,137,136,136,164,165,161,162,163,163]);
ALF("3x2.(S6xS4)","6.O7(3)",[1,4,10,18,21,7,34,74,13,10,13,34,124,61,66,
24,25,33,32,85,86,65,66,77,124,18,21,71,30,31,58,127,71,13,10,46,13,10,46,
13,7,58,37,40,46,137,34,46,43,46,46,34,127,175,178,117,158,161,114,49,52,
71,137,58,74,78,78,5,2,11,22,19,8,35,75,14,11,14,35,125,61,67,24,25,33,32,
85,86,65,67,77,125,22,19,72,30,31,59,128,72,14,11,47,14,11,47,14,8,59,41,
38,47,138,35,47,44,47,47,35,128,179,176,118,162,159,115,53,50,72,138,59,
75,78,78,3,6,12,20,23,9,36,76,15,12,15,36,126,61,68,24,25,33,32,85,86,65,
68,77,126,20,23,73,30,31,60,129,73,15,12,48,15,12,48,15,9,60,39,42,48,139,
36,48,45,48,48,36,129,177,180,119,160,163,116,51,54,73,139,60,76,78,78],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("6.(A4x2(A4xA4).2).2",
0,
[82944,82944,82944,82944,82944,82944,41472,41472,41472,768,768,768,1152,1152,
1152,6912,6912,6912,6912,6912,6912,13824,13824,13824,13824,13824,13824,2304,
2304,2304,216,216,108,108,108,108,108,72,72,432,432,432,432,144,144,144,1728,
1728,1728,1728,288,288,864,864,864,864,864,864,2592,2592,2592,2592,2592,2592,
1296,1296,1296,432,432,432,432,432,432,72,72,432,432,432,432,288,288,288,3456,
3456,1728,288,288,216,216,108,432,432,432,432,432,432,864,864,432,384,384,384,
384,384,384,192,192,192,96,96,96,96,96,96,96,96,96,48,48,48,192,192,192,192,
192,192,96,96,96,576,576,576,576,576,576,576,576,576,576,576,576,96,96,96,96,
96,96,72,72,72,72,72,72,72,72,72,72,72,72,36,36,1152,1152,1152,1152,1152,1152,
192,192,192,576,576,576,3456,3456,3456,3456,3456,3456,144,144,144,144,144,144,
144,144,72,72,72,144,144,36,36],
[,[1,3,5,1,3,5,1,3,5,1,3,5,7,9,8,7,9,8,7,9,8,4,6,2,4,6,2,4,6,2,31,31,31,34,34,
34,34,40,40,42,42,42,42,47,47,47,49,49,49,49,48,48,50,50,50,50,50,50,62,64,60,
62,64,60,62,64,60,59,61,63,59,61,63,76,76,79,79,79,79,83,83,83,84,84,84,85,85,
89,89,89,97,97,97,97,97,97,98,98,98,10,12,11,10,12,11,10,12,11,13,15,14,13,15,
14,1,3,5,16,18,20,28,30,29,28,30,29,22,24,23,1,3,5,4,6,2,22,24,23,22,24,23,10,
12,11,28,30,29,59,61,63,62,64,60,71,73,72,71,73,72,31,32,1,3,5,4,6,2,28,30,29,
28,30,29,4,6,2,1,3,5,97,97,97,98,98,98,97,98,82,81,80,83,84,89,88],[1,4,1,4,1,
4,7,7,7,10,10,10,13,13,13,16,19,16,19,16,19,22,22,22,25,25,25,28,28,28,1,4,7,1
,4,7,7,16,19,7,7,1,4,13,13,13,7,7,1,4,19,16,25,25,25,22,22,22,4,1,4,1,4,1,7,7,
7,25,25,25,22,22,22,19,16,7,7,4,1,28,28,28,4,1,7,19,16,4,1,7,22,22,22,25,25,25
,4,1,7,100,103,100,103,100,103,106,106,106,109,112,109,112,109,112,115,115,115
,118,118,118,121,121,121,124,124,124,127,127,127,130,130,130,133,133,133,136,
136,136,139,139,139,142,142,142,145,145,145,133,133,133,130,130,130,136,136,
136,139,139,139,177,174,162,162,162,165,165,165,168,168,168,171,171,171,174,
174,174,177,177,177,165,165,165,162,162,162,174,177,171,171,171,174,177,177,
174]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[(100,103)(101,104)(102,105)(109,112)(110,113)(111,114),
( 31, 89)( 32, 88)( 33, 90)( 36, 37)( 38, 75)( 39, 74)( 40, 76)( 41, 77)
( 42, 79)( 43, 78)(160,193)(161,194)
,
(  2,  6)(  3,  5)(  8,  9)( 11, 12)( 14, 15)( 17, 21)( 18, 20)( 23, 24)
( 26, 27)( 29, 30)( 44, 45)( 53, 54)( 56, 57)( 60, 64)( 61, 63)( 66, 67)
( 69, 70)( 72, 73)( 80, 81)( 92, 93)( 95, 96)(101,105)(102,104)(107,108)
(110,114)(111,113)(116,117)(119,120)(122,123)(125,126)(128,129)(131,132)
(134,135)(137,138)(140,141)(143,144)(146,147)(149,150)(152,153)(155,156)
(158,159)(163,164)(166,167)(169,170)(172,173)(175,176)(178,179)(180,181)
(183,184)(189,190)
]);
ALF("6.(A4x2(A4xA4).2).2","(A4x2(A4xA4).2).2",[1,1,1,1,1,1,2,2,2,3,3,3,4,4,4,
5,5,5,5,5,5,6,6,6,7,7,7,8,8,8,9,9,10,11,11,12,12,13,13,14,14,15,15,16,16,16,
17,17,18,18,19,19,20,20,20,21,21,21,22,22,22,22,22,22,23,23,23,24,24,24,
25,25,25,26,26,27,27,28,28,29,29,29,30,30,31,32,32,33,33,34,35,35,35,36,
36,36,37,37,38,39,39,39,39,39,39,40,40,40,41,41,41,41,41,41,42,42,42,43,
43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,49,49,50,50,50,51,
51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,58,59,59,59,60,60,
60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65,66,66,66,67,68,69,69,69,
70,71,72,73]);
ALF("6.(A4x2(A4xA4).2).2","2.(A4x2(A4xA4).2).2",[1,2,1,2,1,2,3,3,3,4,4,4,5,5,
5,6,7,6,7,6,7,8,8,8,9,9,9,10,10,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,24,24,25,26,27,28,29,30,31,31,31,32,32,32,33,34,33,34,33,34,35,35,35,
36,36,36,37,37,37,38,39,40,41,42,43,44,44,44,45,46,47,48,49,50,51,52,53,
53,53,54,54,54,55,56,57,58,59,58,59,58,59,60,60,60,61,62,61,62,61,62,63,
63,63,64,64,64,65,65,65,66,66,66,67,67,67,68,68,68,69,69,69,70,70,70,71,
71,71,72,72,72,73,73,73,74,74,74,75,75,75,76,76,76,77,77,77,78,79,80,80,
80,81,81,81,82,82,82,83,83,83,84,84,84,85,85,85,86,86,86,87,87,87,88,89,
90,90,90,91,92,93,94]);
ALF("6.(A4x2(A4xA4).2).2","3.(A4x2(A4xA4).2).2",[1,2,3,1,2,3,4,5,6,22,23,24,
16,17,18,13,14,15,13,14,15,10,11,12,7,8,9,19,20,21,33,33,34,85,85,86,86,
89,89,88,88,87,87,82,83,84,74,74,73,73,81,81,75,76,77,78,79,80,61,62,63,
61,62,63,64,65,66,67,68,69,70,71,72,92,92,91,91,90,90,38,39,40,35,35,36,
37,37,41,41,42,30,31,32,27,28,29,25,25,26,161,162,163,161,162,163,158,159,
160,149,150,151,149,150,151,140,141,142,146,147,148,152,153,154,155,156,
157,143,144,145,43,44,45,46,47,48,49,50,51,52,53,54,58,59,60,55,56,57,96,
97,98,93,94,95,99,100,101,102,103,104,139,138,114,115,116,111,112,113,120,
121,122,117,118,119,105,106,107,108,109,110,125,126,127,128,129,130,123,
124,133,134,135,131,132,137,136]);
ALF("6.(A4x2(A4xA4).2).2","6.O7(3)",[1,2,3,4,5,6,13,14,15,13,14,15,43,44,
45,37,38,39,40,41,42,10,11,12,7,8,9,10,11,12,30,31,83,32,33,86,85,135,136,
81,82,28,29,131,132,130,69,70,16,17,123,122,56,57,55,63,64,62,21,22,23,18,
19,20,74,75,76,58,59,60,71,72,73,134,133,79,80,27,26,67,68,66,25,24,65,
121,120,31,30,84,66,67,68,61,61,61,25,24,77,37,38,39,40,41,42,43,44,45,96,
97,98,99,100,101,13,14,15,93,94,95,46,47,48,34,35,36,46,47,48,13,14,15,10,
11,12,46,47,48,34,35,36,43,44,45,46,47,48,71,72,73,74,75,76,137,138,139,
127,128,129,84,78,13,14,15,10,11,12,46,47,48,34,35,36,7,8,9,13,14,15,67,
68,66,77,77,77,61,65,124,125,126,61,77,83,78],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3^6:(L4(3)x2)",
[
"constructed using Dixon's Algorithm plus character theoretic methods"
],
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10368,5184,944784,472392,472392,472392,472392,13122,314928,52488,39366,26244,
5832,314928,52488,39366,26244,5832,1458,729,729,729,729,2880,1728,864,864,864,
864,576,144,144,360,90,90,1296,648,216,1296,648,216,1296,648,648,648,648,648,
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108,26,26,26,26,40,40,12130560,51840,12960,12960,186624,7776,7776,5832,11664,
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-32,16,-32,16,-180,-180,90,90,90,0,72,0,18,-18,0,-72,-36,36,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[18720,
-720,-720,1224,-80,28,-8,-8,0,0,0,0,-72,-72,-72,-72,-72,9,36,36,36,36,-18,-18,
-18,-18,-18,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,-2,-2,-2,1,0,0,0,0,0,0,0,0
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,0,80,-28,8,8,0,0,0,0,0,0,0,0,0,0,0,0,8,-1,-4,-4,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,
-4,-4,2,2,2,-1,0,0,0,0,0,0,0],[18720,-720,-720,1224,-80,28,-8,-8,0,0,0,0,-72,
-72,-72,-72,-72,9,-18,-18,-18,-18,9,36,36,36,36,-18,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-2,-2,1,4,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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-1,2,2,-1,-4,-4,2,0,0,0,0,0,0,0,0,0,0,2,2,-1,-4,-4,2,0,0,0,0,0,0,0],
[TENSOR,[135,30]],
[TENSOR,[136,30]],[18954,-729,1458,-729,-90,-9,18,-9,18,18,-9,-9,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,3,-6,3,-4,2,-1,4,1,-2,0,0,0,0,0,0,0,0,0,0
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-2,1,0,0,4,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[139,30]],[18954,1458,-729,-729,-90,-9,-9,18,18,-9,18,-9,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,3,3,-6,-4,-1,2,4,-2,1,0,0,0,0,0,0,0,0,0,0
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,-2,0,0,4,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[141,30]],[21060,-810,1620,-810,-180,-18,36,-18,-12,-12,6,6,162,-81,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[21060,1620,-810,-810,-180,-18,-18,36
,-12,6,-12,6,162,162,-81,-81,-81,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2,-2,-2,
4,8,2,-4,0,0,0,0,0,0,0,0,0,-6,3,3,3,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
1,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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[( 15, 16)( 32, 33)( 36, 37)( 53, 54)( 76, 78)(123,124),( 84, 85)(143,144),
(  2,  3)(  7,  8)( 10, 11)( 14, 17)( 19, 24)( 20, 25)( 21, 26)( 22, 27)
( 23, 28)( 30, 31)( 38, 39)( 41, 42)( 44, 45)( 46, 49)( 47, 50)( 48, 51)
( 55, 56)( 57, 61)( 58, 62)( 59, 63)( 60, 64)( 66, 69)( 67, 70)( 68, 71)
( 73, 74)( 77, 79)( 88, 89)( 91, 92)( 95, 96)(100,101)(104,105)(108,111)
(109,112)(110,113)(116,119)(117,120)(118,121)(125,126)(127,128)(130,131)
(132,135)(133,136)(134,137)
,( 80, 83, 81, 82)(139,142,140,141)]);
ALF("3^6:(L4(3)x2)","O8+(3).2_1",[1,7,10,6,2,23,30,27,5,34,31,26,6,11,9,8,
12,14,7,13,11,14,46,10,13,12,14,49,14,50,51,47,48,16,15,58,59,63,60,16,70,
67,20,76,79,27,35,80,30,35,83,26,33,32,39,38,31,42,40,38,34,42,41,39,44,
49,50,53,46,51,52,54,67,70,57,61,66,62,65,71,71,72,72,84,84,87,88,95,94,
87,96,97,93,93,96,97,100,89,112,114,113,92,91,118,119,117,111,94,99,101,
95,98,101,93,100,96,100,122,97,100,123,102,125,126,130,129,123,122,108,
137,138,113,116,139,114,116,140,120,131,131,132,132,124,124],[
"fusion map is unique up to table automorphisms"
]);
ALN("3^6:(L4(3)x2)",["O8+(3).2_1M4"]);
ALF("3^6:(L4(3)x2)","L4(3)x2",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,
5,5,6,6,6,6,6,7,7,7,7,7,8,9,9,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,
14,14,14,14,14,15,15,15,15,16,16,16,16,17,18,18,18,19,19,19,20,21,22,23,
23,23,23,23,24,25,26,27,28,29,30,31,31,31,32,32,32,32,33,34,35,36,37,37,
37,37,38,39,39,39,39,40,41,41,41,42,42,42,43,43,44,44,44,45,45,45,46,46,
46,46,46,47,48,49,49,49,50,50,50,51,51,51,52,53,54,55,56,57,58]);

MOT("L4(3)x2",
0,
0,
0,
0,
[(28,29)(57,58),(24,26,25,27)(53,55,54,56),
( 5, 6)(12,13)(15,16)(18,19)(21,22)(34,35)(41,42)(44,45)(47,48)(50,51)],
["ConstructDirectProduct",[["Cyclic",2],["L4(3)"]]]);
ALF("L4(3)x2","3^6:(L4(3)x2)",[1,5,9,13,19,24,29,34,35,40,43,46,49,52,57,
61,65,66,69,72,73,74,75,80,81,82,83,84,85,86,87,90,94,95,96,97,98,102,103,
107,108,111,114,116,119,122,127,128,129,132,135,138,139,140,141,142,143,
144],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^6:2U4(3).2_1",
[
"origin: Dixon's Algorithm,\n",
"stabilizer of an isotropic point in O8-(3)"
],
[9523422720,42515280,37791360,37791360,13063680,41472,10368,10368,373248,15552
,15552,11664,1889568,472392,472392,26244,23328,314928,52488,39366,26244,5832,
3888,314928,52488,39366,26244,5832,3888,2916,729,729,324,3456,864,864,384,288,
144,144,72,180,90,90,90,90,20,2592,648,648,2592,324,1296,324,324,1296,648,216,
1296,324,324,1296,648,216,28,28,28,28,32,32,486,243,81,54,486,243,81,54,432,
108,108,48,24192,24192,25920,12960,12960,6480,233280,11664,7776,7776,186624,
7776,7776,5832,2304,1152,288,288,432,432,648,324,324,162,648,324,108,648,324,
324,162,648,324,108,36,36,288,72,72,32,180,90,90,90,90,20,2592,324,288,2592,
324,288,648,324,108,72,648,324,108,72,28,28,28,28],
[,[1,2,3,4,1,1,4,3,1,3,4,2,13,14,15,16,13,18,19,20,21,22,18,24,25,26,27,28,24,
30,31,32,30,6,8,7,6,9,11,10,12,42,43,44,46,45,42,13,14,15,13,16,18,19,21,18,19
,22,24,25,27,24,25,28,65,65,67,67,37,37,71,72,73,71,75,76,77,75,48,50,49,48,5,
5,1,3,4,2,1,2,4,3,9,11,10,12,9,9,11,10,17,17,18,21,19,20,18,21,22,24,27,25,26,
24,27,28,33,33,34,36,35,34,42,43,44,46,45,42,51,52,51,51,52,51,56,57,58,56,62,
63,64,62,66,66,68,68],[1,1,1,1,5,6,6,6,9,9,9,9,1,1,1,1,5,1,1,1,1,2,5,1,1,1,1,2
,5,1,2,2,5,34,34,34,37,38,38,38,38,42,42,42,42,42,47,6,6,6,9,9,6,6,6,9,9,12,6,
6,6,9,9,12,67,68,65,66,70,69,13,13,14,17,13,13,15,17,34,34,34,37,84,83,85,85,
85,85,89,89,89,89,93,93,93,93,97,98,98,98,84,83,85,85,85,85,89,89,90,85,85,85,
85,89,89,90,84,83,119,119,119,122,123,123,123,123,123,128,93,93,97,93,93,97,93
,93,96,97,93,93,96,97,146,145,144,143],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
1,3,4,2,2,5,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,67,68,65,66,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,
96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,
116,117,118,119,120,121,122,85,86,87,88,88,89,129,130,131,132,133,134,135,136,
137,138,139,140,141,142,145,146,143,144],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41
,42,43,44,46,45,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,1,5,1,5,
70,69,71,72,73,74,75,76,77,78,79,80,81,82,84,83,85,86,87,88,89,90,91,92,93,94,
95,96,97,98,99,100,102,101,103,104,105,106,107,108,109,110,111,112,113,114,115
,116,118,117,119,120,121,122,123,124,125,127,126,128,132,133,134,129,130,131,
135,136,137,138,139,140,141,142,84,83,84,83]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1
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,-1,-1,-1,-1,-1,-1,-1,-1,-1],[21,21,21,21,21,5,5,5,5,5,5,5,-6,-6,-6,-6,-6,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-7,-7,1,1,1,
1,1,1,1,1,5,5,5,5,5,-3,-3,-3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1
,1,1,1,1,1,1,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0],
[TENSOR,[3,2]],[35,35,35,35,35,3,3,3,3,3,3,3,8,8,8,8,8,8,8,8,8,8,8,-1,-1,-1,
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,-1,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,0,0,0,0],
[TENSOR,[5,2]],[35,35,35,35,35,3,3,3,3,3,3,3,8,8,8,8,8,-1,-1,-1,-1,-1,-1,8,8,
8,8,8,8,-1,-1,-1,-1,3,3,3,3,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,3,0,0,
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-1,-1,-1,-1,-1,-1,-1,-1,-2,-2,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,-2,-2,1,1,-1,-1,-1,
-1,0,0,0,0,0,0,2,2,2,2,2,2,-1,-1,-1,-1,2,2,2,2,0,0,0,0],
[TENSOR,[7,2]],[90,90,90,90,90,10,10,10,10,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9
,9,9,9,9,0,0,0,0,-2,-2,-2,-2,2,2,2,2,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
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,10,10,10,2,2,2,-3,-3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[9,2]],[140,140,140,140,140,12,12,12,12,12,12,12,5,5,5,5,5,-4,-4,-4,
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[TENSOR,[11,2]],[189,189,189,189,189,-3,-3,-3,-3,-3,-3,-3,27,27,27,27,27,0,0,
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[( 45, 46)(126,127),
(  3,  4)(  7,  8)( 10, 11)( 14, 15)( 18, 24)( 19, 25)( 20, 26)( 21, 27)
( 22, 28)( 23, 29)( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 49, 50)( 53, 59)
( 54, 60)( 55, 61)( 56, 62)( 57, 63)( 58, 64)( 71, 75)( 72, 76)( 73, 77)
( 74, 78)( 80, 81)( 86, 87)( 91, 92)( 94, 95)( 99,100)(103,110)(104,111)
(105,112)(106,113)(107,114)(108,115)(109,116)(120,121)(124,125)(135,139)
(136,140)(137,141)(138,142)
,( 65, 67)( 66, 68)(143,145)(144,146),
( 69, 70)( 83, 84)(101,102)(117,118)(129,132)(130,133)(131,134)(143,144)
(145,146)
]);
ALF("3^6:2U4(3).2_1","Isoclinic(2.U4(3).2_1)",[1,1,1,1,2,3,3,3,4,4,4,4,5,
5,5,5,6,7,7,7,7,7,8,9,9,9,9,9,10,11,11,11,12,13,13,13,14,15,15,15,15,16,
16,16,16,16,17,18,18,18,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,25,
26,27,28,29,30,30,30,31,32,32,32,33,34,34,34,35,36,37,38,38,38,38,39,39,
39,39,40,40,40,40,41,42,42,42,43,44,45,45,45,45,46,46,46,47,47,47,47,48,
48,48,49,50,51,51,51,52,53,53,53,53,53,54,55,55,56,57,57,58,59,59,59,60,
61,61,61,62,63,64,65,66]);
ALF("3^6:2U4(3).2_1","O8-(3)",[1,5,6,7,3,4,27,26,2,22,23,19,5,9,8,11,20,7,
11,9,10,43,29,6,11,8,10,42,28,10,44,45,31,13,55,56,17,16,63,62,59,18,73,
74,71,72,50,21,33,32,19,30,25,36,35,23,30,76,24,37,34,22,30,75,38,70,38,
70,41,41,43,44,47,78,42,45,46,77,54,64,65,66,14,14,4,24,25,21,3,20,29,28,
12,53,52,51,16,15,61,60,57,57,27,35,37,33,29,31,78,26,34,36,32,28,31,77,
67,67,39,84,83,40,48,91,92,89,90,50,51,58,59,51,58,59,53,58,94,63,52,58,
93,62,88,87,87,88],[
"fusion map is uniqe up to table automorphisms,\n",
"compatible with Brauer tables"
]);
ALN("3^6:2U4(3).2_1",["O8-(3)M1"]);

MOT("2^8:O8+(2):2",
[
"origin: Dixon's Algorithm"
],
[89181388800,743178240,660602880,14155776,2359296,1572864,294912,5898240,
393216,983040,589824,184320,737280,49152,98304,98304,16384,12288,9953280,
368640,276480,77760,15552,5184,20736,3456,2304,147456,49152,12288,16384,16384,
8192,4096,2048,6144,6144,2048,2048,1536,1536,768,256,512,512,256,9600,1920,960
,300,55296,18432,4608,1728,9216,3072,9216,3072,1152,288,1728,576,6912,1152,768
,864,288,576,576,288,288,96,192,192,96,56,56,28,256,256,128,256,256,128,216,72
,27,160,160,80,20,1152,384,144,288,96,192,192,192,192,24,120,120,60,15,
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[]);
ALF("2^8:O8+(2):2","O8+(2).2",[1,1,1,2,2,2,2,3,3,3,3,3,4,4,5,5,5,5,6,6,6,
7,8,8,9,9,9,10,10,10,11,11,11,11,11,12,12,12,12,12,12,13,13,14,14,14,15,
15,15,16,17,17,17,18,19,19,19,19,19,20,21,21,22,22,22,23,23,24,24,24,25,
25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,31,32,32,32,33,34,34,35,36,
36,37,37,37,37,38,39,39,39,40,41,41,41,41,42,42,42,42,42,42,43,43,43,43,
44,44,44,44,45,45,45,45,46,46,46,47,47,47,47,47,48,48,48,48,49,49,50,50,
50,50,51,51,51,51,52,52,53,53,53,53,54,54,54,55,55,55,55,56,56,57,57,57,
57,58,58,58,59,59,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,66,67,67]);
ALF("2^8:O8+(2):2","O10+(2).2",[1,3,2,2,5,4,11,3,5,10,11,12,4,13,5,13,14,
15,6,21,22,8,9,27,7,29,26,10,14,16,14,11,13,18,17,16,12,18,15,36,35,17,37,
18,37,38,19,43,44,20,21,24,47,28,22,24,47,46,49,32,25,33,23,31,30,26,50,
29,50,52,30,54,31,54,56,34,59,58,38,35,39,38,36,40,41,66,42,44,67,68,45,
46,51,53,48,55,51,49,72,71,57,61,76,74,63,85,86,88,89,86,87,90,91,93,92,
88,90,93,108,89,93,91,109,95,92,96,94,91,95,110,95,93,96,112,111,97,99,
119,120,102,121,99,122,125,123,100,104,124,126,105,128,101,106,127,130,
108,111,113,109,112,110,114,114,135,115,117,138,139,119,125,140,120,125,
122,141,126,142,130,143,131,133,134,145,136,152,139,153,144,141,146,155],[
"fusion map is unique"
]);
ALN("2^8:O8+(2):2",["O10+(2).2M3"]);

MOT("2^8:O8-(2):2",
[
"origin: Dixon's Algorithm"
],
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107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
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ALF("2^8:O8-(2):2","O8-(2).2",[1,1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,6,6,
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ALF("2^8:O8-(2):2","O10-(2).2",[1,2,3,2,4,5,12,3,5,12,11,14,5,13,15,17,6,
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"fusion map is unique up to table automorphisms"
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ALN("2^8:O8-(2):2",["O10-(2).2M2"]);

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(27,43)(28,44)(29,45)(30,46)(31,48)(32,47)
,
(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)
(28,44)(29,45)(30,46)(31,47)(32,48)
],
["ConstructDirectProduct",[["Cyclic",3],["U3(3).2"]]]);
ALF("3xU3(3).2","3.G2(3)",[1,4,8,11,15,12,19,22,28,37,4,15,21,25,38,39,2,
5,8,11,16,13,19,23,29,38,5,16,21,26,39,37,3,6,8,11,17,14,19,24,30,39,6,17,
21,27,37,38],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3xU3(3).2","3D4(2).3",[1,2,5,4,7,6,9,12,14,16,3,7,10,13,16,16,22,26,
22,24,34,38,26,44,46,36,28,36,30,48,34,36,23,27,23,25,35,39,27,45,47,37,
29,37,31,49,37,35],[
"fusion map is unique up to table aut."
]);

MOT("3.G2(3)M2",
[
"2nd maximal subgroup of 3.G2(3),\n",
"differs from 3.G2(3)M1 = 3xU3(3).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3xU3(3).2"]]);
ALF("3.G2(3)M2","3.G2(3)",[1,4,7,11,12,15,18,22,25,34,4,12,21,28,36,35,
3,6,7,11,14,17,18,24,27,36,6,14,21,30,35,34,2,5,7,11,13,16,18,23,26,35,
5,13,21,29,34,36],[
"fusion 3xU3(3).2 -> 3.G2(3) mapped under 3.G2(3).2"
]);
ALF("3.G2(3)M2","G2(3)M2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]);

MOT("3.(3^(1+2)+x3^2):2S4",
[
"origin: Dixon's Algorithm"
],
[34992,5832,34992,34992,243,162,486,162,1458,729,432,72,432,432,72,36,36,36,72
,72,162,162,162,27,81,81,81,27,27,18,18,18,24,24,24,24,24,24,108,108,108,18,18
,18,18],
[,[1,2,4,3,5,6,7,8,9,10,1,2,4,3,11,12,12,12,14,13,21,22,23,28,25,26,27,24,29,
21,22,23,15,19,20,15,19,20,1,3,4,6,9,8,7],[1,1,1,1,1,1,1,1,1,1,11,11,11,11,15,
15,15,15,15,15,1,1,1,10,1,1,1,10,10,11,11,11,33,33,33,36,36,36,39,39,39,39,39,
39,39]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2
,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,
-E(8)-E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,0,0
,0,0,0,0,0],
[TENSOR,[4,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0
,0,0,0,0,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1],
[TENSOR,[6,2]],[4,4,4,4,4,4,4,4,4,4,-4,-4,-4,-4,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1
,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,-3,6,6,0,0,0,0,6,-3,-2,1,-2,-2,2,-1,-1
,-1,2,2,-3,0,3,0,0,3,-3,0,0,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,-3,6,6,0,0,0,
0,6,-3,-2,1,-2,-2,2,-1,-1,-1,2,2,0,3,-3,0,3,-3,0,0,0,-2,1,1,0,0,0,0,0,0,0,0,0,
0,0,0,0],[6,-3,6,6,0,0,0,0,6,-3,-2,1,-2,-2,2,-1,-1,-1,2,2,3,-3,0,0,-3,0,3,0,0,
1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-1,-1,-1,-1,8,8,0,0,0,0,0,0,0,0,0,0
,2,2,2,-1,2,2,2,-1,-1,0,0,0,0,0,0,0,0,0,-2,-2,-2,1,-2,1,1],
[TENSOR,[12,2]],[8,8,8,8,-4,-1,5,2,-1,-1,0,0,0,0,0,0,0,0,0,0,2,2,2,-1,-1,-1,
-1,-1,2,0,0,0,0,0,0,0,0,0,-2,-2,-2,1,1,-2,1],
[TENSOR,[14,2]],[12,-6,12,12,0,0,0,0,12,-6,4,-2,4,4,0,0,0,0,0,0,-3,3,0,0,3,0,
-3,0,0,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,-6,12,12,0,0,0,0,12,-6,4,-2,4,4,0
,0,0,0,0,0,3,0,-3,0,0,-3,3,0,0,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,-6,12,12,
0,0,0,0,12,-6,4,-2,4,4,0,0,0,0,0,0,0,-3,3,0,-3,3,0,0,0,-2,1,1,0,0,0,0,0,0,0,0,
0,0,0,0,0],[16,16,16,16,-2,-2,-2,-2,16,16,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,1,-2,-2
,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,16,-8,-2,10,4,-2,-2,0,0,0,0
,0,0,0,0,0,0,-2,-2,-2,1,1,1,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,
16,1,-2,-8,4,-2,-2,0,0,0,0,0,0,0,0,0,0,4,4,4,1,-2,-2,-2,1,-2,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0],[16,16,16,16,1,-2,-8,4,-2,-2,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,
-E(3)+2*E(3)^2,1,1,1,2*E(3)-E(3)^2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[22,2]],[18,-9,18,18,0,0,0,0,18,-9,-6,3,-6,-6,-2,1,1,1,-2,-2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,24,24,-3,6,-3,-3,-3,-3,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1],
[TENSOR,[25,2]],[24,24,24,24,6,-3,6,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,1,1,1,-2],
[TENSOR,[27,2]],[27,0,27*E(3)^2,27*E(3),0,0,0,0,0,0,3,0,3*E(3)^2,3*E(3),-1,
2*E(3)^2,2*E(3),2,-E(3)^2,-E(3),0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-1,
-E(3),-E(3)^2,3,3*E(3),3*E(3)^2,0,0,0,0],
[GALOIS,[29,2]],
[TENSOR,[29,2]],
[TENSOR,[30,2]],[27,0,27*E(3)^2,27*E(3),0,0,0,0,0,0,3,0,3*E(3)^2,3*E(3),3,0,0
,0,3*E(3)^2,3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,
-3,-3*E(3),-3*E(3)^2,0,0,0,0],
[GALOIS,[33,2]],
[TENSOR,[33,2]],
[TENSOR,[34,2]],[48,-24,48,48,0,0,0,0,-6,3,0,0,0,0,0,0,0,0,0,0,6,-6,0,0,3,0,
-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[48,-24,48,48,0,0,0,0,-6,3,0,0,0,0,0,0
,0,0,0,0,0,6,-6,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[48,-24,48,48,0,
0,0,0,-6,3,0,0,0,0,0,0,0,0,0,0,-6,0,6,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0],[54,0,54*E(3)^2,54*E(3),0,0,0,0,0,0,-6,0,-6*E(3)^2,-6*E(3),0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,-E(24)^11-E(24)^17,-E(24)-E(24)^19,
E(8)+E(8)^3,E(24)^11+E(24)^17,E(24)+E(24)^19,0,0,0,0,0,0,0],
[TENSOR,[40,2]],
[GALOIS,[40,11]],
[TENSOR,[42,2]],[54,0,54*E(3)^2,54*E(3),0,0,0,0,0,0,6,0,6*E(3)^2,6*E(3),-2,
-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0],
[GALOIS,[44,2]]],
[(24,28),(21,22,23)(25,26,27)(30,31,32),
( 3, 4)(13,14)(16,17)(19,20)(34,35)(37,38)(40,41),(33,36)(34,37)(35,38)]);
ALF("3.(3^(1+2)+x3^2):2S4","3.G2(3)",[1,7,2,3,9,11,7,10,8,9,4,18,5,6,12,
35,36,34,13,14,11,10,8,32,11,10,9,33,31,21,20,19,25,27,26,25,27,26,4,6,5,
21,19,20,18],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.(3^(1+2)+x3^2):2S4","(3^(1+2)+x3^2):2S4",[1,2,1,1,6,7,5,8,3,4,10,9,
10,10,12,11,11,11,12,12,19,20,21,13,17,18,16,14,15,22,23,24,29,29,29,30,
30,30,31,31,31,27,25,28,26]);

MOT("3.G2(3)M4",
[
"4th maximal subgroup of 3.G2(3),\n",
"differs from 3.G2(3)M3 = 3.(3^(1+2)+x3^2):2S4 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.(3^(1+2)+x3^2):2S4"]]);
ALF("3.G2(3)M4","G2(3)M4",[1,2,1,1,6,7,5,8,3,4,10,9,10,10,12,11,11,11,12,
12,19,20,21,13,17,18,16,14,15,22,23,24,29,29,29,30,30,30,31,31,31,27,25,
28,26]);
ALF("3.G2(3)M4","3.G2(3)",[1,8,3,2,9,11,8,10,7,9,4,19,6,5,15,39,38,37,17,
16,11,10,7,32,11,10,9,33,31,21,20,18,28,29,30,28,29,30,4,5,6,21,18,20,19],[
"fusion 3.(3^(1+2)+x3^2):2S4 -> 3.G2(3) mapped under 3.G2(3).2"
]);

MOT("3.G2(3)M6",
[
"6th maximal subgroup of 3.G2(3),\n",
"differs from 3.G2(3)M5 = 3xL3(3).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3xL3(3).2"]]);
ALF("3.G2(3)M6","3.G2(3)",[1,4,8,10,12,19,25,43,40,4,15,20,25,37,37,3,
6,8,10,14,19,27,45,42,6,17,20,27,39,39,2,5,8,10,13,19,26,44,41,5,16,20,
26,38,38],[
"fusion 3xL3(3).2 -> 3.G2(3) mapped under 3.G2(3).2"
]);
ALF("3.G2(3)M6","G2(3)M6",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]);

MOT("3xL2(8).3",
0,
0,
0,
0,
[
( 6, 7)( 8, 9)(10,11)(12,23)(13,24)(14,25)(15,26)(16,27)(17,29)(18,28)(19,31)
(20,30)(21,33)(22,32)
,(12,23)(13,24)(14,25)(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)
,( 6,17,28)( 7,29,18)( 8,19,30)( 9,31,20)(10,21,32)(11,33,22)],
["ConstructDirectProduct",[["Cyclic",3],["L2(8).3"]]]);
ALF("3xL2(8).3","3.G2(3)",[1,4,9,22,31,11,11,21,21,32,33,2,5,9,23,31,11,
11,21,21,32,33,3,6,9,24,31,11,11,21,21,32,33],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3x2^3.L3(2)",
0,
0,
0,
0,
[(12,23)(13,24)(14,25)(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)
,(10,11)(21,22)(32,33),( 4, 5)( 8, 9)(15,16)(19,20)(26,27)(30,31)],
["ConstructDirectProduct",[["Cyclic",3],["2^3.L3(2)"]]]);
ALF("3x2^3.L3(2)","3.G2(3)",[1,4,4,12,15,11,21,25,28,22,22,2,5,5,13,16,11,
21,26,29,23,23,3,6,6,14,17,11,21,27,30,24,24],[
"fusion map determined up to table autom.\n",
"by Brauer tables and factors"
]);

MOT("3xL2(13)",
0,
0,
0,
0,
[(10,19)(11,20)(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27),
( 8, 9)(17,18)(26,27),( 5, 7, 6)(14,16,15)(23,25,24)],
["ConstructDirectProduct",[["Cyclic",3],["L2(13)"]]]);
ALF("3xL2(13)","3.G2(3)",[1,4,10,20,22,22,22,40,43,2,5,10,20,23,23,23,41,
44,3,6,10,20,24,24,24,42,45],[
"fusion map determined up to table aut. by compatibility\n",
"with factors"
]);

MOT("3.2^(1+4)+:3^2.2",
[
"origin: Dixon's Algorithm"
],
[1728,1728,288,72,72,288,1728,1728,288,1728,1728,288,96,36,36,96,288,36,96,288
,18,18,18,18,72,72,36,36,36,24,24,24,24,24,24,24,48,48,48,48,24,48,48,24],
[,[1,1,2,4,4,10,11,11,7,8,8,2,1,5,5,11,10,5,8,7,21,21,23,23,25,25,26,26,26,1,3
,9,11,6,8,12,13,13,19,19,20,16,16,17],[1,2,3,1,2,3,2,1,3,2,1,12,13,12,12,13,12
,12,13,12,1,2,1,2,1,2,3,3,3,30,31,31,30,31,30,36,37,38,37,38,36,38,37,36]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,-1,-1,2,2,
2,2,2,2,2,2,-1,-1,2,2,-1,2,2,-1,-1,-1,-1,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0],[2,2,2,-1,-1,2,2,2,2,2,2,2,2,-1,-1,2,2,-1,2,2,-1,-1,2,2,-1,-1,-1,-1,-1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,-1,-1,2,2,2,2,2,2,2,2,-1,-1,2,2,-1,2,2,2,2,
-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,-1,0,0,-1,3,3,-1,3,3,
3,-1,0,0,-1,3,0,-1,3,0,0,0,0,3,3,-1,-1,-1,-1,1,1,-1,1,-1,-1,1,1,1,1,-1,1,1,-1]
,
[TENSOR,[7,2]],[3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,
0,0,0,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1],
[TENSOR,[9,2]],[3,3,3,0,0,3*E(3)^2,3*E(3)^2,3*E(3)^2,3*E(3),3*E(3),3*E(3),3,3
,0,0,3*E(3)^2,3*E(3)^2,0,3*E(3),3*E(3),0,0,0,0,0,0,0,0,0,-1,-1,-E(3)^2,-E(3)^2
,-E(3),-E(3),-1,-1,-1,-E(3)^2,-E(3)^2,-E(3)^2,-E(3),-E(3),-E(3)],
[GALOIS,[11,2]],
[TENSOR,[11,2]],
[TENSOR,[12,2]],[3,3,-1,0,0,-E(3),3*E(3),3*E(3),-E(3)^2,3*E(3)^2,3*E(3)^2,3,
-1,0,0,-E(3),3*E(3),0,-E(3)^2,3*E(3)^2,0,0,0,0,0,0,2*E(3),2,2*E(3)^2,-1,1,E(3)
,-E(3),E(3)^2,-E(3)^2,-1,1,1,E(3),E(3),-E(3),E(3)^2,E(3)^2,-E(3)^2],
[GALOIS,[15,2]],
[TENSOR,[15,2]],
[TENSOR,[16,2]],[3,3,3,0,0,3*E(3),3*E(3),3*E(3),3*E(3)^2,3*E(3)^2,3*E(3)^2,-1
,-1,2,2*E(3),-E(3),-E(3),2*E(3)^2,-E(3)^2,-E(3)^2,0,0,0,0,0,0,0,0,0,-1,-1,
-E(3),-E(3),-E(3)^2,-E(3)^2,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2],
[GALOIS,[19,2]],
[TENSOR,[19,2]],
[TENSOR,[20,2]],[4,-4,0,-2,2,0,-4,4,0,-4,4,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-2,2,0
,0,0,0,0,0,0,0,0,0,-2,2,-2,2,0,2,-2,0],
[TENSOR,[23,2]],[6,6,-2,0,0,-2,6,6,-2,6,6,6,-2,0,0,-2,6,0,-2,6,0,0,0,0,-3,-3,
1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,-3,-3,6,6,6,6,6,6,-2,-2,1,1,-2,-2,
1,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,-2,0,0,-2*E(3),
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[GALOIS,[37,2]],
[TENSOR,[37,2]],
[TENSOR,[38,2]],[12,-12,0,0,0,0,-12*E(3),12*E(3),0,-12*E(3)^2,12*E(3)^2,0,0,0
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[GALOIS,[41,2]],
[TENSOR,[41,2]],
[TENSOR,[42,2]]],
[(37,38)(39,40)(42,43),(21,23)(22,24),
( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(27,29)(32,34)(33,35)(39,43)(40,42)
(41,44)
,( 3,12)( 4,25)( 5,26)( 6,17)( 9,20)(14,28)(15,27)(18,29)(31,36)(32,41)(34,44)
]);
ALF("3.2^(1+4)+:3^2.2","3.G2(3)",[1,4,12,8,19,13,5,2,14,6,3,15,4,37,38,5,
16,39,6,17,11,21,10,20,7,18,35,34,36,4,25,26,5,27,6,28,12,15,13,16,29,17,
14,30],[
"compatible with 2^(1+4)+:3^2.2 -> G2(3)"
]);
ALF("3.2^(1+4)+:3^2.2","2^(1+4)+:3^2.2",[1,2,3,14,11,3,2,1,3,2,1,5,4,10,
10,4,5,10,4,5,6,7,8,13,12,15,9,9,9,16,20,20,16,20,16,19,17,18,17,18,19,18,
17,19]);

MOT("2.2^(4+6).(A5x3)",
0,
[368640,368640,24576,24576,1024,1024,512,3840,768,5760,5760,384,384,5760,5760,
384,384,12,72,72,12,72,72,12,72,72,48,96,96,96,96,48,96,96,48,48,96,96,64,64,
1536,1536,768,768,1536,1536,32,256,256,256,256,30,30,30,30,120,120,20,30,30,20
,120,120,30,30],
[,[1,1,1,1,4,4,4,2,2,14,14,14,14,10,10,10,10,22,23,23,19,20,20,26,25,25,16,14,
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46,45,42,41,43,45,46,44,43,41,42,39,40,41,42,43,44,45,46,47,48,49,50,51,62,63,
62,63,62,63,61,57,56,58,56,57,56,57],,[1,2,3,4,5,6,7,8,9,14,15,16,17,10,11,12,
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[TENSOR,[2,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,0,0,-1,-1,-1,
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-E(5)^2-E(5)^3,-E(5)^2-E(5)^3],
[GALOIS,[4,2]],
[TENSOR,[5,2]],
[TENSOR,[4,2]],
[TENSOR,[4,3]],
[TENSOR,[5,3]],[4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,1,1,1,1,1,1,1,1,1,0,0,0,0,0
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[TENSOR,[10,3]],
[TENSOR,[10,2]],[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,-1,-1,-1,-1,-1,-1,-1,-1,-1
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[TENSOR,[13,3]],
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[TENSOR,[16,3]],
[TENSOR,[16,2]],
[TENSOR,[17,3]],
[TENSOR,[17,2]],[15,15,15,15,-1,-1,-1,15,-1,0,0,0,0,0,0,0,0,-1,3,3,-1,3,3,0,0
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[TENSOR,[22,3]],
[TENSOR,[22,2]],[18,18,18,18,2,2,2,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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-E(5)-E(5)^4],
[GALOIS,[27,2]],
[TENSOR,[27,3]],
[TENSOR,[28,3]],
[TENSOR,[28,2]],
[TENSOR,[27,2]],[30,30,30,30,-2,-2,-2,-10,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,3,
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,0,0,0,0],[30,30,30,30,-2,-2,-2,-10,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,3,3,0,0,0
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],[36,36,36,36,4,4,4,-12,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,-E(5)^2-E(5)^3,0,0,-E(5)-E(5)^4,3*E(5)+3*E(5)^4,3*E(5)+3*E(5)^4,0,0],
[GALOIS,[35,2]],[45,45,45,45,-3,-3,-3,45,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0],[60,60,-4,-4,4,4,-4,0,0,15,15,-1,-1,15,15,-1,-1,0,0,0,0,0,0,0,0,0,
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,0,0,0],
[TENSOR,[38,2]],
[TENSOR,[38,3]],
[TENSOR,[39,2]],
[TENSOR,[39,3]],
[TENSOR,[40,2]],
[TENSOR,[40,3]],
[TENSOR,[41,2]],
[TENSOR,[41,3]],[80,-80,-16,16,0,0,0,0,0,-10,10,2,-2,-10,10,2,-2,0,-2,2,0,-2,
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,0,2,-2,0,2,-2,-2,2,0,-2,2,0,0,2,-2,0,0,8,-8,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],
[TENSOR,[51,3]],
[TENSOR,[51,2]],
[TENSOR,[52,3]],
[TENSOR,[52,2]],[160,-160,-32,32,0,0,0,0,0,-20,20,4,-4,-20,20,4,-4,0,2,-2,0,2
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,0,0,0,0,0],
[TENSOR,[57,3]],
[TENSOR,[57,2]],[180,-180,60,-60,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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0,0,0,0],[180,-180,60,-60,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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0,0,0,0,-12,-12,0,0,12,12,0,8,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[180,180,
-12,-12,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-12,12,0,0,0,-4,8,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[180,180,-12,-12,
-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
12,-12,0,0,0,-4,0,8,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(28,29)(30,31)(33,34)(37,38)(39,40)(41,42)(45,46),
(27,32)(35,36)(43,44)(49,50),(52,64)(53,65)(54,60)(55,59)(56,62)(57,63)(58,61)
,
(10,14)(11,15)(12,16)(13,17)(18,21)(19,22)(20,23)(27,35)(28,34)(29,33)(30,38)
(31,37)(32,36)(52,54)(53,55)(59,65)(60,64)
]);
ALF("2.2^(4+6).(A5x3)","2.G2(4)",[1,2,4,3,11,10,13,5,5,6,7,23,22,6,7,23,
22,24,9,8,24,9,8,24,8,9,38,22,23,36,37,39,23,22,39,38,37,36,28,29,11,10,
12,12,4,3,27,5,13,13,12,47,46,47,46,17,16,35,44,45,34,15,14,45,44],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.2^(4+6).(A5x3)","2^(4+6):(A5x3)",[1,1,2,2,5,5,6,3,4,33,33,35,35,23,
23,25,25,37,34,34,27,24,24,18,9,9,39,36,36,38,38,40,26,26,30,29,28,28,20,
20,10,10,11,12,7,7,19,8,14,15,13,41,41,31,31,17,17,21,32,32,22,16,16,42,
42]);

MOT("Isoclinic(2xU3(4).2)",
0,
0,
0,
0,
[(17,18)(37,38),(15,35)(16,36)(17,38)(18,37)(19,39)(20,40),(11,12)(31,32),
( 5, 6)( 7, 8)( 9,10)(13,14)(19,20)(25,26)(27,28)(29,30)(33,34)(39,40)],
["ConstructIsoclinic",[["Cyclic",2],["U3(4).2"]]]);
ALF("Isoclinic(2xU3(4).2)","U3(4).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]);
ALF("Isoclinic(2xU3(4).2)","2.G2(4)",[1,3,8,13,18,20,14,16,30,32,40,42,48,
50,5,24,28,29,34,35,2,4,9,13,19,21,15,17,31,33,41,43,49,51,5,24,29,28,34,
35],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("Isoclinic(2xU3(3).2)",
0,
0,
0,
0,
[(15,16)(31,32),(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)],
["ConstructIsoclinic",[["Cyclic",2],["U3(3).2"]]]);
ALF("Isoclinic(2xU3(3).2)","U3(3).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]);
ALF("Isoclinic(2xU3(3).2)","2.G2(4)",[1,3,6,8,10,11,22,25,27,36,5,12,24,
27,38,39,2,4,7,9,11,10,23,26,27,37,5,12,24,27,38,39],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("Isoclinic(2xU3(3).2)","2.J2.2",[1,3,6,8,11,10,16,19,21,26,29,30,33,
36,37,38,2,4,7,9,10,11,17,20,21,25,29,30,33,36,38,37],[
"fusion map is unique up to table autom."
]);
ALN("Isoclinic(2xU3(3).2)",["2.J2.2M2"]);

MOT("2.A5xA5",
0,
0,
0,
0,
[
( 4, 5)( 9,10)(14,15)(19,20)(24,25)(26,36)(27,37)(28,38)(29,40)(30,39)(31,41)
(32,42)(33,43)(34,45)(35,44)
,( 4, 5)( 9,10)(14,15)(19,20)(24,25)(29,30)(34,35)(39,40)(44,45)],
["ConstructDirectProduct",[["2.A5"],["A5"]]]);
ALF("2.A5xA5","A5xA5",[1,2,3,4,5,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,11,
12,13,14,15,16,17,18,19,20,16,17,18,19,20,21,22,23,24,25,21,22,23,24,25]);
ALF("2.A5xA5","2.G2(4)",[1,3,8,14,16,2,4,9,15,17,5,5,24,34,35,6,22,8,44,
46,7,23,9,45,47,18,30,48,16,20,19,31,49,17,21,20,32,50,18,14,21,33,51,19,
15],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("U3(5)M2",
[
"2nd maximal subgroup of U3(5),\n",
"differs from U3(5)M1 = A7 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A7"]]);
ALF("U3(5)M2","U3(5)",[1,2,3,3,4,7,9,10,11],[
"fusion A7 -> U3(5) mapped under U3(5).3"
]);

MOT("U3(5)M3",
[
"3rd maximal subgroup of U3(5),\n",
"differs from U3(5)M1 = A7 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A7"]]);
ALF("U3(5)M3","U3(5)",[1,2,3,3,4,8,9,10,11],[
"fusion U3(5)M2 -> U3(5) mapped under U3(5).3"
]);

MOT("U3(5)M6",
[
"6th maximal subgroup of U3(5),\n",
"differs from U3(5)M5 = A6.2_3 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A6.2_3"]]);
ALF("U3(5)M6","U3(5)",[1,2,3,4,7,4,12,13],[
"fusion A6.2_3 -> U3(5) mapped under U3(5).3"
]);

MOT("U3(5)M7",
[
"7th maximal subgroup of U3(5),\n",
"differs from U3(5)M5 = A6.2_3 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A6.2_3"]]);
ALF("U3(5)M7","U3(5)",[1,2,3,4,8,4,12,13],[
"fusion U3(5)M6 -> U3(5) mapped under U3(5).3"
]);

MOT("3.U3(5)M2",
[
"2nd maximal subgroup of 3.U3(5),\n",
"differs from 3.U3(5)M1 = 3.A7 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.A7"]]);
ALF("3.U3(5)M2","3.U3(5)",[1,2,3,4,5,6,7,7,8,9,10,17,18,19,23,24,25,26,
27,28,29,30,31],[
"fusion 3.A7 -> 3.U3(5) mapped under 3.U3(5).3"
]);
ALF("3.U3(5)M2","U3(5)M2",[1,1,1,2,2,2,3,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9]);

MOT("3.U3(5)M3",
[
"3rd maximal subgroup of 3.U3(5),\n",
"differs from 3.U3(5)M1 = 3.A7 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.A7"]]);
ALF("3.U3(5)M3","3.U3(5)",[1,2,3,4,5,6,7,7,8,9,10,20,21,22,23,24,25,26,
27,28,29,30,31],[
"fusion 3.U3(5)M2 -> 3.U3(5) mapped under 3.U3(5).3"
]);
ALF("3.U3(5)M3","U3(5)M3",[1,1,1,2,2,2,3,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9]);

MOT("3x5^(1+2)_+:8",
0,
0,
0,
0,
[
(14,27)(15,28)(16,29)(17,30)(18,31)(19,32)(20,33)(21,34)(22,35)(23,36)(24,37)
(25,38)(26,39)
,(10,11)(12,13)(23,24)(25,26)(36,37)(38,39),
( 8, 9)(10,13)(11,12)(21,22)(23,26)(24,25)(34,35)(36,39)(37,38),
( 4, 5)(17,18)(30,31),( 3, 4)(16,17)(29,30)],
["ConstructDirectProduct",[["Cyclic",3],["5^(1+2)+:8"]]]);
ALF("3x5^(1+2)_+:8","3.U3(5)",[1,11,14,17,20,4,38,8,8,32,35,32,35,2,12,15,
18,21,5,39,9,9,33,36,33,36,3,13,16,19,22,6,40,10,10,34,37,34,37],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3.U3(5)M6",
[
"6th maximal subgroup of 3.U3(5),\n",
"differs from 3.U3(5)M5 = 3.A6.2_3 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.A6.2_3"]]);
ALF("3.U3(5)M6","3.U3(5)",[1,2,3,4,5,6,7,8,9,10,17,18,19,8,9,10,32,33,
34,35,36,37],[
"fusion map is unique up to table automorphisms,\n",
"equals the map from 3.U3(5)M5, mapped under an outer autom. of order 3"
]);
ALF("3.U3(5)M6","U3(5)M6",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8]);

MOT("3.U3(5)M7",
[
"7th maximal subgroup of 3.U3(5),\n",
"differs from 3.U3(5)M5 = 3.A6.2_3 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.A6.2_3"]]);
ALF("3.U3(5)M7","3.U3(5)",[1,2,3,4,5,6,7,8,9,10,20,21,22,8,9,10,32,33,
34,35,36,37],[
"fusion 3.U3(5)M6 -> 3.U3(5) mapped under 3.U3(5).3"
]);
ALF("3.U3(5)M7","U3(5)M7",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8]);

MOT("2.2^(3+3):7",
[
"origin: Dixon's Algorithm"
],
[896,64,896,16,16,14,14,14,14,14,14,14,14,14,14,14,14],
[,[1,1,1,2,2,10,10,12,12,14,14,16,16,6,6,8,8],,,,,[1,2,3,5,4,1,3,1,3,1,3,1,3,1
,3,1,3]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,E(7)^6,E(7)^6,E(7)^4,E(7)^4,
E(7)^5,E(7)^5,E(7),E(7),E(7)^3,E(7)^3,E(7)^2,E(7)^2],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[7,7,7,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[8,0,-8,0,0,1,-1,1,-1,1,
-1,1,-1,1,-1,1,-1],
[TENSOR,[9,7]],
[TENSOR,[9,6]],
[TENSOR,[9,5]],
[TENSOR,[9,4]],
[TENSOR,[9,3]],
[TENSOR,[9,2]],[14,-2,14,-2*E(4),2*E(4),0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[16,3]]],
[(4,5),( 6, 8,10,12,14,16)( 7, 9,11,13,15,17)]);
ALF("2.2^(3+3):7","2^(3+3):7",[1,2,1,3,4,5,5,6,6,7,7,8,8,9,9,10,10]);
ALF("2.2^(3+3):7","2.Sz(8)",[1,3,2,4,5,8,9,12,13,10,11,8,9,12,13,10,11],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2.2^(3+3):7",["2.Sz(8)N2"]);

MOT("2x13:4",
0,
0,
0,
0,
[( 5, 7)(12,14),( 5,12)( 7,14),( 2, 3, 4)( 9,10,11)],
["ConstructDirectProduct",[["Cyclic",2],["13:4"]]]);
ALF("2x13:4","2.Sz(8)",[1,14,16,18,4,3,5,2,15,17,19,4,3,5],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2x13:4",["2.Sz(8)N13"]);

MOT("2^2.2^(3+3):7",
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[1792,1792,1792,1792,64,16,16,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
28,28,28,28,28,28,28,28],
[,[1,1,1,1,1,5,5,16,16,16,16,20,20,20,20,24,24,24,24,28,28,28,28,8,8,8,8,12,12
,12,12],,,,,[1,2,3,4,5,7,6,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,E(7)^6,E(7)^6,E(7)^6,E(7)^6,E(7)^4,E(7)^4,E(7)^4,E(7)^4,E(7)^5,E(7)^5,E(7)^5
,E(7)^5,E(7),E(7),E(7),E(7),E(7)^3,E(7)^3,E(7)^3,E(7)^3,E(7)^2,E(7)^2,E(7)^2,
E(7)^2],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[7,7,7,7,7,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0],[8,8,-8,-8,0,0,0,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,
-1],
[TENSOR,[9,7]],
[TENSOR,[9,6]],
[TENSOR,[9,5]],
[TENSOR,[9,4]],
[TENSOR,[9,3]],
[TENSOR,[9,2]],[14,14,14,14,-2,-2*E(4),2*E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0],
[GALOIS,[16,3]],[8,-8,8,-8,0,0,0,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1
,1,-1,1,-1,1,-1],
[TENSOR,[18,7]],
[TENSOR,[18,6]],
[TENSOR,[18,5]],
[TENSOR,[18,4]],
[TENSOR,[18,3]],
[TENSOR,[18,2]],[8,-8,-8,8,0,0,0,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1
,-1,1,1,-1,-1,1],
[TENSOR,[25,7]],
[TENSOR,[25,6]],
[TENSOR,[25,5]],
[TENSOR,[25,4]],
[TENSOR,[25,3]],
[TENSOR,[25,2]]],
[(6,7),
( 8,12,16,20,24,28)( 9,13,17,21,25,29)(10,14,18,22,26,30)(11,15,19,23,27,31),
( 3, 4)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31),
( 2, 3)( 9,10)(13,14)(17,18)(21,22)(25,26)(29,30)]);
ALF("2^2.2^(3+3):7","2^2.Sz(8)",[1,2,3,4,5,6,7,12,13,14,15,20,21,22,23,16,
17,18,19,12,13,14,15,20,21,22,23,16,17,18,19],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.2^(3+3):7","2^(3+3):7",[1,1,1,1,2,3,4,5,5,5,5,6,6,6,6,7,7,7,
7,8,8,8,8,9,9,9,9,10,10,10,10]);
ALF("2^2.2^(3+3):7","2.2^(3+3):7",[1,1,3,3,2,4,5,6,6,7,7,8,8,9,9,10,
10,11,11,12,12,13,13,14,14,15,15,16,16,17,17]);

MOT("2^2x13:4",
0,
0,
0,
0,
[( 5, 7)(12,14)(19,21)(26,28),( 5,12)( 7,14)(19,26)(21,28),
( 2, 3, 4)( 9,10,11)(16,17,18)(23,24,25),
(15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28),
( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)],
["ConstructDirectProduct",[["Cyclic",2],["Cyclic",2],["13:4"]]]);
ALF("2^2x13:4","2^2.Sz(8)",[1,24,28,32,6,5,7,2,25,29,33,6,5,7,3,26,30,34,
6,5,7,4,27,31,35,6,5,7],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2x13:4","2x13:4",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,3,4,5,6,7,8,
9,10,11,12,13,14]);

MOT("2^2xD14",
0,
0,
0,
0,
[( 5,10)(15,20),( 2, 4, 3)( 7, 9, 8)(12,14,13)(17,19,18),
(11,16)(12,17)(13,18)(14,19)(15,20),( 6,11)( 7,12)( 8,13)( 9,14)(10,15)],
["ConstructDirectProduct",[["Cyclic",2],["Cyclic",2],["D14"]]]);
ALF("2^2xD14","D28",[1,9,10,6,3,1,9,10,6,3,2,5,7,8,4,2,5,7,8,4]);
ALF("2^2xD14","2^2.Sz(8)",[1,12,16,20,5,2,13,17,21,5,3,14,18,22,5,4,15,19,
23,5],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("L3(7)M2",
[
"2nd maximal subgroup of L3(7),\n",
"differs from L3(7)M1 = 7^2:2.L2(7).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["7^2:2.L2(7).2"]]);
ALF("L3(7)M2","L3(7)",[1,6,2,4,3,5,10,11,6,7,9,8,12,2,12,5,5,14,13,15,16],[
"fusion 7^2:2.L2(7).2 -> L3(7) mapped under L3(7).2"
]);

MOT("L3(7)M4",
[
"4th maximal subgroup of L3(7),\n",
"differs from L3(7)M3 = L3(2).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L3(2).2"]]);
ALF("L3(7)M4","L3(7)",[1,2,3,4,8,2,5,11,10],[
"fusion L3(2).2 -> L3(7) mapped under L3(7).3"
]);

MOT("L3(7)M5",
[
"5th maximal subgroup of L3(7),\n",
"differs from L3(7)M3 = L3(2).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L3(2).2"]]);
ALF("L3(7)M5","L3(7)",[1,2,3,4,9,2,5,11,10],[
"fusion L3(7)M4 -> L3(7) mapped under L3(7).3"
]);

MOT("3x7^2:2.L2(7).2",
0,
0,
0,
0,
[(18,19)(20,21)(39,40)(41,42)(60,61)(62,63),
(16,17)(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)
(32,53)(33,54)(34,55)(35,56)(36,57)(37,59)(38,58)(39,60)(40,61)(41,62)(42,63)
,(11,12)(32,33)(53,54),(10,11)(31,32)(52,53),
( 7, 8)(18,21,19,20)(28,29)(39,42,40,41)(49,50)(60,63,61,62),
(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)
(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63)
],
["ConstructDirectProduct",[["Cyclic",3],["7^2:2.L2(7).2"]]]);
ALF("3x7^2:2.L2(7).2","3.L3(7)",[1,14,4,8,7,11,26,29,14,17,20,23,32,4,32,
12,13,35,38,44,41,2,15,5,9,7,12,27,30,15,18,21,24,33,5,33,13,11,36,39,45,
42,3,16,6,10,7,13,28,31,16,19,22,25,34,6,34,11,12,37,40,46,43],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3x7^2:2.L2(7).2","3.ON",[1,18,4,11,7,17,24,24,18,18,21,21,37,4,37,17,
17,42,42,45,45,2,19,5,12,7,17,25,25,19,19,22,22,38,5,38,17,17,43,43,46,46,
3,20,6,13,7,17,26,26,20,20,23,23,39,6,39,17,17,44,44,47,47],[
"fusion map is unique up to table aut."
]);

MOT("3.L3(7)M2",
[
"2nd maximal subgroup of 3.L3(7),\n",
"differs from 3.L3(7)M1 = 3x7^2:2.L2(7).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3x7^2:2.L2(7).2"]]);
ALF("3.L3(7)M2","(7^2)b:2.L2(7).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]);
ALF("3.L3(7)M2","3.L3(7)",[1,14,4,8,7,11,26,29,14,17,23,20,32,4,32,13,
12,38,35,41,44,3,16,6,10,7,13,28,31,16,19,25,22,34,6,34,12,11,40,37,43,
46,2,15,5,9,7,12,27,30,15,18,24,21,33,5,33,11,13,39,36,42,45],[
"fusion 3x7^2:2.L2(7).2 -> 3.L3(7) mapped under 3.L3(7).2"
]);
ALF("3.L3(7)M2","3.ON",[1,18,4,11,7,17,27,27,18,18,21,21,37,4,37,17,17,48,
48,51,51,3,20,6,13,7,17,29,29,20,20,23,23,39,6,39,17,17,50,50,53,53,2,19,
5,12,7,17,28,28,19,19,22,22,38,5,38,17,17,49,49,52,52],[
"fusion 3x7^2:2.L2(7).2 -> 3.ON mapped under 3.ON.2"
]);

MOT("3xL3(2).2",
0,
0,
0,
0,
[(10,19)(11,20)(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27),
( 8, 9)(17,18)(26,27)],
["ConstructDirectProduct",[["Cyclic",3],["L3(2).2"]]]);
ALF("3xL3(2).2","3.L3(7)",[1,4,7,8,17,4,11,29,26,2,5,7,9,18,5,12,30,27,3,
6,7,10,19,6,13,31,28],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3.L3(7)M4",
[
"4th maximal subgroup of 3.L3(7),\n",
"differs from 3.L3(7)M3 = 3xL2(7).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3xL3(2).2"]]);
ALF("3.L3(7)M4","3.L3(7)",[1,4,7,8,20,4,11,29,26,2,5,7,9,21,5,12,30,27,
3,6,7,10,22,6,13,31,28],[
"fusion 3xL3(2).2 -> 3.L3(7) mapped under 3.L3(7).3"
]);

MOT("3.L3(7)M5",
[
"5th maximal subgroup of 3.L3(7),\n",
"differs from 3.L3(7)M3 = 3xL2(7).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3xL3(2).2"]]);
ALF("3.L3(7)M5","3.L3(7)",[1,4,7,8,23,4,11,29,26,2,5,7,9,24,5,12,30,27,
3,6,7,10,25,6,13,31,28],[
"fusion 3.L3(7)M4 -> 3.L3(7) mapped under 3.L3(7).3"
]);

MOT("3x19:3",
0,
0,
0,
0,
[( 8, 9)(10,19)(11,20)(12,21)(13,22)(14,23)(15,24)(16,25)(17,27)(18,26),
( 8,17,26)( 9,27,18),( 2, 3, 4, 6, 5, 7)(11,12,13,15,14,16)(20,21,22,24,23,25)
,(10,19)(11,20)(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)],
["ConstructDirectProduct",[["Cyclic",3],["19:3"]]]);
ALF("3x19:3","3.L3(7)",[1,47,56,59,53,50,62,7,7,2,48,57,60,54,51,63,7,7,3,
49,58,61,55,52,64,7,7],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2.(A6xA6).2^2",
0,
[1036800,1036800,100,100,3600,3600,100,100,20,20,90,90,90,90,40,40,40,20,20,
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144,144,36,36,36,36,36,36,36,36,256,128,128,32,32,32,32,64,32,32,2304,2304,
5760,2880,192,64,192,1152,1440,1440],
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,63,64,65,66,67]],
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[TENSOR,[28,4]],
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[TENSOR,[40,2]],
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[TENSOR,[50,2]],[128,-128,2,-2,8,-8,3,-3,0,0,-1,1,-1,1,0,0,0,
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[TENSOR,[58,3]],[200,-200,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-20,20,20,-20,-2,
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[TENSOR,[60,2]],[200,-200,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-20,20,20,-20,-2,
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[TENSOR,[62,2]],[288,288,-2,-2,-7,-7,-2,-2,0,0,2,2,2,2,1,1,1,0,0,-18,-18,-18,
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0,16,16,0,0,0,0,0,0],[320,320,0,0,10,10,0,0,0,0,1,1,1,1,-2,0,0,0,0,-4,-4,-4,-4
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-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,
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[GALOIS,[66,7]]],
[(53,54),(51,52),(46,47),(18,19),(16,17),( 9,10),
( 3, 8)( 4, 7)( 9,18)(10,19)(41,42)(43,45)(49,50)(51,53)(52,54)(56,57)(66,67),
(11,13)(12,14)(20,23)(21,22)(24,27)(25,26)(30,35)(31,36)(32,37)(33,39)(34,38)
(40,44)(41,43)(42,45)(58,59)(62,64)
]);
ALF("2.(A6xA6).2^2","(A6xA6):2^2",[1,1,3,3,2,2,4,4,23,23,5,5,6,6,7,8,8,
29,29,9,9,10,10,11,11,13,13,12,12,14,30,15,31,32,16,33,17,34,35,36,24,37,
25,39,40,38,38,18,19,19,42,42,26,26,41,43,27,45,44,20,21,48,22,47,46,28,
49]);
ALF("2.(A6xA6).2^2","2.A12",[1,2,21,20,18,19,20,21,42,43,53,54,55,56,41,
57,58,42,43,7,6,8,9,9,8,10,11,12,13,22,48,48,23,22,24,51,49,25,26,24,25,
25,27,27,27,28,29,5,17,17,33,34,33,34,15,17,17,4,3,3,14,16,16,14,5,4,4],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2.(A8xA4).2",
0,
[967680,967680,161280,120960,120960,48,48,24,36,96,288,1080,1080,1440,8640,
8640,768,2304,288,192,192,72,72,2880,2880,90,90,60,360,360,90,90,90,90,120,720
,720,40,40,20,36,36,48,144,144,864,864,108,108,576,4608,1536,24,24,192,192,72,
72,42,42,42,42,28,168,168,24,64,192,64,64,48,128,384,32,32,16],
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,45,47,61,61,60,60,65,64,64,19,18,18,18,17,50,51,51,72,72,73],[1,2,3,1,2,21,21
,20,18,17,18,1,2,3,1,2,17,18,18,20,21,25,24,24,25,37,36,35,37,36,36,37,36,37,
35,36,37,38,39,40,51,51,52,51,3,1,2,2,1,51,51,52,56,55,55,56,25,24,65,64,64,65
,63,64,65,68,67,68,69,70,73,72,73,74,75,76],,[1,2,3,4,5,7,6,8,9,10,11,12,13,14
,15,16,17,18,19,20,21,22,23,24,25,13,12,14,16,15,12,13,4,5,3,1,2,25,25,24,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,75,74,76],,[1,2,3,4,5,7,6,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,32,31,28,29,30,27,26,33,34,35,36,37,39,38,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,5,4,4,5,3,1,2,66,67,68,69,70,71,72,73,
75,74,76]],
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35,-1,-1,-1,-1,-1,-1,1,1,0,0,0,0,0,0],[216,-216,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[76,2]]],
[(70,71),(55,56),(53,54),(50,51),(48,49),(40,41),(38,39),(74,76)(75,77)]);
ALF("2.(A7xA5).2","2.A12",[1,2,3,7,6,3,22,14,3,5,22,5,23,16,6,7,22,8,9,
22,24,48,22,23,24,9,8,24,12,13,14,48,15,14,16,48,48,49,49,50,50,19,18,41,
54,53,41,61,61,57,58,26,28,29,51,51,30,31,52,60,59,19,18,41,54,53,61,55,
56,57,58,20,21,62,63,64,65]);

MOT("2.2^5.S6",
[
"origin: Dixon's Algorithm"
],
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32,32,32,20,288,72,48,192,192,32,32,32,16,20,144,48,36,24,24,12,12,20,20,24,24
],
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20,21,22,2,2,3,26,27,28,29,30,31,32,8,9,8,11,10,12,13,40,41,27,26],,[1,2,3,4,5
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[GALOIS,[40,11]],[80,-80,0,0,0,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2,0,0,0,
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[GALOIS,[42,5]]],
[(40,41),(29,30),(12,13)(20,21)(38,39),
(10,11)(18,19)(20,21)(26,27)(36,37)(42,43)]);
ALF("2.2^5.S6","2^5:S6",[1,1,2,9,28,12,10,4,3,26,27,22,23,8,6,5,21,31,30,
17,18,19,12,10,15,24,25,7,16,16,29,19,14,13,11,37,36,33,32,20,20,35,34]);
ALF("2.2^5.S6","2.A12",[1,2,5,5,5,8,10,4,3,3,4,4,4,4,15,17,17,17,15,17,17,
20,9,11,26,14,16,16,33,34,32,21,25,24,27,25,24,27,27,42,43,51,49],[
"fusion map is unique up to table autom."
]);

MOT("2^(1+6)_-.3^3.S4",
[
"origin: Dixon's Algorithm"
],
[82944,82944,1536,4608,1536,3456,432,324,324,3456,432,324,324,192,288,72,128,
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,144,36,36,36,36,32,32,16,16,48,48,24],
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33,33,33,46,47,48,49,35,35,34]],
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0],
[TENSOR,[37,2]],[81,81,9,-27,-3,0,0,0,0,0,0,0,0,0,0,0,1,-3,-3,1,3,-1,0,0,0,0,
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[TENSOR,[41,2]],[32,-32,0,0,0,-16,8,-4,-4,16,-8,4,4,0,0,0,0,0,0,0,0,0,0,0,0,2
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[GALOIS,[44,2]],
[TENSOR,[44,2]],
[TENSOR,[45,2]],[64,-64,0,0,0,16,4,2*E(3)-4*E(3)^2,-4*E(3)+2*E(3)^2,-16,-4,
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[GALOIS,[48,2]],[96,-96,0,0,0,-24,0,6,6,24,0,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[96,-96,0,0,0,0,-6,-3,-3,
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0],
[TENSOR,[51,2]]],
[(46,47),(40,41)(42,44)(43,45),
( 8, 9)(12,13)(28,29)(31,32)(38,39)(42,45)(43,44)(50,51)]);
ALF("2^(1+6)_-.3^3.S4","2^6:3^3:S4",[1,1,3,2,4,5,8,10,11,5,8,10,11,7,6,9,
15,12,14,17,13,16,18,20,19,24,24,21,22,23,21,22,35,36,33,34,26,38,40,29,
29,31,32,31,32,28,28,25,27,37,39,30]);
ALF("2^(1+6)_-.3^3.S4","2.A12",[1,2,5,3,4,6,8,12,12,7,9,13,13,23,22,24,5,
3,15,17,14,16,22,50,48,10,11,37,39,27,38,40,5,4,15,17,17,23,23,26,26,28,
28,29,29,33,34,16,32,50,50,25],[
"fusion map is unique up to table autom."
]);

MOT("2.3^4.2^3.S4",
[
"origin: Dixon's Algorithm"
],
[31104,31104,3888,1944,1296,972,3888,1944,1296,972,384,384,64,64,64,64,288,144
,72,72,36,36,108,54,108,54,12,12,54,54,54,54,54,54,72,36,36,36,36,288,288,32,
32,16,16,16,16,72,72,72,72],
[,[1,1,3,4,5,6,3,4,5,6,1,1,11,11,12,12,2,2,9,7,8,9,23,24,23,24,23,23,29,31,30,
29,31,30,1,3,6,6,5,17,17,17,17,15,15,13,13,19,19,20,20],[1,2,1,1,1,1,2,2,2,2,
11,12,13,14,15,16,17,18,17,17,18,18,1,1,2,2,11,12,6,6,6,10,10,10,35,35,35,35,
35,40,41,42,43,44,45,46,47,40,41,40,41]],
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1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[TENSOR,[6,2]],[3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,3,-1,3,3,-1,-1,0,0,0,0,0,
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[TENSOR,[8,2]],[4,4,4,4,4,4,4,4,4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-1,-1,1
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[TENSOR,[10,2]],[6,6,6,6,6,6,6,6,6,6,6,6,-2,-2,-2,-2,-2,2,-2,-2,2,2,0,0,0,0,0
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[TENSOR,[14,2]],[16,16,10,-8,4,-2,10,-8,4,-2,0,0,0,0,0,0,8,0,-4,2,0,0,-2,1,-2
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[TENSOR,[31,2]],[2,-2,2,2,2,2,-2,-2,-2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,-1,-1,1,1
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,-E(8)-E(8)^3],
[TENSOR,[33,2]],[4,-4,4,4,4,4,-4,-4,-4,-4,-4,4,0,0,4,-4,0,0,0,0,0,0,1,1,-1,-1
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],
[TENSOR,[39,2]],[16,-16,10,-8,4,-2,-10,8,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,2,
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[TENSOR,[45,2]],[32,-32,-16,2,8,-4,16,-2,-8,4,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,-2
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[TENSOR,[49,2]],[64,-64,-8,-8,-8,10,8,8,8,-10,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2
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[(37,38),(30,31)(33,34),(40,41)(42,43)(44,45)(46,47)(48,49)(50,51),
(11,12)(13,15)(14,16)(27,28)(42,43)(44,46)(45,47)]);
ALF("2.3^4.2^3.S4","3^4:2^3.S4",[1,1,2,5,3,4,2,5,3,4,9,9,10,10,14,14,6,
11,8,7,13,12,16,17,16,17,15,15,18,19,20,18,19,20,27,28,26,26,25,22,22,21,
21,29,29,30,30,24,24,23,23]);
ALF("2.3^4.2^3.S4","2.A12",[1,2,6,10,8,12,7,11,9,13,5,5,17,17,17,17,3,4,
24,22,27,25,12,10,13,11,28,29,35,37,39,36,38,40,5,23,28,29,26,14,14,16,16,
33,34,34,33,49,49,48,48],[
"fusion map determined using the groups"
]);

MOT("2.(2^4:A5)",
[
"origin: Dixon's Algorithm"
],
[1920,1920,192,96,8,32,32,16,10,10,10,10,24,24,12,12,12],
[,[1,1,1,2,4,3,3,2,11,11,10,10,13,13,14,13,13],[1,2,3,4,5,6,7,8,12,11,10,9,1,2
,4,3,3],,[1,2,3,4,5,6,7,8,2,1,1,2,13,14,15,17,16]],
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[GALOIS,[2,2]],[4,4,4,4,0,0,0,0,-1,-1,-1,-1,1,1,1,1,1],[4,-4,0,0,0,-2,2,0,1,
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1,0,0,0,0,2,2,-2,0,0],[5,5,-3,1,-1,1,1,1,0,0,0,0,-1,-1,1,-E(3)+E(3)^2,
E(3)-E(3)^2],
[GALOIS,[8,2]],[10,10,2,-2,0,2,2,-2,0,0,0,0,1,1,1,-1,-1],[10,10,2,-2,0,-2,-2,
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E(5)^2+E(5)^3,-E(5)^2-E(5)^3,0,0,0,0,0],
[GALOIS,[12,2]],[15,15,-9,3,1,-1,-1,-1,0,0,0,0,0,0,0,0,0],[16,-16,0,0,0,0,0,0
,-1,1,1,-1,-2,2,0,0,0],[20,20,4,-4,0,0,0,0,0,0,0,0,-1,-1,-1,1,1],[20,-20,0,0,0
,-2,2,0,0,0,0,0,2,-2,0,0,0]],
[(16,17),( 9,12)(10,11)]);
ALF("2.(2^4:A5)","2.U4(2)",[1,2,3,4,15,14,13,4,17,16,16,17,9,10,26,22,23],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(2^4:A5)","P1/G1/L1/V1/ext2",[1,1,3,2,5,6,6,4,12,12,11,11,7,7,10,8,
9]);

MOT("2x3^(1+2)+:2A4",
0,
0,
0,
0,
[
( 2, 3)( 6, 7)( 9,10)(11,18)(12,20)(13,19)(14,21)(15,22)(16,24)(17,23)(26,27)
(30,31)(33,34)(35,42)(36,44)(37,43)(38,45)(39,46)(40,48)(41,47)
,
(11,12,13)(15,16,17)(18,20,19)(22,24,23)(35,36,37)(39,40,41)(42,44,43)
(46,48,47)
],
["ConstructDirectProduct",[["Cyclic",2],["3^(1+2)+:2A4"]]]);
ALF("2x3^(1+2)+:2A4","2.U4(2)",[1,5,7,11,3,19,21,13,31,33,5,9,11,29,18,23,
24,7,11,9,27,20,25,22,2,6,8,12,3,18,20,14,32,34,6,10,12,30,19,23,25,8,12,
10,28,21,24,22],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("(2x3^3).S4`",
[
"origin: Dixon's Algorithm"
],
[1296,324,324,216,108,1296,324,324,216,108,24,12,18,18,18,18,18,18,36,36,36,36
,36,36,36,36,36,8,8],
[,[1,3,2,4,5,1,3,2,4,5,6,9,13,15,14,13,15,14,1,3,2,4,5,3,4,2,5,11,11],[1,1,1,1
,1,6,6,6,6,6,11,11,1,3,2,6,8,7,19,19,19,19,19,19,19,19,19,28,29]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2
,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,-2,-2,-2,-2,-2,0,0,-1,-1,
-1,1,1,1,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[4,2]],[3,3,3,3,3,3,3,3,3,3,-1,-1,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1
,-1,1,1],
[TENSOR,[6,2]],[4,4,4,4,4,-4,-4,-4,-4,-4,0,0,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0
,0,0],[4,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,-2,1,-4,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,2,
-1,0,0,1,E(3)^2,E(3),-1,-E(3)^2,-E(3),0,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,0,
-E(3)+E(3)^2,E(3)+2*E(3)^2,0,2*E(3)+E(3)^2,E(3)-E(3)^2,0,0],
[GALOIS,[9,2]],
[TENSOR,[9,2]],
[TENSOR,[10,2]],[4,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,-2,1,4,-E(3)+2*E(3)^2,
2*E(3)-E(3)^2,-2,1,0,0,1,E(3)^2,E(3),1,E(3)^2,E(3),-2,E(3),E(3)^2,-2*E(3)^2,1,
E(3),-2*E(3),E(3)^2,1,0,0],
[GALOIS,[13,2]],
[TENSOR,[13,2]],
[TENSOR,[14,2]],[6,-3,-3,3,0,6,-3,-3,3,0,2,-1,0,0,0,0,0,0,2,-1,-1,-1,2,-1,-1,
-1,2,0,0],
[TENSOR,[17,2]],[6,-3,-3,3,0,6,-3,-3,3,0,-2,1,0,0,0,0,0,0,0,-E(3)+E(3)^2,
E(3)-E(3)^2,E(3)-E(3)^2,0,-E(3)+E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0],
[TENSOR,[19,2]],[8,-2*E(3)+4*E(3)^2,4*E(3)-2*E(3)^2,-4,2,-8,2*E(3)-4*E(3)^2,
-4*E(3)+2*E(3)^2,4,-2,0,0,-1,-E(3)^2,-E(3),1,E(3)^2,E(3),0,0,0,0,0,0,0,0,0,0,0
],
[GALOIS,[21,2]],[8,-2*E(3)+4*E(3)^2,4*E(3)-2*E(3)^2,-4,2,8,-2*E(3)+4*E(3)^2,
4*E(3)-2*E(3)^2,-4,2,0,0,-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),0,0,0,0,0,0,0,0,0,0
,0],
[GALOIS,[23,2]],[12,-6,-6,6,0,-12,6,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[12,3,3,0,-3,12,3,3,0,-3,0,0,0,0,0,0,0,0,-2,1,1,-2,1,1,-2,1,1,0,0],
[TENSOR,[26,2]],[12,3,3,0,-3,-12,-3,-3,0,3,0,0,0,0,0,0,0,0,0,-E(3)+E(3)^2,
E(3)-E(3)^2,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0],
[TENSOR,[28,2]]],
[(28,29),(20,24)(21,26)(23,27),
( 2, 3)( 7, 8)(14,15)(17,18)(20,26)(21,24)(22,25)]);
ALF("(2x3^3).S4`","2.U4(2)",[1,5,7,9,11,2,6,8,10,12,4,26,11,29,27,12,30,
28,3,18,20,23,25,19,22,21,24,15,15],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(2x3^3).S4`","3^3:S4`",[1,2,3,4,5,1,2,3,4,5,6,7,9,10,8,9,10,8,15,14,
13,16,12,14,17,13,12,11,11]);

MOT("2.(2.(A4xA4).2)",
[
"origin: Dixon's Algorithm"
],
[1152,1152,576,96,96,32,36,36,36,36,48,48,8,72,72,36,144,144,144,144,24,24,12,
12,72,72,36,144,144,144,144,24,24,12,12],
[,[1,1,1,3,3,2,7,7,7,7,1,2,6,25,25,25,28,28,28,28,31,31,25,26,14,14,14,17,17,
17,17,19,19,14,15],[1,2,3,4,5,6,1,2,3,3,11,12,13,1,2,3,1,2,3,3,4,5,11,12,1,2,3
,1,2,3,3,4,5,11,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,
1,1,1,1,1,1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,1,1,-1,-1],[1,1
,1,1,1,1,1,1,1,1,-1,-1,-1,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,
E(3)^2,E(3)^2,-E(3)^2,-E(3)^2,E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3),
-E(3),-E(3)],
[GALOIS,[3,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],[2,2,2,2,2,2,-1,-1,-1,-1,0,0,0,2,2,2,-1,-1,-1,-1,-1,-1,0,0,2,2
,2,-1,-1,-1,-1,-1,-1,0,0],
[TENSOR,[7,4]],
[TENSOR,[7,3]],[4,-4,0,2,-2,0,-2,2,0,0,0,0,0,-2,2,0,1,-1,-3,3,-1,1,0,0,-2,2,0
,1,-1,3,-3,-1,1,0,0],[4,4,-4,0,0,0,1,1,-1,-1,-2,2,0,1,1,-1,-2,-2,2,2,0,0,1,-1,
1,1,-1,-2,-2,2,2,0,0,1,-1],
[TENSOR,[11,2]],[4,-4,0,2,-2,0,1,-1,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,-2*E(3)^2,
2*E(3)^2,0,-3*E(3)-2*E(3)^2,3*E(3)+2*E(3)^2,E(3)+2*E(3)^2,-E(3)-2*E(3)^2,-E(3)
,E(3),0,0,-2*E(3),2*E(3),0,-2*E(3)-3*E(3)^2,2*E(3)+3*E(3)^2,-2*E(3)-E(3)^2,
2*E(3)+E(3)^2,-E(3)^2,E(3)^2,0,0],
[GALOIS,[13,2]],
[TENSOR,[13,4]],
[TENSOR,[14,3]],
[TENSOR,[13,3]],
[TENSOR,[14,4]],
[TENSOR,[10,3]],
[TENSOR,[10,4]],
[TENSOR,[11,5]],
[TENSOR,[11,6]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],[6,6,6,2,2,-2,0,0,0,0,0,0,0,0,0,0,3,3,3,3,-1,-1,0,0,0,0,0,3,3
,3,3,-1,-1,0,0],
[TENSOR,[25,4]],
[TENSOR,[25,3]],[8,8,-8,0,0,0,-1,-1,1,1,0,0,0,2,2,-2,2,2,-2,-2,0,0,0,0,2,2,-2
,2,2,-2,-2,0,0,0,0],
[TENSOR,[28,3]],
[TENSOR,[28,4]],[9,9,9,-3,-3,1,0,0,0,0,-3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],
[TENSOR,[31,2]],[12,-12,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,-3,3,-3,3,1,-1,0,0,0,0,0
,-3,3,3,-3,1,-1,0,0],
[TENSOR,[33,4]],
[TENSOR,[33,3]]],
[
( 9,10)(14,25)(15,26)(16,27)(17,28)(18,29)(19,31)(20,30)(21,32)(22,33)(23,34)
(24,35)
]);
ALF("2.(2.(A4xA4).2)","2.U4(2)",[1,2,3,13,14,4,11,12,24,25,3,4,15,9,10,22,
5,6,19,18,31,32,23,26,9,10,23,7,8,20,21,33,34,22,26],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(2.(A4xA4).2)","b33141",[1,1,4,3,3,2,5,5,6,6,21,23,22,11,11,13,17,
17,19,19,15,15,8,10,12,12,14,18,18,20,20,16,16,7,9]);

MOT("3xF4(2)",
[
"3rd maximal subgroup of 3.2E6(2)"
],
0,
0,
0,
[( 80, 81)(175,176)(270,271),( 78, 79)(173,174)(268,269),
( 69, 70)( 96,191)( 97,192)( 98,193)( 99,194)(100,195)(101,196)(102,197)
(103,198)(104,199)(105,200)(106,201)(107,202)(108,203)(109,204)(110,205)
(111,206)(112,207)(113,208)(114,209)(115,210)(116,211)(117,212)(118,213)
(119,214)(120,215)(121,216)(122,217)(123,218)(124,219)(125,220)(126,221)
(127,222)(128,223)(129,224)(130,225)(131,226)(132,227)(133,228)(134,229)
(135,230)(136,231)(137,232)(138,233)(139,234)(140,235)(141,236)(142,237)
(143,238)(144,239)(145,240)(146,241)(147,242)(148,243)(149,244)(150,245)
(151,246)(152,247)(153,248)(154,249)(155,250)(156,251)(157,252)(158,253)
(159,254)(160,255)(161,256)(162,257)(163,258)(164,260)(165,259)(166,261)
(167,262)(168,263)(169,264)(170,265)(171,266)(172,267)(173,268)(174,269)
(175,270)(176,271)(177,272)(178,273)(179,274)(180,275)(181,276)(182,277)
(183,278)(184,279)(185,280)(186,281)(187,282)(188,283)(189,284)(190,285)
,
( 96,191)( 97,192)( 98,193)( 99,194)(100,195)(101,196)(102,197)(103,198)
(104,199)(105,200)(106,201)(107,202)(108,203)(109,204)(110,205)(111,206)
(112,207)(113,208)(114,209)(115,210)(116,211)(117,212)(118,213)(119,214)
(120,215)(121,216)(122,217)(123,218)(124,219)(125,220)(126,221)(127,222)
(128,223)(129,224)(130,225)(131,226)(132,227)(133,228)(134,229)(135,230)
(136,231)(137,232)(138,233)(139,234)(140,235)(141,236)(142,237)(143,238)
(144,239)(145,240)(146,241)(147,242)(148,243)(149,244)(150,245)(151,246)
(152,247)(153,248)(154,249)(155,250)(156,251)(157,252)(158,253)(159,254)
(160,255)(161,256)(162,257)(163,258)(164,259)(165,260)(166,261)(167,262)
(168,263)(169,264)(170,265)(171,266)(172,267)(173,268)(174,269)(175,270)
(176,271)(177,272)(178,273)(179,274)(180,275)(181,276)(182,277)(183,278)
(184,279)(185,280)(186,281)(187,282)(188,283)(189,284)(190,285)
,
(  2,  3)(  6,  7)(  9, 10)( 11, 12)( 15, 16)( 18, 19)( 25, 26)( 27, 28)
( 29, 30)( 31, 32)( 33, 34)( 36, 37)( 40, 41)( 42, 43)( 44, 45)( 49, 50)
( 51, 52)( 54, 55)( 56, 57)( 58, 59)( 60, 61)( 62, 63)( 64, 65)( 66, 67)
( 72, 73)( 74, 75)( 82, 83)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 94, 95)
( 97, 98)(101,102)(104,105)(106,107)(110,111)(113,114)(120,121)(122,123)
(124,125)(126,127)(128,129)(131,132)(135,136)(137,138)(139,140)(144,145)
(146,147)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)
(167,168)(169,170)(177,178)(181,182)(183,184)(185,186)(187,188)(189,190)
(192,193)(196,197)(199,200)(201,202)(205,206)(208,209)(215,216)(217,218)
(219,220)(221,222)(223,224)(226,227)(230,231)(232,233)(234,235)(239,240)
(241,242)(244,245)(246,247)(248,249)(250,251)(252,253)(254,255)(256,257)
(262,263)(264,265)(272,273)(276,277)(278,279)(280,281)(282,283)(284,285)
],
["ConstructDirectProduct",[["Cyclic",3],["F4(2)"]]]);
ALF("3xF4(2)","3.2E6(2)",[1,4,7,7,10,13,16,17,21,27,18,27,39,39,36,42,42,
54,39,51,54,57,60,63,66,76,70,69,73,82,70,76,79,85,86,90,87,126,126,93,
105,96,105,117,126,117,135,138,144,141,145,148,148,174,163,160,183,192,
201,192,201,174,173,195,201,198,208,205,218,222,223,229,226,235,232,256,
256,247,247,265,268,277,278,290,290,294,293,308,303,308,304,326,317,332,
329,2,5,8,8,11,14,16,17,22,28,19,28,40,40,37,43,43,55,40,52,55,58,61,64,
67,77,71,69,74,83,71,77,80,85,86,91,88,127,127,94,106,97,106,118,127,118,
136,139,144,142,146,149,149,175,163,161,184,193,202,193,202,175,173,196,
202,199,209,205,219,220,224,230,227,236,233,257,257,248,248,266,269,277,
279,291,291,295,293,309,303,309,304,327,318,333,330,3,6,9,9,12,15,16,17,
23,29,20,29,41,41,38,44,44,56,41,53,56,59,62,65,68,78,72,69,75,84,72,78,
81,85,86,92,89,128,128,95,107,98,107,119,128,119,137,140,144,143,147,150,
150,176,163,162,185,194,203,194,203,176,173,197,203,200,210,205,217,221,
225,231,228,237,234,258,258,249,249,267,270,277,280,292,292,296,293,310,
303,310,304,328,319,334,331],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("3xF4(2)",["3.2E6(2)M3"]);

MOT("3.2E6(2)M4",
[
"4th maximal subgroup of 3.2E6(2),\n",
"differs from 3.2E6(2)M3 = 3xF4(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3xF4(2)"]]);
ALF("3.2E6(2)M4","2E6(2)M4",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
95,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95]);
ALF("3.2E6(2)M4","3.2E6(2)",[1,4,7,7,10,13,16,17,21,30,18,30,39,39,36,45,
45,54,39,51,54,57,60,63,66,76,70,69,73,82,70,76,79,85,86,90,87,129,129,93,
108,96,108,120,129,120,135,138,144,141,145,148,148,177,163,160,186,192,
201,192,201,177,173,195,201,198,211,206,219,221,223,229,226,235,232,259,
259,250,250,265,268,277,278,290,290,294,293,311,303,311,304,326,320,332,
329,2,5,8,8,11,14,16,17,22,31,19,31,40,40,37,46,46,55,40,52,55,58,61,64,
67,77,71,69,74,83,71,77,80,85,86,91,88,130,130,94,109,97,109,121,130,121,
136,139,144,142,146,149,149,178,163,161,187,193,202,193,202,178,173,196,
202,199,212,206,217,222,224,230,227,236,233,260,260,251,251,266,269,277,
279,291,291,295,293,312,303,312,304,327,321,333,330,3,6,9,9,12,15,16,17,
23,32,20,32,41,41,38,47,47,56,41,53,56,59,62,65,68,78,72,69,75,84,72,78,
81,85,86,92,89,131,131,95,110,98,110,122,131,122,137,140,144,143,147,150,
150,179,163,162,188,194,203,194,203,179,173,197,203,200,213,206,218,220,
225,231,228,237,234,261,261,252,252,267,270,277,280,292,292,296,293,313,
303,313,304,328,322,334,331],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3.2E6(2)M5",
[
"5th maximal subgroup of 3.2E6(2),\n",
"differs from 3.2E6(2)M3 = 3xF4(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3xF4(2)"]]);
ALF("3.2E6(2)M5","2E6(2)M5",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
95,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95]);
ALF("3.2E6(2)M5","3.2E6(2)",[1,4,7,7,10,13,16,17,21,33,18,33,39,39,36,48,
48,54,39,51,54,57,60,63,66,76,70,69,73,82,70,76,79,85,86,90,87,132,132,93,
111,96,111,123,132,123,135,138,144,141,145,148,148,180,163,160,189,192,
201,192,201,180,173,195,201,198,214,207,217,220,223,229,226,235,232,262,
262,253,253,265,268,277,278,290,290,294,293,314,303,314,304,326,323,332,
329,2,5,8,8,11,14,16,17,22,34,19,34,40,40,37,49,49,55,40,52,55,58,61,64,
67,77,71,69,74,83,71,77,80,85,86,91,88,133,133,94,112,97,112,124,133,124,
136,139,144,142,146,149,149,181,163,161,190,193,202,193,202,181,173,196,
202,199,215,207,218,221,224,230,227,236,233,263,263,254,254,266,269,277,
279,291,291,295,293,315,303,315,304,327,324,333,330,3,6,9,9,12,15,16,17,
23,35,20,35,41,41,38,50,50,56,41,53,56,59,62,65,68,78,72,69,75,84,72,78,
81,85,86,92,89,134,134,95,113,98,113,125,134,125,137,140,144,143,147,150,
150,182,163,162,191,194,203,194,203,182,173,197,203,200,216,207,219,222,
225,231,228,237,234,264,264,255,255,267,270,277,280,292,292,296,293,316,
303,316,304,328,325,334,331],[
"equals the map from 3xF4(2), mapped under an outer autom."
]);

MOT("3.2E6(2)M8",
[
"8th maximal subgroup of 3.2E6(2),\n",
"differs from 3.2E6(2)M7 = 3.Fi22 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.Fi22"]]);
ALF("3.2E6(2)M8","2E6(2)M8",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,7,8,9,9,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,
18,18,19,20,20,20,21,22,23,23,23,24,25,26,26,26,27,27,27,28,28,28,29,29,
29,30,30,30,31,31,31,32,33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,
39,39,39,40,40,40,41,41,41,42,43,44,45,45,45,46,46,46,47,47,47,48,49,49,
49,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,58,
58,58,59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65]);
ALF("3.2E6(2)M8","3.2E6(2)",[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,17,16,17,
30,32,31,39,41,40,45,47,46,51,53,52,54,56,55,63,65,64,66,68,67,73,75,74,
82,84,83,70,72,71,69,79,81,80,86,85,76,78,77,85,86,90,92,91,108,110,109,
108,110,109,120,122,121,135,137,136,141,143,142,144,144,145,147,146,148,
150,149,151,153,152,154,156,155,186,188,187,177,179,178,177,179,178,192,
194,193,207,205,204,211,213,212,195,197,196,201,203,202,206,223,225,224,
223,225,224,229,231,230,235,237,236,250,252,251,250,252,251,271,273,272,
274,276,275,277,278,280,279,290,292,291,294,296,295,297,299,298,300,302,
301,311,313,312,311,313,312,332,334,333],[
"fusion map is unique up to table automorphisms,\n",
"representative compatible with factors,\n",
"equals the map from 3.2E6(2)M7, mapped under an outer autom."
]);

MOT("3.2E6(2)M9",
[
"9th maximal subgroup of 3.2E6(2),\n",
"differs from 3.2E6(2)M7 = 3.Fi22 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.Fi22"]]);
ALF("3.2E6(2)M9","2E6(2)M9",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,7,8,9,9,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,
18,18,19,20,20,20,21,22,23,23,23,24,25,26,26,26,27,27,27,28,28,28,29,29,
29,30,30,30,31,31,31,32,33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,
39,39,39,40,40,40,41,41,41,42,43,44,45,45,45,46,46,46,47,47,47,48,49,49,
49,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,58,
58,58,59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65]);
ALF("3.2E6(2)M9","3.2E6(2)",[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,17,16,17,
33,35,34,39,41,40,48,50,49,51,53,52,54,56,55,63,65,64,66,68,67,73,75,74,
82,84,83,70,72,71,69,79,81,80,86,85,76,78,77,85,86,90,92,91,111,113,112,
111,113,112,123,125,124,135,137,136,141,143,142,144,144,145,147,146,148,
150,149,151,153,152,154,156,155,189,191,190,180,182,181,180,182,181,192,
194,193,205,206,204,214,216,215,195,197,196,201,203,202,207,223,225,224,
223,225,224,229,231,230,235,237,236,253,255,254,253,255,254,271,273,272,
274,276,275,277,278,280,279,290,292,291,294,296,295,297,299,298,300,302,
301,314,316,315,314,316,315,332,334,333],[
"equals the map from 3.2E6(2)M7, mapped under an outer autom."
]);

MOT("6xF4(2)",
[
"3rd maximal subgroup of 6.2E6(2)"
],
0,
0,
0,
[( 80, 81)(175,176)(270,271)(365,366)(460,461)(555,556),
( 78, 79)(173,174)(268,269)(363,364)(458,459)(553,554),
( 69, 70)(164,165)(259,260)(354,355)(449,450)(544,545),
( 96,476)( 97,477)( 98,478)( 99,479)(100,480)(101,481)(102,482)(103,483)
(104,484)(105,485)(106,486)(107,487)(108,488)(109,489)(110,490)(111,491)
(112,492)(113,493)(114,494)(115,495)(116,496)(117,497)(118,498)(119,499)
(120,500)(121,501)(122,502)(123,503)(124,504)(125,505)(126,506)(127,507)
(128,508)(129,509)(130,510)(131,511)(132,512)(133,513)(134,514)(135,515)
(136,516)(137,517)(138,518)(139,519)(140,520)(141,521)(142,522)(143,523)
(144,524)(145,525)(146,526)(147,527)(148,528)(149,529)(150,530)(151,531)
(152,532)(153,533)(154,534)(155,535)(156,536)(157,537)(158,538)(159,539)
(160,540)(161,541)(162,542)(163,543)(164,544)(165,545)(166,546)(167,547)
(168,548)(169,549)(170,550)(171,551)(172,552)(173,553)(174,554)(175,555)
(176,556)(177,557)(178,558)(179,559)(180,560)(181,561)(182,562)(183,563)
(184,564)(185,565)(186,566)(187,567)(188,568)(189,569)(190,570)(191,381)
(192,382)(193,383)(194,384)(195,385)(196,386)(197,387)(198,388)(199,389)
(200,390)(201,391)(202,392)(203,393)(204,394)(205,395)(206,396)(207,397)
(208,398)(209,399)(210,400)(211,401)(212,402)(213,403)(214,404)(215,405)
(216,406)(217,407)(218,408)(219,409)(220,410)(221,411)(222,412)(223,413)
(224,414)(225,415)(226,416)(227,417)(228,418)(229,419)(230,420)(231,421)
(232,422)(233,423)(234,424)(235,425)(236,426)(237,427)(238,428)(239,429)
(240,430)(241,431)(242,432)(243,433)(244,434)(245,435)(246,436)(247,437)
(248,438)(249,439)(250,440)(251,441)(252,442)(253,443)(254,444)(255,445)
(256,446)(257,447)(258,448)(259,449)(260,450)(261,451)(262,452)(263,453)
(264,454)(265,455)(266,456)(267,457)(268,458)(269,459)(270,460)(271,461)
(272,462)(273,463)(274,464)(275,465)(276,466)(277,467)(278,468)(279,469)
(280,470)(281,471)(282,472)(283,473)(284,474)(285,475)
,
(  2,  3)(  6,  7)(  9, 10)( 11, 12)( 15, 16)( 18, 19)( 25, 26)( 27, 28)
( 29, 30)( 31, 32)( 33, 34)( 36, 37)( 40, 41)( 42, 43)( 44, 45)( 49, 50)
( 51, 52)( 54, 55)( 56, 57)( 58, 59)( 60, 61)( 62, 63)( 64, 65)( 66, 67)
( 72, 73)( 74, 75)( 82, 83)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 94, 95)
( 97, 98)(101,102)(104,105)(106,107)(110,111)(113,114)(120,121)(122,123)
(124,125)(126,127)(128,129)(131,132)(135,136)(137,138)(139,140)(144,145)
(146,147)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)
(167,168)(169,170)(177,178)(181,182)(183,184)(185,186)(187,188)(189,190)
(192,193)(196,197)(199,200)(201,202)(205,206)(208,209)(215,216)(217,218)
(219,220)(221,222)(223,224)(226,227)(230,231)(232,233)(234,235)(239,240)
(241,242)(244,245)(246,247)(248,249)(250,251)(252,253)(254,255)(256,257)
(262,263)(264,265)(272,273)(276,277)(278,279)(280,281)(282,283)(284,285)
(287,288)(291,292)(294,295)(296,297)(300,301)(303,304)(310,311)(312,313)
(314,315)(316,317)(318,319)(321,322)(325,326)(327,328)(329,330)(334,335)
(336,337)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(357,358)(359,360)(367,368)(371,372)(373,374)(375,376)(377,378)(379,380)
(382,383)(386,387)(389,390)(391,392)(395,396)(398,399)(405,406)(407,408)
(409,410)(411,412)(413,414)(416,417)(420,421)(422,423)(424,425)(429,430)
(431,432)(434,435)(436,437)(438,439)(440,441)(442,443)(444,445)(446,447)
(452,453)(454,455)(462,463)(466,467)(468,469)(470,471)(472,473)(474,475)
(477,478)(481,482)(484,485)(486,487)(490,491)(493,494)(500,501)(502,503)
(504,505)(506,507)(508,509)(511,512)(515,516)(517,518)(519,520)(524,525)
(526,527)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)
(547,548)(549,550)(557,558)(561,562)(563,564)(565,566)(567,568)(569,570)
],
["ConstructDirectProduct",[["Cyclic",6],["F4(2)"]]]);
ALF("6xF4(2)","6.2E6(2)",[1,7,13,13,19,22,28,30,38,44,32,44,59,59,56,68,
65,83,59,77,83,86,89,92,98,118,106,104,112,127,106,118,124,133,135,143,
137,191,191,149,167,152,164,182,191,179,203,206,218,212,220,226,226,263,
250,247,275,287,299,287,299,263,261,293,299,296,316,307,326,330,331,343,
337,355,349,385,382,370,370,394,400,418,420,444,444,452,450,480,470,477,
472,501,489,513,507,2,8,14,14,20,23,29,31,39,45,33,45,60,60,57,69,66,84,
60,78,84,87,90,93,99,119,107,105,113,128,107,119,125,134,136,144,138,192,
192,150,168,153,165,183,192,180,204,207,219,213,221,227,227,264,251,248,
276,288,300,288,300,264,262,294,300,297,317,308,327,328,332,344,338,356,
350,386,383,371,371,395,401,419,421,445,445,453,451,481,471,478,473,502,
490,514,508,3,9,15,15,21,24,28,30,40,46,34,46,61,61,58,70,67,85,61,79,85,
88,91,94,100,120,108,104,114,129,108,120,126,133,135,145,139,193,193,151,
169,154,166,184,193,181,205,208,218,214,222,228,228,265,250,249,277,289,
301,289,301,265,261,295,301,298,318,307,325,329,333,345,339,357,351,387,
384,372,372,396,402,418,422,446,446,454,450,482,470,479,472,503,491,515,
509,4,10,16,16,19,25,29,31,38,47,35,47,62,62,56,65,68,83,62,80,83,86,89,
95,101,121,109,105,115,130,109,121,124,134,136,146,140,194,194,149,164,
155,167,179,194,182,203,209,219,215,223,229,229,266,251,247,278,290,302,
290,302,266,262,293,302,296,313,308,326,330,334,346,340,358,352,382,385,
373,373,397,403,419,423,447,447,455,451,477,471,480,473,504,492,516,510,5,
11,17,17,20,26,28,30,39,48,36,48,63,63,57,66,69,84,63,81,84,87,90,96,102,
122,110,104,116,131,110,122,125,133,135,147,141,195,195,150,165,156,168,
180,195,183,204,210,218,216,224,230,230,267,250,248,279,291,303,291,303,
267,261,294,303,297,314,307,327,328,335,347,341,359,353,383,386,374,374,
398,404,418,424,448,448,456,450,478,470,481,472,505,493,517,511,6,12,18,
18,21,27,29,31,40,49,37,49,64,64,58,67,70,85,64,82,85,88,91,97,103,123,
111,105,117,132,111,123,126,134,136,148,142,196,196,151,166,157,169,181,
196,184,205,211,219,217,225,231,231,268,251,249,280,292,304,292,304,268,
262,295,304,298,315,308,325,329,336,348,342,360,354,384,387,375,375,399,
405,419,425,449,449,457,451,479,471,482,473,506,494,518,512],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("6xF4(2)",["6.2E6(2)M3"]);

MOT("3x2.F4(2)",
[
"4th maximal subgroup of 6.2E6(2)"
],
0,
0,
0,
[(139,141)(140,142)(309,311)(310,312)(479,481)(480,482),
(137,138)(307,308)(477,478),(133,134)(303,304)(473,474),
(121,122)(291,292)(461,462),
(171,341)(172,342)(173,343)(174,344)(175,345)(176,346)(177,347)(178,348)
(179,349)(180,350)(181,351)(182,352)(183,353)(184,354)(185,355)(186,356)
(187,357)(188,358)(189,359)(190,360)(191,361)(192,362)(193,363)(194,364)
(195,365)(196,366)(197,367)(198,368)(199,369)(200,370)(201,371)(202,372)
(203,373)(204,374)(205,375)(206,376)(207,377)(208,378)(209,379)(210,380)
(211,381)(212,382)(213,383)(214,384)(215,385)(216,386)(217,387)(218,388)
(219,389)(220,390)(221,391)(222,392)(223,393)(224,394)(225,395)(226,396)
(227,397)(228,398)(229,399)(230,400)(231,401)(232,402)(233,403)(234,404)
(235,405)(236,406)(237,407)(238,408)(239,409)(240,410)(241,411)(242,412)
(243,413)(244,414)(245,415)(246,416)(247,417)(248,418)(249,419)(250,420)
(251,421)(252,422)(253,423)(254,424)(255,425)(256,426)(257,427)(258,428)
(259,429)(260,430)(261,431)(262,432)(263,433)(264,434)(265,435)(266,436)
(267,437)(268,438)(269,439)(270,440)(271,441)(272,442)(273,443)(274,444)
(275,445)(276,446)(277,447)(278,448)(279,449)(280,450)(281,451)(282,452)
(283,453)(284,454)(285,455)(286,456)(287,457)(288,458)(289,459)(290,460)
(291,461)(292,462)(293,463)(294,464)(295,465)(296,466)(297,467)(298,468)
(299,469)(300,470)(301,471)(302,472)(303,473)(304,474)(305,475)(306,476)
(307,477)(308,478)(309,479)(310,480)(311,481)(312,482)(313,483)(314,484)
(315,485)(316,486)(317,487)(318,488)(319,489)(320,490)(321,491)(322,492)
(323,493)(324,494)(325,495)(326,496)(327,497)(328,498)(329,499)(330,500)
(331,501)(332,502)(333,503)(334,504)(335,505)(336,506)(337,507)(338,508)
(339,509)(340,510)
,
(  3,  5)(  4,  6)( 11, 13)( 12, 14)( 17, 18)( 19, 21)( 20, 22)( 25, 26)
( 27, 28)( 31, 33)( 32, 34)( 42, 44)( 43, 45)( 46, 48)( 47, 49)( 50, 52)
( 51, 53)( 54, 56)( 55, 57)( 58, 60)( 59, 61)( 64, 66)( 65, 67)( 71, 73)
( 72, 74)( 75, 77)( 76, 78)( 79, 80)( 85, 87)( 86, 88)( 89, 91)( 90, 92)
( 95, 97)( 96, 98)( 99,100)(101,103)(102,104)(105,108)(106,107)(109,111)
(110,112)(113,115)(114,116)(117,118)(125,127)(126,128)(129,131)(130,132)
(143,145)(144,146)(149,150)(151,153)(152,154)(155,157)(156,158)(159,161)
(160,162)(163,165)(164,166)(167,170)(168,169)(173,175)(174,176)(181,183)
(182,184)(187,188)(189,191)(190,192)(195,196)(197,198)(201,203)(202,204)
(212,214)(213,215)(216,218)(217,219)(220,222)(221,223)(224,226)(225,227)
(228,230)(229,231)(234,236)(235,237)(241,243)(242,244)(245,247)(246,248)
(249,250)(255,257)(256,258)(259,261)(260,262)(265,267)(266,268)(269,270)
(271,273)(272,274)(275,278)(276,277)(279,281)(280,282)(283,285)(284,286)
(287,288)(295,297)(296,298)(299,301)(300,302)(313,315)(314,316)(319,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,340)(338,339)(343,345)(344,346)(351,353)(352,354)(357,358)(359,361)
(360,362)(365,366)(367,368)(371,373)(372,374)(382,384)(383,385)(386,388)
(387,389)(390,392)(391,393)(394,396)(395,397)(398,400)(399,401)(404,406)
(405,407)(411,413)(412,414)(415,417)(416,418)(419,420)(425,427)(426,428)
(429,431)(430,432)(435,437)(436,438)(439,440)(441,443)(442,444)(445,448)
(446,447)(449,451)(450,452)(453,455)(454,456)(457,458)(465,467)(466,468)
(469,471)(470,472)(483,485)(484,486)(489,490)(491,493)(492,494)(495,497)
(496,498)(499,501)(500,502)(503,505)(504,506)(507,510)(508,509)
],
["ConstructDirectProduct",[["Cyclic",3],["2.F4(2)"]]]);
ALF("3x2.F4(2)","2E6(2)M4",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,
12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,
27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,
39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,
53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,
67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,
81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,
93,94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,
14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,
29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,
41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,
55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,
70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,
83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,
95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,
17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,
31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,
43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,
58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,
72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,
85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95]);
ALF("3x2.F4(2)","3.2E6(2)M4",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,
12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,
26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,
38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,
53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,
66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,
81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,
93,93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,
104,105,106,106,107,107,108,108,109,109,110,111,112,112,113,113,114,114,
115,115,116,117,118,119,119,120,120,121,121,122,122,123,123,124,124,125,
125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,133,133,134,
135,135,136,136,137,137,138,138,139,140,141,142,143,143,144,144,145,145,
146,146,147,147,148,148,149,149,150,150,151,152,153,153,154,154,155,155,
156,156,157,157,158,158,159,159,160,160,161,162,163,163,164,165,166,166,
167,167,168,168,169,169,170,170,171,171,172,172,173,174,175,175,176,176,
177,177,178,178,179,179,180,180,181,181,182,182,183,183,184,184,185,185,
186,186,187,187,188,188,189,189,190,190,191,191,192,192,193,193,194,194,
195,195,196,196,197,197,198,198,199,200,201,201,202,202,203,203,204,204,
205,206,207,207,208,208,209,209,210,210,211,212,213,214,214,215,215,216,
216,217,217,218,218,219,219,220,220,221,221,222,222,223,223,224,224,225,
225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,234,235,
236,237,238,238,239,239,240,240,241,241,242,242,243,243,244,244,245,245,
246,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,255,255,
256,257,258,258,259,260,261,261,262,262,263,263,264,264,265,265,266,266,
267,267,268,269,270,270,271,271,272,272,273,273,274,274,275,275,276,276,
277,277,278,278,279,279,280,280,281,281,282,282,283,283,284,284,285,285]);
ALF("3x2.F4(2)","6.2E6(2)",[1,4,7,10,16,13,13,16,19,19,22,25,28,29,30,31,
38,50,32,35,50,50,62,59,62,59,56,71,71,71,83,83,59,62,77,80,83,86,89,92,
95,98,101,121,118,109,106,104,105,112,115,130,127,106,109,118,121,124,124,
134,133,136,135,143,146,137,140,197,197,197,149,149,170,170,152,155,170,
170,185,197,185,203,206,209,218,219,212,215,220,223,229,226,226,229,269,
269,250,251,247,281,290,287,302,299,290,287,302,299,269,269,261,262,293,
293,299,302,296,319,309,310,327,329,331,334,343,346,340,337,355,358,349,
352,388,388,388,388,376,376,394,397,400,403,418,419,423,420,447,444,447,
444,452,455,450,451,483,483,471,470,483,483,472,473,501,504,495,495,516,
513,510,507,5,2,11,8,14,17,17,14,20,20,26,23,28,29,30,31,39,51,36,33,51,
51,60,63,60,63,57,72,72,72,84,84,63,60,81,78,84,87,90,96,93,102,99,119,
122,107,110,104,105,116,113,128,131,110,107,122,119,125,125,134,133,136,
135,147,144,141,138,198,198,198,150,150,171,171,156,153,171,171,186,198,
186,204,210,207,218,219,216,213,224,221,227,230,230,227,270,270,250,251,
248,282,288,291,300,303,288,291,300,303,270,270,261,262,294,294,303,300,
297,320,309,310,325,330,335,332,347,344,338,341,359,356,353,350,389,389,
389,389,377,377,398,395,404,401,418,419,421,424,445,448,445,448,456,453,
450,451,484,484,471,470,484,484,472,473,505,502,496,496,514,517,508,511,3,
6,9,12,18,15,15,18,21,21,24,27,28,29,30,31,40,52,34,37,52,52,64,61,64,61,
58,73,73,73,85,85,61,64,79,82,85,88,91,94,97,100,103,123,120,111,108,104,
105,114,117,132,129,108,111,120,123,126,126,134,133,136,135,145,148,139,
142,199,199,199,151,151,172,172,154,157,172,172,187,199,187,205,208,211,
218,219,214,217,222,225,231,228,228,231,271,271,250,251,249,283,292,289,
304,301,292,289,304,301,271,271,261,262,295,295,301,304,298,321,309,310,
326,328,333,336,345,348,342,339,357,360,351,354,390,390,390,390,378,378,
396,399,402,405,418,419,425,422,449,446,449,446,454,457,450,451,485,485,
471,470,485,485,472,473,503,506,497,497,518,515,512,509],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);
ALN("3x2.F4(2)",["6.2E6(2)M4"]);

MOT("6.2E6(2)M5",
[
"5th maximal subgroup of 6.2E6(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["3x2.F4(2)"]]);
ALF("6.2E6(2)M5","2E6(2)M5",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,
12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,
26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,
38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,
53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,
66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,
81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,
93,93,94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,
14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,
28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,
41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,
55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,
69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,
83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,
95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,
17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,
30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,
43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,
58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,
72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,
85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95]);
ALF("6.2E6(2)M5","2.2E6(2)M5",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,
90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,
129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,
147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,
165,166,167,168,169,170,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,
132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,
150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,
168,169,170]);
ALF("6.2E6(2)M5","3.2E6(2)M5",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,
12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,
26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,
38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,
53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,
66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,
81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,
93,93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,
104,105,106,106,107,107,108,108,109,109,110,111,112,112,113,113,114,114,
115,115,116,117,118,119,119,120,120,121,121,122,122,123,123,124,124,125,
125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,133,133,134,
135,135,136,136,137,137,138,138,139,140,141,142,143,143,144,144,145,145,
146,146,147,147,148,148,149,149,150,150,151,152,153,153,154,154,155,155,
156,156,157,157,158,158,159,159,160,160,161,162,163,163,164,165,166,166,
167,167,168,168,169,169,170,170,171,171,172,172,173,174,175,175,176,176,
177,177,178,178,179,179,180,180,181,181,182,182,183,183,184,184,185,185,
186,186,187,187,188,188,189,189,190,190,191,191,192,192,193,193,194,194,
195,195,196,196,197,197,198,198,199,200,201,201,202,202,203,203,204,204,
205,206,207,207,208,208,209,209,210,210,211,212,213,214,214,215,215,216,
216,217,217,218,218,219,219,220,220,221,221,222,222,223,223,224,224,225,
225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,234,235,
236,237,238,238,239,239,240,240,241,241,242,242,243,243,244,244,245,245,
246,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,255,255,
256,257,258,258,259,260,261,261,262,262,263,263,264,264,265,265,266,266,
267,267,268,269,270,270,271,271,272,272,273,273,274,274,275,275,276,276,
277,277,278,278,279,279,280,280,281,281,282,282,283,283,284,284,285,285]);
ALF("6.2E6(2)M5","6.2E6(2)",[1,4,7,10,16,13,13,16,19,19,22,25,28,29,30,31,
38,53,32,35,53,53,62,59,62,59,56,74,74,74,83,83,59,62,77,80,83,86,89,92,
95,98,101,121,118,109,106,104,105,112,115,130,127,106,109,118,121,124,124,
134,133,136,135,143,146,137,140,200,200,200,149,149,173,173,152,155,173,
173,188,200,188,203,206,209,218,219,212,215,220,223,229,226,226,229,272,
272,250,251,247,284,290,287,302,299,290,287,302,299,272,272,261,262,293,
293,299,302,296,322,311,312,325,328,331,334,343,346,340,337,355,358,349,
352,391,391,391,391,379,379,394,397,400,403,418,419,423,420,447,444,447,
444,452,455,450,451,486,486,471,470,486,486,472,473,501,504,498,498,516,
513,510,507,5,2,11,8,14,17,17,14,20,20,26,23,28,29,30,31,39,54,36,33,54,
54,60,63,60,63,57,75,75,75,84,84,63,60,81,78,84,87,90,96,93,102,99,119,
122,107,110,104,105,116,113,128,131,110,107,122,119,125,125,134,133,136,
135,147,144,141,138,201,201,201,150,150,174,174,156,153,174,174,189,201,
189,204,210,207,218,219,216,213,224,221,227,230,230,227,273,273,250,251,
248,285,288,291,300,303,288,291,300,303,273,273,261,262,294,294,303,300,
297,323,311,312,326,329,335,332,347,344,338,341,359,356,353,350,392,392,
392,392,380,380,398,395,404,401,418,419,421,424,445,448,445,448,456,453,
450,451,487,487,471,470,487,487,472,473,505,502,499,499,514,517,508,511,3,
6,9,12,18,15,15,18,21,21,24,27,28,29,30,31,40,55,34,37,55,55,64,61,64,61,
58,76,76,76,85,85,61,64,79,82,85,88,91,94,97,100,103,123,120,111,108,104,
105,114,117,132,129,108,111,120,123,126,126,134,133,136,135,145,148,139,
142,202,202,202,151,151,175,175,154,157,175,175,190,202,190,205,208,211,
218,219,214,217,222,225,231,228,228,231,274,274,250,251,249,286,292,289,
304,301,292,289,304,301,274,274,261,262,295,295,301,304,298,324,311,312,
327,330,333,336,345,348,342,339,357,360,351,354,393,393,393,393,381,381,
396,399,402,405,418,419,425,422,449,446,449,446,454,457,450,451,488,488,
471,470,488,488,472,473,503,506,500,500,518,515,512,509],[
"fusion map is unique up to table automorphisms,\n",
"equals the map from 3x2.F4(2), mapped under an outer autom."
]);

MOT("6x2.F4(2)",
[
"3rd maximal subgroup of (2^2x3).2E6(2)"
],
0,
0,
0,
[
(139,141)(140,142)(309,311)(310,312)(479,481)(480,482)(649,651)(650,652)
(819,821)(820,822)(989,991)(990,992)
,(137,138)(307,308)(477,478)(647,648)(817,818)(987,988),
(133,134)(303,304)(473,474)(643,644)(813,814)(983,984),
(121,122)(291,292)(461,462)(631,632)(801,802)(971,972),
( 171, 172)( 173, 174)( 175, 176)( 177, 178)( 179, 180)( 181, 182)( 183, 184)
( 185, 186)( 189, 190)( 191, 192)( 193, 194)( 195, 196)( 199, 200)( 201, 202)
( 203, 204)( 205, 206)( 210, 211)( 212, 213)( 214, 215)( 216, 217)( 218, 219)
( 220, 221)( 222, 223)( 224, 225)( 226, 227)( 228, 229)( 230, 231)( 232, 233)
( 234, 235)( 236, 237)( 238, 239)( 241, 242)( 243, 244)( 245, 246)( 247, 248)
( 253, 254)( 255, 256)( 257, 258)( 259, 260)( 261, 262)( 263, 264)( 265, 266)
( 267, 268)( 271, 272)( 273, 274)( 275, 276)( 277, 278)( 279, 280)( 281, 282)
( 283, 284)( 285, 286)( 289, 290)( 293, 294)( 295, 296)( 297, 298)( 299, 300)
( 301, 302)( 303, 304)( 305, 306)( 309, 310)( 311, 312)( 313, 314)( 315, 316)
( 317, 318)( 319, 320)( 321, 322)( 323, 324)( 325, 326)( 327, 328)( 329, 330)
( 331, 332)( 333, 334)( 335, 336)( 337, 338)( 339, 340)( 511, 512)( 513, 514)
( 515, 516)( 517, 518)( 519, 520)( 521, 522)( 523, 524)( 525, 526)( 529, 530)
( 531, 532)( 533, 534)( 535, 536)( 539, 540)( 541, 542)( 543, 544)( 545, 546)
( 550, 551)( 552, 553)( 554, 555)( 556, 557)( 558, 559)( 560, 561)( 562, 563)
( 564, 565)( 566, 567)( 568, 569)( 570, 571)( 572, 573)( 574, 575)( 576, 577)
( 578, 579)( 581, 582)( 583, 584)( 585, 586)( 587, 588)( 593, 594)( 595, 596)
( 597, 598)( 599, 600)( 601, 602)( 603, 604)( 605, 606)( 607, 608)( 611, 612)
( 613, 614)( 615, 616)( 617, 618)( 619, 620)( 621, 622)( 623, 624)( 625, 626)
( 629, 630)( 633, 634)( 635, 636)( 637, 638)( 639, 640)( 641, 642)( 643, 644)
( 645, 646)( 649, 650)( 651, 652)( 653, 654)( 655, 656)( 657, 658)( 659, 660)
( 661, 662)( 663, 664)( 665, 666)( 667, 668)( 669, 670)( 671, 672)( 673, 674)
( 675, 676)( 677, 678)( 679, 680)( 851, 852)( 853, 854)( 855, 856)( 857, 858)
( 859, 860)( 861, 862)( 863, 864)( 865, 866)( 869, 870)( 871, 872)( 873, 874)
( 875, 876)( 879, 880)( 881, 882)( 883, 884)( 885, 886)( 890, 891)( 892, 893)
( 894, 895)( 896, 897)( 898, 899)( 900, 901)( 902, 903)( 904, 905)( 906, 907)
( 908, 909)( 910, 911)( 912, 913)( 914, 915)( 916, 917)( 918, 919)( 921, 922)
( 923, 924)( 925, 926)( 927, 928)( 933, 934)( 935, 936)( 937, 938)( 939, 940)
( 941, 942)( 943, 944)( 945, 946)( 947, 948)( 951, 952)( 953, 954)( 955, 956)
( 957, 958)( 959, 960)( 961, 962)( 963, 964)( 965, 966)( 969, 970)( 973, 974)
( 975, 976)( 977, 978)( 979, 980)( 981, 982)( 983, 984)( 985, 986)( 989, 990)
( 991, 992)( 993, 994)( 995, 996)( 997, 998)( 999,1000)(1001,1002)(1003,1004)
(1005,1006)(1007,1008)(1009,1010)(1011,1012)(1013,1014)(1015,1016)(1017,1018)
(1019,1020)
,
( 171, 851)( 172, 852)( 173, 853)( 174, 854)( 175, 855)( 176, 856)( 177, 857)
( 178, 858)( 179, 859)( 180, 860)( 181, 861)( 182, 862)( 183, 863)( 184, 864)
( 185, 865)( 186, 866)( 187, 867)( 188, 868)( 189, 869)( 190, 870)( 191, 871)
( 192, 872)( 193, 873)( 194, 874)( 195, 875)( 196, 876)( 197, 877)( 198, 878)
( 199, 879)( 200, 880)( 201, 881)( 202, 882)( 203, 883)( 204, 884)( 205, 885)
( 206, 886)( 207, 887)( 208, 888)( 209, 889)( 210, 890)( 211, 891)( 212, 892)
( 213, 893)( 214, 894)( 215, 895)( 216, 896)( 217, 897)( 218, 898)( 219, 899)
( 220, 900)( 221, 901)( 222, 902)( 223, 903)( 224, 904)( 225, 905)( 226, 906)
( 227, 907)( 228, 908)( 229, 909)( 230, 910)( 231, 911)( 232, 912)( 233, 913)
( 234, 914)( 235, 915)( 236, 916)( 237, 917)( 238, 918)( 239, 919)( 240, 920)
( 241, 921)( 242, 922)( 243, 923)( 244, 924)( 245, 925)( 246, 926)( 247, 927)
( 248, 928)( 249, 929)( 250, 930)( 251, 931)( 252, 932)( 253, 933)( 254, 934)
( 255, 935)( 256, 936)( 257, 937)( 258, 938)( 259, 939)( 260, 940)( 261, 941)
( 262, 942)( 263, 943)( 264, 944)( 265, 945)( 266, 946)( 267, 947)( 268, 948)
( 269, 949)( 270, 950)( 271, 951)( 272, 952)( 273, 953)( 274, 954)( 275, 955)
( 276, 956)( 277, 957)( 278, 958)( 279, 959)( 280, 960)( 281, 961)( 282, 962)
( 283, 963)( 284, 964)( 285, 965)( 286, 966)( 287, 967)( 288, 968)( 289, 969)
( 290, 970)( 291, 971)( 292, 972)( 293, 973)( 294, 974)( 295, 975)( 296, 976)
( 297, 977)( 298, 978)( 299, 979)( 300, 980)( 301, 981)( 302, 982)( 303, 983)
( 304, 984)( 305, 985)( 306, 986)( 307, 987)( 308, 988)( 309, 989)( 310, 990)
( 311, 991)( 312, 992)( 313, 993)( 314, 994)( 315, 995)( 316, 996)( 317, 997)
( 318, 998)( 319, 999)( 320,1000)( 321,1001)( 322,1002)( 323,1003)( 324,1004)
( 325,1005)( 326,1006)( 327,1007)( 328,1008)( 329,1009)( 330,1010)( 331,1011)
( 332,1012)( 333,1013)( 334,1014)( 335,1015)( 336,1016)( 337,1017)( 338,1018)
( 339,1019)( 340,1020)( 341, 681)( 342, 682)( 343, 683)( 344, 684)( 345, 685)
( 346, 686)( 347, 687)( 348, 688)( 349, 689)( 350, 690)( 351, 691)( 352, 692)
( 353, 693)( 354, 694)( 355, 695)( 356, 696)( 357, 697)( 358, 698)( 359, 699)
( 360, 700)( 361, 701)( 362, 702)( 363, 703)( 364, 704)( 365, 705)( 366, 706)
( 367, 707)( 368, 708)( 369, 709)( 370, 710)( 371, 711)( 372, 712)( 373, 713)
( 374, 714)( 375, 715)( 376, 716)( 377, 717)( 378, 718)( 379, 719)( 380, 720)
( 381, 721)( 382, 722)( 383, 723)( 384, 724)( 385, 725)( 386, 726)( 387, 727)
( 388, 728)( 389, 729)( 390, 730)( 391, 731)( 392, 732)( 393, 733)( 394, 734)
( 395, 735)( 396, 736)( 397, 737)( 398, 738)( 399, 739)( 400, 740)( 401, 741)
( 402, 742)( 403, 743)( 404, 744)( 405, 745)( 406, 746)( 407, 747)( 408, 748)
( 409, 749)( 410, 750)( 411, 751)( 412, 752)( 413, 753)( 414, 754)( 415, 755)
( 416, 756)( 417, 757)( 418, 758)( 419, 759)( 420, 760)( 421, 761)( 422, 762)
( 423, 763)( 424, 764)( 425, 765)( 426, 766)( 427, 767)( 428, 768)( 429, 769)
( 430, 770)( 431, 771)( 432, 772)( 433, 773)( 434, 774)( 435, 775)( 436, 776)
( 437, 777)( 438, 778)( 439, 779)( 440, 780)( 441, 781)( 442, 782)( 443, 783)
( 444, 784)( 445, 785)( 446, 786)( 447, 787)( 448, 788)( 449, 789)( 450, 790)
( 451, 791)( 452, 792)( 453, 793)( 454, 794)( 455, 795)( 456, 796)( 457, 797)
( 458, 798)( 459, 799)( 460, 800)( 461, 801)( 462, 802)( 463, 803)( 464, 804)
( 465, 805)( 466, 806)( 467, 807)( 468, 808)( 469, 809)( 470, 810)( 471, 811)
( 472, 812)( 473, 813)( 474, 814)( 475, 815)( 476, 816)( 477, 817)( 478, 818)
( 479, 819)( 480, 820)( 481, 821)( 482, 822)( 483, 823)( 484, 824)( 485, 825)
( 486, 826)( 487, 827)( 488, 828)( 489, 829)( 490, 830)( 491, 831)( 492, 832)
( 493, 833)( 494, 834)( 495, 835)( 496, 836)( 497, 837)( 498, 838)( 499, 839)
( 500, 840)( 501, 841)( 502, 842)( 503, 843)( 504, 844)( 505, 845)( 506, 846)
( 507, 847)( 508, 848)( 509, 849)( 510, 850)
,
(   3,   5)(   4,   6)(  11,  13)(  12,  14)(  17,  18)(  19,  21)(  20,  22)
(  25,  26)(  27,  28)(  31,  33)(  32,  34)(  42,  44)(  43,  45)(  46,  48)
(  47,  49)(  50,  52)(  51,  53)(  54,  56)(  55,  57)(  58,  60)(  59,  61)
(  64,  66)(  65,  67)(  71,  73)(  72,  74)(  75,  77)(  76,  78)(  79,  80)
(  85,  87)(  86,  88)(  89,  91)(  90,  92)(  95,  97)(  96,  98)(  99, 100)
( 101, 103)( 102, 104)( 105, 108)( 106, 107)( 109, 111)( 110, 112)( 113, 115)
( 114, 116)( 117, 118)( 125, 127)( 126, 128)( 129, 131)( 130, 132)( 143, 145)
( 144, 146)( 149, 150)( 151, 153)( 152, 154)( 155, 157)( 156, 158)( 159, 161)
( 160, 162)( 163, 165)( 164, 166)( 167, 170)( 168, 169)( 173, 175)( 174, 176)
( 181, 183)( 182, 184)( 187, 188)( 189, 191)( 190, 192)( 195, 196)( 197, 198)
( 201, 203)( 202, 204)( 212, 214)( 213, 215)( 216, 218)( 217, 219)( 220, 222)
( 221, 223)( 224, 226)( 225, 227)( 228, 230)( 229, 231)( 234, 236)( 235, 237)
( 241, 243)( 242, 244)( 245, 247)( 246, 248)( 249, 250)( 255, 257)( 256, 258)
( 259, 261)( 260, 262)( 265, 267)( 266, 268)( 269, 270)( 271, 273)( 272, 274)
( 275, 278)( 276, 277)( 279, 281)( 280, 282)( 283, 285)( 284, 286)( 287, 288)
( 295, 297)( 296, 298)( 299, 301)( 300, 302)( 313, 315)( 314, 316)( 319, 320)
( 321, 323)( 322, 324)( 325, 327)( 326, 328)( 329, 331)( 330, 332)( 333, 335)
( 334, 336)( 337, 340)( 338, 339)( 343, 345)( 344, 346)( 351, 353)( 352, 354)
( 357, 358)( 359, 361)( 360, 362)( 365, 366)( 367, 368)( 371, 373)( 372, 374)
( 382, 384)( 383, 385)( 386, 388)( 387, 389)( 390, 392)( 391, 393)( 394, 396)
( 395, 397)( 398, 400)( 399, 401)( 404, 406)( 405, 407)( 411, 413)( 412, 414)
( 415, 417)( 416, 418)( 419, 420)( 425, 427)( 426, 428)( 429, 431)( 430, 432)
( 435, 437)( 436, 438)( 439, 440)( 441, 443)( 442, 444)( 445, 448)( 446, 447)
( 449, 451)( 450, 452)( 453, 455)( 454, 456)( 457, 458)( 465, 467)( 466, 468)
( 469, 471)( 470, 472)( 483, 485)( 484, 486)( 489, 490)( 491, 493)( 492, 494)
( 495, 497)( 496, 498)( 499, 501)( 500, 502)( 503, 505)( 504, 506)( 507, 510)
( 508, 509)( 513, 515)( 514, 516)( 521, 523)( 522, 524)( 527, 528)( 529, 531)
( 530, 532)( 535, 536)( 537, 538)( 541, 543)( 542, 544)( 552, 554)( 553, 555)
( 556, 558)( 557, 559)( 560, 562)( 561, 563)( 564, 566)( 565, 567)( 568, 570)
( 569, 571)( 574, 576)( 575, 577)( 581, 583)( 582, 584)( 585, 587)( 586, 588)
( 589, 590)( 595, 597)( 596, 598)( 599, 601)( 600, 602)( 605, 607)( 606, 608)
( 609, 610)( 611, 613)( 612, 614)( 615, 618)( 616, 617)( 619, 621)( 620, 622)
( 623, 625)( 624, 626)( 627, 628)( 635, 637)( 636, 638)( 639, 641)( 640, 642)
( 653, 655)( 654, 656)( 659, 660)( 661, 663)( 662, 664)( 665, 667)( 666, 668)
( 669, 671)( 670, 672)( 673, 675)( 674, 676)( 677, 680)( 678, 679)( 683, 685)
( 684, 686)( 691, 693)( 692, 694)( 697, 698)( 699, 701)( 700, 702)( 705, 706)
( 707, 708)( 711, 713)( 712, 714)( 722, 724)( 723, 725)( 726, 728)( 727, 729)
( 730, 732)( 731, 733)( 734, 736)( 735, 737)( 738, 740)( 739, 741)( 744, 746)
( 745, 747)( 751, 753)( 752, 754)( 755, 757)( 756, 758)( 759, 760)( 765, 767)
( 766, 768)( 769, 771)( 770, 772)( 775, 777)( 776, 778)( 779, 780)( 781, 783)
( 782, 784)( 785, 788)( 786, 787)( 789, 791)( 790, 792)( 793, 795)( 794, 796)
( 797, 798)( 805, 807)( 806, 808)( 809, 811)( 810, 812)( 823, 825)( 824, 826)
( 829, 830)( 831, 833)( 832, 834)( 835, 837)( 836, 838)( 839, 841)( 840, 842)
( 843, 845)( 844, 846)( 847, 850)( 848, 849)( 853, 855)( 854, 856)( 861, 863)
( 862, 864)( 867, 868)( 869, 871)( 870, 872)( 875, 876)( 877, 878)( 881, 883)
( 882, 884)( 892, 894)( 893, 895)( 896, 898)( 897, 899)( 900, 902)( 901, 903)
( 904, 906)( 905, 907)( 908, 910)( 909, 911)( 914, 916)( 915, 917)( 921, 923)
( 922, 924)( 925, 927)( 926, 928)( 929, 930)( 935, 937)( 936, 938)( 939, 941)
( 940, 942)( 945, 947)( 946, 948)( 949, 950)( 951, 953)( 952, 954)( 955, 958)
( 956, 957)( 959, 961)( 960, 962)( 963, 965)( 964, 966)( 967, 968)( 975, 977)
( 976, 978)( 979, 981)( 980, 982)( 993, 995)( 994, 996)( 999,1000)(1001,1003)
(1002,1004)(1005,1007)(1006,1008)(1009,1011)(1010,1012)(1013,1015)(1014,1016)
(1017,1020)(1018,1019)
],
["ConstructDirectProduct",[["Cyclic",6],["2.F4(2)"]]]);
ALF("6x2.F4(2)","6xF4(2)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,
12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,
27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,
39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,
53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,
67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,
81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,
93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,
104,105,106,106,107,107,108,108,109,109,110,111,112,112,113,113,114,114,
115,115,116,117,118,119,119,120,120,121,121,122,122,123,123,124,124,125,
125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,133,133,134,
135,135,136,136,137,137,138,138,139,140,141,142,143,143,144,144,145,145,
146,146,147,147,148,148,149,149,150,150,151,152,153,153,154,154,155,155,
156,156,157,157,158,158,159,159,160,160,161,162,163,163,164,165,166,166,
167,167,168,168,169,169,170,170,171,171,172,172,173,174,175,175,176,176,
177,177,178,178,179,179,180,180,181,181,182,182,183,183,184,184,185,185,
186,186,187,187,188,188,189,189,190,190,191,191,192,192,193,193,194,194,
195,195,196,196,197,197,198,198,199,200,201,201,202,202,203,203,204,204,
205,206,207,207,208,208,209,209,210,210,211,212,213,214,214,215,215,216,
216,217,217,218,218,219,219,220,220,221,221,222,222,223,223,224,224,225,
225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,234,235,
236,237,238,238,239,239,240,240,241,241,242,242,243,243,244,244,245,245,
246,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,255,255,
256,257,258,258,259,260,261,261,262,262,263,263,264,264,265,265,266,266,
267,267,268,269,270,270,271,271,272,272,273,273,274,274,275,275,276,276,
277,277,278,278,279,279,280,280,281,281,282,282,283,283,284,284,285,285,
286,286,287,287,288,288,289,289,290,290,291,291,292,292,293,293,294,295,
296,296,297,297,298,298,299,299,300,301,302,302,303,303,304,304,305,305,
306,307,308,309,309,310,310,311,311,312,312,313,313,314,314,315,315,316,
316,317,317,318,318,319,319,320,320,321,321,322,322,323,323,324,325,325,
326,326,327,327,328,328,329,330,331,332,333,333,334,334,335,335,336,336,
337,337,338,338,339,339,340,340,341,342,343,343,344,344,345,345,346,346,
347,347,348,348,349,349,350,350,351,352,353,353,354,355,356,356,357,357,
358,358,359,359,360,360,361,361,362,362,363,364,365,365,366,366,367,367,
368,368,369,369,370,370,371,371,372,372,373,373,374,374,375,375,376,376,
377,377,378,378,379,379,380,380,381,381,382,382,383,383,384,384,385,385,
386,386,387,387,388,388,389,390,391,391,392,392,393,393,394,394,395,396,
397,397,398,398,399,399,400,400,401,402,403,404,404,405,405,406,406,407,
407,408,408,409,409,410,410,411,411,412,412,413,413,414,414,415,415,416,
416,417,417,418,418,419,420,420,421,421,422,422,423,423,424,425,426,427,
428,428,429,429,430,430,431,431,432,432,433,433,434,434,435,435,436,437,
438,438,439,439,440,440,441,441,442,442,443,443,444,444,445,445,446,447,
448,448,449,450,451,451,452,452,453,453,454,454,455,455,456,456,457,457,
458,459,460,460,461,461,462,462,463,463,464,464,465,465,466,466,467,467,
468,468,469,469,470,470,471,471,472,472,473,473,474,474,475,475,476,476,
477,477,478,478,479,479,480,480,481,481,482,482,483,483,484,485,486,486,
487,487,488,488,489,489,490,491,492,492,493,493,494,494,495,495,496,497,
498,499,499,500,500,501,501,502,502,503,503,504,504,505,505,506,506,507,
507,508,508,509,509,510,510,511,511,512,512,513,513,514,515,515,516,516,
517,517,518,518,519,520,521,522,523,523,524,524,525,525,526,526,527,527,
528,528,529,529,530,530,531,532,533,533,534,534,535,535,536,536,537,537,
538,538,539,539,540,540,541,542,543,543,544,545,546,546,547,547,548,548,
549,549,550,550,551,551,552,552,553,554,555,555,556,556,557,557,558,558,
559,559,560,560,561,561,562,562,563,563,564,564,565,565,566,566,567,567,
568,568,569,569,570,570]);
ALF("6x2.F4(2)","2x2.F4(2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,
129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,
147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,
165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,
183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,
201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,
219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,
237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,
255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,
273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,
291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,
309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,
327,328,329,330,331,332,333,334,335,336,337,338,339,340,1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,
105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,
159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,
177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,
195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,
213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,
231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,
249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,
267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,
285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,
303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,
321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,
339,340,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,
98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,
135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,
171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,
189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,
207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,
225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,
243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,
261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,
279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,
297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,
315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,
333,334,335,336,337,338,339,340]);
ALF("6x2.F4(2)","3xF4(2)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,
12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,
27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,
39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,
53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,
67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,
81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,
93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,
104,105,106,106,107,107,108,108,109,109,110,111,112,112,113,113,114,114,
115,115,116,117,118,119,119,120,120,121,121,122,122,123,123,124,124,125,
125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,133,133,134,
135,135,136,136,137,137,138,138,139,140,141,142,143,143,144,144,145,145,
146,146,147,147,148,148,149,149,150,150,151,152,153,153,154,154,155,155,
156,156,157,157,158,158,159,159,160,160,161,162,163,163,164,165,166,166,
167,167,168,168,169,169,170,170,171,171,172,172,173,174,175,175,176,176,
177,177,178,178,179,179,180,180,181,181,182,182,183,183,184,184,185,185,
186,186,187,187,188,188,189,189,190,190,191,191,192,192,193,193,194,194,
195,195,196,196,197,197,198,198,199,200,201,201,202,202,203,203,204,204,
205,206,207,207,208,208,209,209,210,210,211,212,213,214,214,215,215,216,
216,217,217,218,218,219,219,220,220,221,221,222,222,223,223,224,224,225,
225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,234,235,
236,237,238,238,239,239,240,240,241,241,242,242,243,243,244,244,245,245,
246,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,255,255,
256,257,258,258,259,260,261,261,262,262,263,263,264,264,265,265,266,266,
267,267,268,269,270,270,271,271,272,272,273,273,274,274,275,275,276,276,
277,277,278,278,279,279,280,280,281,281,282,282,283,283,284,284,285,285,1,
1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,
18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,
32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,
45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,
59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,
73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,
86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,96,96,97,97,98,
98,99,99,100,100,101,101,102,102,103,103,104,105,106,106,107,107,108,108,
109,109,110,111,112,112,113,113,114,114,115,115,116,117,118,119,119,120,
120,121,121,122,122,123,123,124,124,125,125,126,126,127,127,128,128,129,
129,130,130,131,131,132,132,133,133,134,135,135,136,136,137,137,138,138,
139,140,141,142,143,143,144,144,145,145,146,146,147,147,148,148,149,149,
150,150,151,152,153,153,154,154,155,155,156,156,157,157,158,158,159,159,
160,160,161,162,163,163,164,165,166,166,167,167,168,168,169,169,170,170,
171,171,172,172,173,174,175,175,176,176,177,177,178,178,179,179,180,180,
181,181,182,182,183,183,184,184,185,185,186,186,187,187,188,188,189,189,
190,190,191,191,192,192,193,193,194,194,195,195,196,196,197,197,198,198,
199,200,201,201,202,202,203,203,204,204,205,206,207,207,208,208,209,209,
210,210,211,212,213,214,214,215,215,216,216,217,217,218,218,219,219,220,
220,221,221,222,222,223,223,224,224,225,225,226,226,227,227,228,228,229,
230,230,231,231,232,232,233,233,234,235,236,237,238,238,239,239,240,240,
241,241,242,242,243,243,244,244,245,245,246,247,248,248,249,249,250,250,
251,251,252,252,253,253,254,254,255,255,256,257,258,258,259,260,261,261,
262,262,263,263,264,264,265,265,266,266,267,267,268,269,270,270,271,271,
272,272,273,273,274,274,275,275,276,276,277,277,278,278,279,279,280,280,
281,281,282,282,283,283,284,284,285,285]);
ALF("6x2.F4(2)","2xF4(2)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,
12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,
27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,
39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,
53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,
67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,
81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,
93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,
104,105,106,106,107,107,108,108,109,109,110,111,112,112,113,113,114,114,
115,115,116,117,118,119,119,120,120,121,121,122,122,123,123,124,124,125,
125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,133,133,134,
135,135,136,136,137,137,138,138,139,140,141,142,143,143,144,144,145,145,
146,146,147,147,148,148,149,149,150,150,151,152,153,153,154,154,155,155,
156,156,157,157,158,158,159,159,160,160,161,162,163,163,164,165,166,166,
167,167,168,168,169,169,170,170,171,171,172,172,173,174,175,175,176,176,
177,177,178,178,179,179,180,180,181,181,182,182,183,183,184,184,185,185,
186,186,187,187,188,188,189,189,190,190,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,
10,11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,
25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,
37,37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,
51,52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,
64,65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,
79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,
91,92,92,93,93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,
102,103,103,104,105,106,106,107,107,108,108,109,109,110,111,112,112,113,
113,114,114,115,115,116,117,118,119,119,120,120,121,121,122,122,123,123,
124,124,125,125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,
133,133,134,135,135,136,136,137,137,138,138,139,140,141,142,143,143,144,
144,145,145,146,146,147,147,148,148,149,149,150,150,151,152,153,153,154,
154,155,155,156,156,157,157,158,158,159,159,160,160,161,162,163,163,164,
165,166,166,167,167,168,168,169,169,170,170,171,171,172,172,173,174,175,
175,176,176,177,177,178,178,179,179,180,180,181,181,182,182,183,183,184,
184,185,185,186,186,187,187,188,188,189,189,190,190,1,1,2,2,3,3,4,4,5,5,6,
6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,
22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,
35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,
49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,
62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,
76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,
89,90,90,91,91,92,92,93,93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,
101,101,102,102,103,103,104,105,106,106,107,107,108,108,109,109,110,111,
112,112,113,113,114,114,115,115,116,117,118,119,119,120,120,121,121,122,
122,123,123,124,124,125,125,126,126,127,127,128,128,129,129,130,130,131,
131,132,132,133,133,134,135,135,136,136,137,137,138,138,139,140,141,142,
143,143,144,144,145,145,146,146,147,147,148,148,149,149,150,150,151,152,
153,153,154,154,155,155,156,156,157,157,158,158,159,159,160,160,161,162,
163,163,164,165,166,166,167,167,168,168,169,169,170,170,171,171,172,172,
173,174,175,175,176,176,177,177,178,178,179,179,180,180,181,181,182,182,
183,183,184,184,185,185,186,186,187,187,188,188,189,189,190,190]);
ALF("6x2.F4(2)","F4(2)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,
13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,
27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,
40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,
68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,
82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,
94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,
15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,
29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,
42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,
56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,
71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,
84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,
1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,
18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,
32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,
45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,
59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,
73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,
86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,
5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,
20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,
34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,
48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,
61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,
75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,
88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,
8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,
24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,
36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,
50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,
63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,
77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,
90,91,91,92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,
11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,
26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,
38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,
52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,
65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,
80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,
92,93,93,94,94,95,95]);
ALF("6x2.F4(2)","(2^2x3).2E6(2)",[1,2,13,14,26,25,25,26,37,37,40,41,52,53,
56,57,72,78,60,61,78,78,100,99,100,99,96,112,111,111,141,141,99,100,129,
130,141,144,147,150,151,162,163,203,202,179,178,174,175,190,191,218,217,
178,179,202,203,214,214,230,229,234,233,249,250,237,238,321,321,321,261,
261,283,283,264,265,282,282,304,321,303,339,342,343,366,367,354,355,370,
371,383,382,382,383,441,441,424,425,421,459,478,477,496,495,478,477,496,
495,441,441,437,438,489,489,495,496,492,524,511,512,542,546,547,548,571,
572,560,559,595,596,583,584,635,635,634,634,616,616,652,653,664,665,700,
701,705,704,753,752,753,752,768,769,764,765,816,816,805,804,815,815,808,
809,851,852,833,833,876,875,864,863,6,5,18,17,29,30,30,29,38,38,45,44,54,
55,58,59,73,80,65,64,80,80,103,104,103,104,97,114,113,113,142,142,104,103,
134,133,142,145,148,155,154,167,166,206,207,182,183,176,177,195,194,221,
222,183,182,207,206,215,215,232,231,236,235,254,253,242,241,323,323,323,
262,262,285,285,269,268,284,284,306,323,305,340,347,346,368,369,359,358,
375,374,386,387,387,386,443,443,426,427,422,461,481,482,499,500,481,482,
499,500,443,443,439,440,490,490,500,499,493,526,513,514,543,544,552,551,
576,575,563,564,600,599,588,587,637,637,636,636,618,618,657,656,669,668,
702,703,708,709,756,757,756,757,773,772,766,767,818,818,807,806,817,817,
810,811,856,855,835,835,879,880,867,868,9,10,21,22,34,33,33,34,39,39,48,
49,52,53,56,57,74,82,68,69,82,82,108,107,108,107,98,116,115,115,143,143,
107,108,137,138,143,146,149,158,159,170,171,211,210,187,186,174,175,198,
199,226,225,186,187,210,211,216,216,230,229,234,233,257,258,245,246,325,
325,325,263,263,287,287,272,273,286,286,308,325,307,341,350,351,366,367,
362,363,378,379,391,390,390,391,445,445,424,425,423,463,486,485,504,503,
486,485,504,503,445,445,437,438,491,491,503,504,494,528,511,512,541,545,
555,556,579,580,568,567,603,604,591,592,639,639,638,638,620,620,660,661,
672,673,700,701,713,712,761,760,761,760,776,777,764,765,820,820,805,804,
819,819,808,809,859,860,837,837,884,883,872,871,3,4,15,16,28,27,27,28,37,
37,42,43,54,55,58,59,72,79,62,63,79,79,102,101,102,101,96,111,112,112,141,
141,101,102,131,132,141,144,147,152,153,164,165,205,204,181,180,176,177,
192,193,220,219,180,181,204,205,214,214,232,231,236,235,251,252,239,240,
322,322,322,261,261,282,282,266,267,283,283,303,322,304,339,344,345,368,
369,356,357,372,373,385,384,384,385,442,442,426,427,421,460,480,479,498,
497,480,479,498,497,442,442,439,440,489,489,497,498,492,523,513,514,542,
546,549,550,573,574,562,561,597,598,585,586,634,634,635,635,617,617,654,
655,666,667,702,703,707,706,755,754,755,754,770,771,766,767,815,815,807,
806,816,816,810,811,853,854,834,834,878,877,866,865,8,7,20,19,31,32,32,31,
38,38,47,46,52,53,56,57,73,81,67,66,81,81,105,106,105,106,97,113,114,114,
142,142,106,105,136,135,142,145,148,157,156,169,168,208,209,184,185,174,
175,197,196,223,224,185,184,209,208,215,215,230,229,234,233,256,255,244,
243,324,324,324,262,262,284,284,271,270,285,285,305,324,306,340,349,348,
366,367,361,360,377,376,388,389,389,388,444,444,424,425,422,462,483,484,
501,502,483,484,501,502,444,444,437,438,490,490,502,501,493,525,511,512,
543,544,554,553,578,577,565,566,602,601,590,589,636,636,637,637,619,619,
659,658,671,670,700,701,710,711,758,759,758,759,775,774,764,765,817,817,
805,804,818,818,808,809,858,857,836,836,881,882,869,870,11,12,23,24,36,35,
35,36,39,39,50,51,54,55,58,59,74,83,70,71,83,83,110,109,110,109,98,115,
116,116,143,143,109,110,139,140,143,146,149,160,161,172,173,213,212,189,
188,176,177,200,201,228,227,188,189,212,213,216,216,232,231,236,235,259,
260,247,248,326,326,326,263,263,286,286,274,275,287,287,307,326,308,341,
352,353,368,369,364,365,380,381,393,392,392,393,446,446,426,427,423,464,
488,487,506,505,488,487,506,505,446,446,439,440,491,491,505,506,494,527,
513,514,541,545,557,558,581,582,570,569,605,606,593,594,638,638,639,639,
621,621,662,663,674,675,702,703,715,714,763,762,763,762,778,779,766,767,
819,819,807,806,820,820,810,811,861,862,838,838,886,885,874,873],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);
ALN("6x2.F4(2)",["(2^2x3).2E6(2)M3"]);

MOT("(2^2x3).2E6(2)M4",
[
"4th maximal subgroup of (2^2x3).2E6(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["6x2.F4(2)"]]);
ALF("(2^2x3).2E6(2)M4","2E6(2)M4",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,
11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,
25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,
37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,
52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,
65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,
80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,
92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,
13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,
27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,
40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,
68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,
82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,
94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,
15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,
29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,
42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,
56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,
71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,
84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,
1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,
18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,
32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,
45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,
59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,
73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,
86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,
5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,
20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,
34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,
48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,
61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,
75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,
88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,
8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,
24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,
36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,
50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,
63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,
77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,
90,91,91,92,92,93,93,94,94,95,95]);
ALF("(2^2x3).2E6(2)M4","2.F4(2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,
128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,
146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,
164,165,166,167,168,169,170,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,17,18,
20,19,22,21,24,23,26,25,27,28,30,29,32,31,34,33,36,35,37,38,39,41,40,43,
42,45,44,47,46,49,48,51,50,53,52,55,54,57,56,59,58,61,60,63,62,65,64,67,
66,69,68,70,72,71,74,73,76,75,78,77,79,80,81,82,84,83,86,85,88,87,90,89,
92,91,94,93,96,95,98,97,99,100,102,101,104,103,106,105,108,107,110,109,
112,111,114,113,116,115,117,118,120,119,121,122,124,123,126,125,128,127,
130,129,132,131,134,133,136,135,137,138,140,139,142,141,144,143,146,145,
148,147,150,149,152,151,154,153,156,155,158,157,160,159,162,161,164,163,
166,165,168,167,170,169,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,17,18,20,19,22,
21,24,23,26,25,27,28,30,29,32,31,34,33,36,35,37,38,39,41,40,43,42,45,44,
47,46,49,48,51,50,53,52,55,54,57,56,59,58,61,60,63,62,65,64,67,66,69,68,
70,72,71,74,73,76,75,78,77,79,80,81,82,84,83,86,85,88,87,90,89,92,91,94,
93,96,95,98,97,99,100,102,101,104,103,106,105,108,107,110,109,112,111,114,
113,116,115,117,118,120,119,121,122,124,123,126,125,128,127,130,129,132,
131,134,133,136,135,137,138,140,139,142,141,144,143,146,145,148,147,150,
149,152,151,154,153,156,155,158,157,160,159,162,161,164,163,166,165,168,
167,170,169,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,
96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,
151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,
169,170,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,17,18,20,19,22,21,24,23,26,
25,27,28,30,29,32,31,34,33,36,35,37,38,39,41,40,43,42,45,44,47,46,49,48,
51,50,53,52,55,54,57,56,59,58,61,60,63,62,65,64,67,66,69,68,70,72,71,74,
73,76,75,78,77,79,80,81,82,84,83,86,85,88,87,90,89,92,91,94,93,96,95,98,
97,99,100,102,101,104,103,106,105,108,107,110,109,112,111,114,113,116,115,
117,118,120,119,121,122,124,123,126,125,128,127,130,129,132,131,134,133,
136,135,137,138,140,139,142,141,144,143,146,145,148,147,150,149,152,151,
154,153,156,155,158,157,160,159,162,161,164,163,166,165,168,167,170,169]);
ALF("(2^2x3).2E6(2)M4","3.2E6(2)M4",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,
11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,
25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,
37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,
52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,
65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,
80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,
92,92,93,93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,
103,103,104,105,106,106,107,107,108,108,109,109,110,111,112,112,113,113,
114,114,115,115,116,117,118,119,119,120,120,121,121,122,122,123,123,124,
124,125,125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,133,
133,134,135,135,136,136,137,137,138,138,139,140,141,142,143,143,144,144,
145,145,146,146,147,147,148,148,149,149,150,150,151,152,153,153,154,154,
155,155,156,156,157,157,158,158,159,159,160,160,161,162,163,163,164,165,
166,166,167,167,168,168,169,169,170,170,171,171,172,172,173,174,175,175,
176,176,177,177,178,178,179,179,180,180,181,181,182,182,183,183,184,184,
185,185,186,186,187,187,188,188,189,189,190,190,191,191,192,192,193,193,
194,194,195,195,196,196,197,197,198,198,199,200,201,201,202,202,203,203,
204,204,205,206,207,207,208,208,209,209,210,210,211,212,213,214,214,215,
215,216,216,217,217,218,218,219,219,220,220,221,221,222,222,223,223,224,
224,225,225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,
234,235,236,237,238,238,239,239,240,240,241,241,242,242,243,243,244,244,
245,245,246,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,
255,255,256,257,258,258,259,260,261,261,262,262,263,263,264,264,265,265,
266,266,267,267,268,269,270,270,271,271,272,272,273,273,274,274,275,275,
276,276,277,277,278,278,279,279,280,280,281,281,282,282,283,283,284,284,
285,285,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,
16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,
30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,
42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,
57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,
71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,
84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,96,
96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,104,105,106,106,107,
107,108,108,109,109,110,111,112,112,113,113,114,114,115,115,116,117,118,
119,119,120,120,121,121,122,122,123,123,124,124,125,125,126,126,127,127,
128,128,129,129,130,130,131,131,132,132,133,133,134,135,135,136,136,137,
137,138,138,139,140,141,142,143,143,144,144,145,145,146,146,147,147,148,
148,149,149,150,150,151,152,153,153,154,154,155,155,156,156,157,157,158,
158,159,159,160,160,161,162,163,163,164,165,166,166,167,167,168,168,169,
169,170,170,171,171,172,172,173,174,175,175,176,176,177,177,178,178,179,
179,180,180,181,181,182,182,183,183,184,184,185,185,186,186,187,187,188,
188,189,189,190,190,191,191,192,192,193,193,194,194,195,195,196,196,197,
197,198,198,199,200,201,201,202,202,203,203,204,204,205,206,207,207,208,
208,209,209,210,210,211,212,213,214,214,215,215,216,216,217,217,218,218,
219,219,220,220,221,221,222,222,223,223,224,224,225,225,226,226,227,227,
228,228,229,230,230,231,231,232,232,233,233,234,235,236,237,238,238,239,
239,240,240,241,241,242,242,243,243,244,244,245,245,246,247,248,248,249,
249,250,250,251,251,252,252,253,253,254,254,255,255,256,257,258,258,259,
260,261,261,262,262,263,263,264,264,265,265,266,266,267,267,268,269,270,
270,271,271,272,272,273,273,274,274,275,275,276,276,277,277,278,278,279,
279,280,280,281,281,282,282,283,283,284,284,285,285]);
ALF("(2^2x3).2E6(2)M4","2^2.2E6(2)M4",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,
63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,
87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,
162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,
198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,
216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,
234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,
252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,
270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,
288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,
306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,
324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,
120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,
156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,
174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,
192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,
210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,
228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,
246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,
264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,
282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,
300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,
318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,
336,337,338,339,340,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,
132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,
150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,
168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,
186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,
204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,
222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,
240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,
258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,
276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,
294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,
312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,
330,331,332,333,334,335,336,337,338,339,340]);
ALF("(2^2x3).2E6(2)M4","3x2.F4(2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,
109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,
127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,
145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,
163,164,165,166,167,168,169,170,172,171,174,173,176,175,178,177,180,179,
182,181,184,183,186,185,187,188,190,189,192,191,194,193,196,195,197,198,
200,199,202,201,204,203,206,205,207,208,209,211,210,213,212,215,214,217,
216,219,218,221,220,223,222,225,224,227,226,229,228,231,230,233,232,235,
234,237,236,239,238,240,242,241,244,243,246,245,248,247,249,250,251,252,
254,253,256,255,258,257,260,259,262,261,264,263,266,265,268,267,269,270,
272,271,274,273,276,275,278,277,280,279,282,281,284,283,286,285,287,288,
290,289,291,292,294,293,296,295,298,297,300,299,302,301,304,303,306,305,
307,308,310,309,312,311,314,313,316,315,318,317,320,319,322,321,324,323,
326,325,328,327,330,329,332,331,334,333,336,335,338,337,340,339,341,342,
343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,
361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,
379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,
397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,
415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,
433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,
451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,
469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,
487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,
505,506,507,508,509,510,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,17,18,20,
19,22,21,24,23,26,25,27,28,30,29,32,31,34,33,36,35,37,38,39,41,40,43,42,
45,44,47,46,49,48,51,50,53,52,55,54,57,56,59,58,61,60,63,62,65,64,67,66,
69,68,70,72,71,74,73,76,75,78,77,79,80,81,82,84,83,86,85,88,87,90,89,92,
91,94,93,96,95,98,97,99,100,102,101,104,103,106,105,108,107,110,109,112,
111,114,113,116,115,117,118,120,119,121,122,124,123,126,125,128,127,130,
129,132,131,134,133,136,135,137,138,140,139,142,141,144,143,146,145,148,
147,150,149,152,151,154,153,156,155,158,157,160,159,162,161,164,163,166,
165,168,167,170,169,171,172,173,174,175,176,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,
220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,
238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,
256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,
274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,
292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,
310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,
328,329,330,331,332,333,334,335,336,337,338,339,340,342,341,344,343,346,
345,348,347,350,349,352,351,354,353,356,355,357,358,360,359,362,361,364,
363,366,365,367,368,370,369,372,371,374,373,376,375,377,378,379,381,380,
383,382,385,384,387,386,389,388,391,390,393,392,395,394,397,396,399,398,
401,400,403,402,405,404,407,406,409,408,410,412,411,414,413,416,415,418,
417,419,420,421,422,424,423,426,425,428,427,430,429,432,431,434,433,436,
435,438,437,439,440,442,441,444,443,446,445,448,447,450,449,452,451,454,
453,456,455,457,458,460,459,461,462,464,463,466,465,468,467,470,469,472,
471,474,473,476,475,477,478,480,479,482,481,484,483,486,485,488,487,490,
489,492,491,494,493,496,495,498,497,500,499,502,501,504,503,506,505,508,
507,510,509]);
ALF("(2^2x3).2E6(2)M4","(2^2x3).2E6(2)",[1,3,13,15,27,25,25,27,37,37,40,
42,52,54,56,58,72,84,60,62,84,84,101,99,101,99,96,118,117,117,141,141,99,
101,129,131,141,144,147,150,152,162,164,204,202,180,178,174,176,190,192,
219,217,178,180,202,204,214,214,231,229,235,233,249,251,237,239,327,327,
327,261,261,289,289,264,266,288,288,310,327,309,339,342,344,366,368,354,
356,370,372,384,382,382,384,447,447,424,426,421,465,479,477,497,495,479,
477,497,495,447,447,437,439,489,489,495,497,492,530,515,517,543,545,547,
549,571,573,561,559,595,597,583,585,641,641,640,640,622,622,652,654,664,
666,700,702,706,704,754,752,754,752,768,770,764,766,822,822,806,804,821,
821,808,810,851,853,839,839,877,875,865,863,5,7,17,19,31,29,29,31,38,38,
44,46,55,53,59,57,73,86,64,66,86,86,105,103,105,103,97,120,119,119,142,
142,103,105,133,135,142,145,148,154,156,166,168,208,206,184,182,177,175,
194,196,223,221,182,184,206,208,215,215,230,232,234,236,253,255,241,243,
329,329,329,262,262,291,291,268,270,290,290,312,329,311,340,346,348,369,
367,358,360,374,376,388,386,386,388,449,449,427,425,422,467,483,481,501,
499,483,481,501,499,449,449,440,438,490,490,499,501,493,532,518,516,541,
546,551,553,575,577,565,563,599,601,587,589,643,643,642,642,624,624,656,
658,668,670,703,701,710,708,758,756,758,756,772,774,767,765,824,824,805,
807,823,823,811,809,855,857,841,841,881,879,869,867,9,11,21,23,35,33,33,
35,39,39,48,50,52,54,56,58,74,88,68,70,88,88,109,107,109,107,98,122,121,
121,143,143,107,109,137,139,143,146,149,158,160,170,172,212,210,188,186,
174,176,198,200,227,225,186,188,210,212,216,216,231,229,235,233,257,259,
245,247,331,331,331,263,263,293,293,272,274,292,292,314,331,313,341,350,
352,366,368,362,364,378,380,392,390,390,392,451,451,424,426,423,469,487,
485,505,503,487,485,505,503,451,451,437,439,491,491,503,505,494,534,515,
517,542,544,555,557,579,581,569,567,603,605,591,593,645,645,644,644,626,
626,660,662,672,674,700,702,714,712,762,760,762,760,776,778,764,766,826,
826,806,804,825,825,808,810,859,861,843,843,885,883,873,871,4,2,16,14,26,
28,28,26,37,37,43,41,55,53,59,57,72,85,63,61,85,85,100,102,100,102,96,117,
118,118,141,141,102,100,132,130,141,144,147,153,151,165,163,203,205,179,
181,177,175,193,191,218,220,181,179,205,203,214,214,230,232,234,236,252,
250,240,238,328,328,328,261,261,288,288,267,265,289,289,309,328,310,339,
345,343,369,367,357,355,373,371,383,385,385,383,448,448,427,425,421,466,
478,480,496,498,478,480,496,498,448,448,440,438,489,489,498,496,492,529,
518,516,543,545,550,548,574,572,560,562,598,596,586,584,640,640,641,641,
623,623,655,653,667,665,703,701,705,707,753,755,753,755,771,769,767,765,
821,821,805,807,822,822,811,809,854,852,840,840,876,878,864,866,8,6,20,18,
30,32,32,30,38,38,47,45,52,54,56,58,73,87,67,65,87,87,104,106,104,106,97,
119,120,120,142,142,106,104,136,134,142,145,148,157,155,169,167,207,209,
183,185,174,176,197,195,222,224,185,183,209,207,215,215,231,229,235,233,
256,254,244,242,330,330,330,262,262,290,290,271,269,291,291,311,330,312,
340,349,347,366,368,361,359,377,375,387,389,389,387,450,450,424,426,422,
468,482,484,500,502,482,484,500,502,450,450,437,439,490,490,502,500,493,
531,515,517,541,546,554,552,578,576,564,566,602,600,590,588,642,642,643,
643,625,625,659,657,671,669,700,702,709,711,757,759,757,759,775,773,764,
766,823,823,806,804,824,824,808,810,858,856,842,842,880,882,868,870,12,10,
24,22,34,36,36,34,39,39,51,49,55,53,59,57,74,89,71,69,89,89,108,110,108,
110,98,121,122,122,143,143,110,108,140,138,143,146,149,161,159,173,171,
211,213,187,189,177,175,201,199,226,228,189,187,213,211,216,216,230,232,
234,236,260,258,248,246,332,332,332,263,263,292,292,275,273,293,293,313,
332,314,341,353,351,369,367,365,363,381,379,391,393,393,391,452,452,427,
425,423,470,486,488,504,506,486,488,504,506,452,452,440,438,491,491,506,
504,494,533,518,516,542,544,558,556,582,580,568,570,606,604,594,592,644,
644,645,645,627,627,663,661,675,673,703,701,713,715,761,763,761,763,779,
777,767,765,825,825,805,807,826,826,811,809,862,860,844,844,884,886,872,
874],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);

MOT("(2^2x3).2E6(2)M5",
[
"5th maximal subgroup of (2^2x3).2E6(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["6x2.F4(2)"]]);
ALF("(2^2x3).2E6(2)M5","2E6(2)M5",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,
11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,
25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,
37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,
52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,
65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,
80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,
92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,
13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,
27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,
40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,
68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,
82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,
94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,
15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,
29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,
42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,
56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,
71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,
84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,
1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,
18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,
32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,
45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,
59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,
73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,
86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,
5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,
20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,
34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,
48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,
61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,
75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,
88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,1,1,2,2,3,3,4,4,5,5,6,6,7,7,
8,8,9,10,11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,
24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,
36,36,37,37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,
50,51,51,52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,
63,64,64,65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,
77,78,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,
90,91,91,92,92,93,93,94,94,95,95],[
"equals the map from (2^2x3).2E6(2)M4, mapped under an outer autom."
]);
ALF("(2^2x3).2E6(2)M5","2.2E6(2)M5",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,
109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,
127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,
145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,
163,164,165,166,167,168,169,170,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,
90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,
129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,
147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,
165,166,167,168,169,170,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,
132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,
150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,
168,169,170,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,
96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,
151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,
169,170,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,
98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,
135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170]);
ALF("(2^2x3).2E6(2)M5","3.2E6(2)M5",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,
11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,
25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,
37,38,38,39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,
52,52,53,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,
65,65,66,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,
80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,
92,92,93,93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,
103,103,104,105,106,106,107,107,108,108,109,109,110,111,112,112,113,113,
114,114,115,115,116,117,118,119,119,120,120,121,121,122,122,123,123,124,
124,125,125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,133,
133,134,135,135,136,136,137,137,138,138,139,140,141,142,143,143,144,144,
145,145,146,146,147,147,148,148,149,149,150,150,151,152,153,153,154,154,
155,155,156,156,157,157,158,158,159,159,160,160,161,162,163,163,164,165,
166,166,167,167,168,168,169,169,170,170,171,171,172,172,173,174,175,175,
176,176,177,177,178,178,179,179,180,180,181,181,182,182,183,183,184,184,
185,185,186,186,187,187,188,188,189,189,190,190,191,191,192,192,193,193,
194,194,195,195,196,196,197,197,198,198,199,200,201,201,202,202,203,203,
204,204,205,206,207,207,208,208,209,209,210,210,211,212,213,214,214,215,
215,216,216,217,217,218,218,219,219,220,220,221,221,222,222,223,223,224,
224,225,225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,
234,235,236,237,238,238,239,239,240,240,241,241,242,242,243,243,244,244,
245,245,246,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,
255,255,256,257,258,258,259,260,261,261,262,262,263,263,264,264,265,265,
266,266,267,267,268,269,270,270,271,271,272,272,273,273,274,274,275,275,
276,276,277,277,278,278,279,279,280,280,281,281,282,282,283,283,284,284,
285,285,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,13,13,14,14,15,
16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,29,29,
30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,40,40,41,41,42,
42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,
57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,68,68,69,70,71,
71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,82,82,83,83,84,
84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,96,
96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,104,105,106,106,107,
107,108,108,109,109,110,111,112,112,113,113,114,114,115,115,116,117,118,
119,119,120,120,121,121,122,122,123,123,124,124,125,125,126,126,127,127,
128,128,129,129,130,130,131,131,132,132,133,133,134,135,135,136,136,137,
137,138,138,139,140,141,142,143,143,144,144,145,145,146,146,147,147,148,
148,149,149,150,150,151,152,153,153,154,154,155,155,156,156,157,157,158,
158,159,159,160,160,161,162,163,163,164,165,166,166,167,167,168,168,169,
169,170,170,171,171,172,172,173,174,175,175,176,176,177,177,178,178,179,
179,180,180,181,181,182,182,183,183,184,184,185,185,186,186,187,187,188,
188,189,189,190,190,191,191,192,192,193,193,194,194,195,195,196,196,197,
197,198,198,199,200,201,201,202,202,203,203,204,204,205,206,207,207,208,
208,209,209,210,210,211,212,213,214,214,215,215,216,216,217,217,218,218,
219,219,220,220,221,221,222,222,223,223,224,224,225,225,226,226,227,227,
228,228,229,230,230,231,231,232,232,233,233,234,235,236,237,238,238,239,
239,240,240,241,241,242,242,243,243,244,244,245,245,246,247,248,248,249,
249,250,250,251,251,252,252,253,253,254,254,255,255,256,257,258,258,259,
260,261,261,262,262,263,263,264,264,265,265,266,266,267,267,268,269,270,
270,271,271,272,272,273,273,274,274,275,275,276,276,277,277,278,278,279,
279,280,280,281,281,282,282,283,283,284,284,285,285]);
ALF("(2^2x3).2E6(2)M5","2^2.2E6(2)M5",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,
63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,
87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,
162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,
198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,
216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,
234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,
252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,
270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,
288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,
306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,
324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,
120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,
156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,
174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,
192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,
210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,
228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,
246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,
264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,
282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,
300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,
318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,
336,337,338,339,340,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,
132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,
150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,
168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,
186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,
204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,
222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,
240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,
258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,
276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,
294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,
312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,
330,331,332,333,334,335,336,337,338,339,340]);
ALF("(2^2x3).2E6(2)M5","6.2E6(2)M5",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,
109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,
127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,
145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,
163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,
181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,
199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,
217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,
235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,
253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,
271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,
289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,
307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,
325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,
343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,
361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,
379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,
397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,
415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,
433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,
451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,
469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,
487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,
505,506,507,508,509,510,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,
220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,
238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,
256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,
274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,
292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,
310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,
328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,
346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,
364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,
382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,
400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,
418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,
436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,
454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,
472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,
490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,
508,509,510]);
ALF("(2^2x3).2E6(2)M5","(2^2x3).2E6(2)",[1,4,13,16,28,25,25,28,37,37,40,
43,52,55,56,59,72,90,60,63,90,90,102,99,102,99,96,124,123,123,141,141,99,
102,129,132,141,144,147,150,153,162,165,205,202,181,178,174,177,190,193,
220,217,178,181,202,205,214,214,232,229,236,233,249,252,237,240,333,333,
333,261,261,295,295,264,267,294,294,316,333,315,339,342,345,366,369,354,
357,370,373,385,382,382,385,453,453,424,427,421,471,480,477,498,495,480,
477,498,495,453,453,437,440,489,489,495,498,492,536,519,522,541,544,547,
550,571,574,562,559,595,598,583,586,647,647,646,646,628,628,652,655,664,
667,700,703,707,704,755,752,755,752,768,771,764,767,828,828,807,804,827,
827,808,811,851,854,845,845,878,875,866,863,7,6,19,18,30,31,31,30,38,38,
46,45,53,54,57,58,73,92,66,65,92,92,104,105,104,105,97,126,125,125,142,
142,105,104,135,134,142,145,148,156,155,168,167,207,208,183,184,175,176,
196,195,222,223,184,183,208,207,215,215,231,230,235,234,255,254,243,242,
335,335,335,262,262,297,297,270,269,296,296,318,335,317,340,348,347,367,
368,360,359,376,375,387,388,388,387,455,455,425,426,422,473,482,483,500,
501,482,483,500,501,455,455,438,439,490,490,501,500,493,538,520,521,542,
545,553,552,577,576,564,565,601,600,589,588,649,649,648,648,630,630,658,
657,670,669,701,702,709,710,757,758,757,758,774,773,765,766,830,830,806,
805,829,829,809,810,857,856,847,847,880,881,868,869,9,12,21,24,36,33,33,
36,39,39,48,51,52,55,56,59,74,94,68,71,94,94,110,107,110,107,98,128,127,
127,143,143,107,110,137,140,143,146,149,158,161,170,173,213,210,189,186,
174,177,198,201,228,225,186,189,210,213,216,216,232,229,236,233,257,260,
245,248,337,337,337,263,263,299,299,272,275,298,298,320,337,319,341,350,
353,366,369,362,365,378,381,393,390,390,393,457,457,424,427,423,475,488,
485,506,503,488,485,506,503,457,457,437,440,491,491,503,506,494,540,519,
522,543,546,555,558,579,582,570,567,603,606,591,594,651,651,650,650,632,
632,660,663,672,675,700,703,715,712,763,760,763,760,776,779,764,767,832,
832,807,804,831,831,808,811,859,862,849,849,886,883,874,871,2,3,14,15,27,
26,26,27,37,37,41,42,53,54,57,58,72,91,61,62,91,91,101,100,101,100,96,123,
124,124,141,141,100,101,130,131,141,144,147,151,152,163,164,204,203,180,
179,175,176,191,192,219,218,179,180,203,204,214,214,231,230,235,234,250,
251,238,239,334,334,334,261,261,294,294,265,266,295,295,315,334,316,339,
343,344,367,368,355,356,371,372,384,383,383,384,454,454,425,426,421,472,
479,478,497,496,479,478,497,496,454,454,438,439,489,489,496,497,492,535,
520,521,541,544,548,549,572,573,561,560,596,597,584,585,646,646,647,647,
629,629,653,654,665,666,701,702,706,705,754,753,754,753,769,770,765,766,
827,827,806,805,828,828,809,810,852,853,846,846,877,876,865,864,8,5,20,17,
29,32,32,29,38,38,47,44,52,55,56,59,73,93,67,64,93,93,103,106,103,106,97,
125,126,126,142,142,106,103,136,133,142,145,148,157,154,169,166,206,209,
182,185,174,177,197,194,221,224,185,182,209,206,215,215,232,229,236,233,
256,253,244,241,336,336,336,262,262,296,296,271,268,297,297,317,336,318,
340,349,346,366,369,361,358,377,374,386,389,389,386,456,456,424,427,422,
474,481,484,499,502,481,484,499,502,456,456,437,440,490,490,502,499,493,
537,519,522,542,545,554,551,578,575,563,566,602,599,590,587,648,648,649,
649,631,631,659,656,671,668,700,703,708,711,756,759,756,759,775,772,764,
767,829,829,807,804,830,830,808,811,858,855,848,848,879,882,867,870,10,11,
22,23,35,34,34,35,39,39,49,50,53,54,57,58,74,95,69,70,95,95,109,108,109,
108,98,127,128,128,143,143,108,109,138,139,143,146,149,159,160,171,172,
212,211,188,187,175,176,199,200,227,226,187,188,211,212,216,216,231,230,
235,234,258,259,246,247,338,338,338,263,263,298,298,273,274,299,299,319,
338,320,341,351,352,367,368,363,364,379,380,392,391,391,392,458,458,425,
426,423,476,487,486,505,504,487,486,505,504,458,458,438,439,491,491,504,
505,494,539,520,521,543,546,556,557,580,581,569,568,604,605,592,593,650,
650,651,651,633,633,661,662,673,674,701,702,714,713,762,761,762,761,777,
778,765,766,831,831,806,805,832,832,809,810,860,861,850,850,885,884,873,
872],[
"equals the map from (2^2x3).2E6(2)M4, mapped under an outer autom."
]);

MOT("2x3.Fi22",
[
"7th maximal subgroup of (2^2x3).2E6(2)"
],
0,
0,
0,
[(129,132)(130,133)(131,134)(294,297)(295,298)(296,299),(104,105)(269,270),
( 86, 89)( 87, 90)( 88, 91)(151,154)(152,155)(153,156)(251,254)(252,255)
(253,256)(316,319)(317,320)(318,321)
,(117,120)(118,121)(119,122)(282,285)(283,286)(284,287),
(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 20, 21)( 23, 24)( 26, 27)
( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 51, 52)
( 56, 57)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)( 76, 77)( 81, 82)
( 84, 85)( 87, 88)( 90, 91)( 93, 94)( 96, 97)( 99,100)(102,103)(108,109)
(111,112)(114,115)(118,119)(121,122)(124,125)(127,128)(130,131)(133,134)
(135,138)(136,140)(137,139)(143,144)(146,147)(149,150)(152,153)(155,156)
(158,159)(161,162)(164,165)(167,168)(170,171)(173,174)(176,177)(179,180)
(185,186)(188,189)(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)
(209,210)(212,213)(216,217)(221,222)(226,227)(229,230)(232,233)(235,236)
(238,239)(241,242)(246,247)(249,250)(252,253)(255,256)(258,259)(261,262)
(264,265)(267,268)(273,274)(276,277)(279,280)(283,284)(286,287)(289,290)
(292,293)(295,296)(298,299)(300,303)(301,305)(302,304)(308,309)(311,312)
(314,315)(317,318)(320,321)(323,324)(326,327)(329,330)
],
["ConstructDirectProduct",[["Cyclic",2],["3.Fi22"]]]);
ALF("2x3.Fi22","6.2E6(2)",[1,3,5,10,12,8,13,15,17,19,21,20,22,24,26,30,28,
30,44,46,48,62,64,60,65,67,69,77,79,81,83,85,84,92,94,96,101,103,99,115,
117,113,127,129,131,106,108,110,105,124,126,125,136,133,118,120,122,134,
135,143,145,147,167,169,165,164,166,168,179,181,183,203,205,204,212,214,
216,218,218,223,225,221,226,228,230,232,234,236,238,240,242,275,277,279,
263,265,267,263,265,267,290,292,288,309,311,305,313,315,317,293,295,294,
302,304,300,307,331,333,335,331,333,335,346,348,344,355,357,359,370,372,
374,370,372,374,409,411,407,415,417,413,419,420,422,424,447,449,445,452,
454,456,461,463,459,467,469,465,477,479,481,480,482,478,516,518,514,4,6,2,
7,9,11,16,18,14,19,21,20,25,27,23,31,29,31,47,49,45,59,61,63,68,70,66,80,
82,78,83,85,84,95,97,93,98,100,102,112,114,116,130,132,128,109,111,107,
104,124,126,125,135,134,121,123,119,133,136,146,148,144,164,166,168,167,
169,165,182,184,180,203,205,204,215,217,213,219,219,220,222,224,229,231,
227,235,237,233,241,243,239,278,280,276,266,268,264,266,268,264,287,289,
291,310,312,306,316,318,314,293,295,294,299,301,303,308,334,336,332,334,
336,332,343,345,347,358,360,356,373,375,371,373,375,371,406,408,410,412,
414,416,418,423,425,421,444,446,448,455,457,453,458,460,462,464,466,468,
480,482,478,477,479,481,513,515,517],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2x3.Fi22",["6.2E6(2)M7"]);

MOT("6.2E6(2)M9",
[
"9th maximal subgroup of 6.2E6(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["6.Fi22"]]);
ALF("6.2E6(2)M9","2E6(2)M9",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,5,
5,5,5,5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,12,12,12,
13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,17,17,
17,17,17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,22,23,23,23,23,23,23,
24,24,25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,30,30,
30,31,31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,35,35,35,35,35,35,36,
36,36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,39,39,39,40,40,40,41,
41,41,41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,47,47,47,47,47,47,48,
48,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,52,52,52,
52,53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,58,58,58,
58,58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,62,62,62,
62,62,62,63,63,63,64,64,64,65,65,65,65,65,65]);
ALF("6.2E6(2)M9","2.2E6(2)M9",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,7,7,
8,9,8,9,8,9,10,11,12,13,14,15,16,16,16,17,18,17,18,17,18,19,19,19,20,21,
20,21,20,21,22,22,22,23,24,23,24,23,24,25,26,25,26,25,26,27,28,27,28,27,
28,29,30,29,30,29,30,31,32,31,32,31,32,33,34,35,35,35,36,37,38,39,40,41,
40,41,40,41,42,43,44,45,46,47,46,47,46,47,48,48,48,49,49,49,50,50,50,51,
52,51,52,51,52,53,54,53,54,53,54,55,56,57,58,59,60,59,60,59,60,61,62,61,
62,61,62,63,64,63,64,63,64,65,66,65,66,65,66,67,67,67,68,69,68,69,68,69,
70,70,70,71,72,71,72,71,72,73,74,75,76,77,78,79,79,79,80,80,80,81,82,81,
82,81,82,83,84,85,86,85,86,85,86,87,88,87,88,87,88,89,90,89,90,89,90,91,
92,91,92,91,92,93,93,93,94,94,94,95,96,95,96,95,96,97,98,97,98,97,98,99,
100,101,102,101,102,101,102,103,104,103,104,103,104,105,106,105,106,105,
106,107,108,107,108,107,108,109,110,109,110,109,110,111,111,111,112,112,
112,113,114,113,114,113,114]);
ALF("6.2E6(2)M9","3.2E6(2)M9",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,
12,13,14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,25,26,
27,28,29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,40,41,
42,40,41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,53,54,
54,55,56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,81,82,
83,84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,96,97,
95,96,97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,107,
108,109,110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,118,
119,120,121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,127,
128,129,130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,139,
140,141,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,150,
148,149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,159,
160,161,162,163,164,165,163,164,165]);
ALF("6.2E6(2)M9","6.2E6(2)",[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,
19,21,20,22,27,26,25,24,23,30,31,28,29,30,31,53,55,54,59,64,63,62,61,60,
74,76,75,77,82,81,80,79,78,83,85,84,92,97,96,95,94,93,98,103,102,101,100,
99,112,117,116,115,114,113,127,132,131,130,129,128,106,111,110,109,108,
107,104,105,124,126,125,135,136,133,134,118,123,122,121,120,119,133,134,
135,136,143,148,147,146,145,144,173,175,174,173,175,174,188,190,189,203,
205,204,203,205,204,212,217,216,215,214,213,218,219,218,219,220,225,224,
223,222,221,226,231,230,229,228,227,232,237,236,235,234,233,238,243,242,
241,240,239,284,286,285,272,274,273,272,274,273,272,274,273,287,292,291,
290,289,288,308,307,310,309,305,306,322,324,323,293,295,294,299,304,303,
302,301,300,311,312,331,336,335,334,333,332,331,336,335,334,333,332,343,
348,347,346,345,344,355,360,359,358,357,356,379,381,380,379,381,380,406,
411,410,409,408,407,412,417,416,415,414,413,418,419,420,425,424,423,422,
421,444,449,448,447,446,445,452,457,456,455,454,453,458,463,462,461,460,
459,464,469,468,467,466,465,486,488,487,486,488,487,513,518,517,516,515,
514],[
"equals the map from 6.2E6(2)M8, mapped under an outer autom."
]);

MOT("2x6.Fi22",
[
"7th maximal subgroup of (2^2x3).2E6(2)"
],
0,
0,
0,
[(221,224)(222,225)(223,226)(503,506)(504,507)(505,508),
(197,203)(198,204)(199,205)(200,206)(201,207)(202,208)(479,485)(480,486)
(481,487)(482,488)(483,489)(484,490)
,
(283,286)(284,287)(285,288)(289,292)(290,293)(291,294)(295,298)(296,299)
(297,300)(304,307)(305,308)(306,309)(310,311)(312,313)(314,315)(319,322)
(320,323)(321,324)(328,331)(329,332)(330,333)(337,340)(338,341)(339,342)
(343,346)(344,347)(345,348)(349,352)(350,353)(351,354)(355,358)(356,359)
(357,360)(361,364)(362,365)(363,366)(367,368)(372,373)(374,375)(376,379)
(377,380)(378,381)(382,383)(384,385)(386,389)(387,390)(388,391)(401,404)
(402,405)(403,406)(407,410)(408,411)(409,412)(413,414)(415,416)(417,420)
(418,421)(419,422)(423,426)(424,427)(425,428)(429,432)(430,433)(431,434)
(435,438)(436,439)(437,440)(444,447)(445,448)(446,449)(453,456)(454,457)
(455,458)(459,460)(461,462)(463,464)(471,474)(472,475)(473,476)(477,478)
(479,482)(480,483)(481,484)(485,488)(486,489)(487,490)(491,494)(492,495)
(493,496)(497,500)(498,501)(499,502)(509,512)(510,513)(511,514)(515,518)
(516,519)(517,520)(521,522)(523,526)(524,527)(525,528)(529,532)(530,533)
(531,534)(535,538)(536,539)(537,540)(541,544)(542,545)(543,546)(547,550)
(548,551)(549,552)(559,562)(560,563)(561,564)
,
(147,153)(148,154)(149,155)(150,156)(151,157)(152,158)(259,265)(260,266)
(261,267)(262,268)(263,269)(264,270)(429,435)(430,436)(431,437)(432,438)
(433,439)(434,440)(541,547)(542,548)(543,549)(544,550)(545,551)(546,552)
,
(  7, 10)(  8, 11)(  9, 12)( 37, 40)( 38, 41)( 39, 42)( 61, 64)( 62, 65)
( 63, 66)( 67, 70)( 68, 71)( 69, 72)( 85, 86)( 90, 91)(100,101)(119,122)
(120,123)(121,124)(135,138)(136,139)(137,140)(171,174)(172,175)(173,176)
(177,179)(178,180)(189,192)(190,193)(191,194)(209,212)(210,213)(211,214)
(227,230)(228,231)(229,232)(233,236)(234,237)(235,238)(239,240)(247,250)
(248,251)(249,252)(259,262)(260,263)(261,264)(265,268)(266,269)(267,270)
(277,280)(278,281)(279,282)(289,292)(290,293)(291,294)(319,322)(320,323)
(321,324)(343,346)(344,347)(345,348)(349,352)(350,353)(351,354)(367,368)
(372,373)(382,383)(401,404)(402,405)(403,406)(417,420)(418,421)(419,422)
(453,456)(454,457)(455,458)(459,461)(460,462)(471,474)(472,475)(473,476)
(491,494)(492,495)(493,496)(509,512)(510,513)(511,514)(515,518)(516,519)
(517,520)(521,522)(529,532)(530,533)(531,534)(541,544)(542,545)(543,546)
(547,550)(548,551)(549,552)(559,562)(560,563)(561,564)
,
(  2,  6)(  3,  5)(  8, 12)(  9, 11)( 14, 18)( 15, 17)( 20, 21)( 23, 27)
( 24, 26)( 35, 36)( 38, 42)( 39, 41)( 44, 45)( 47, 51)( 48, 50)( 53, 54)
( 56, 60)( 57, 59)( 62, 66)( 63, 65)( 68, 72)( 69, 71)( 74, 78)( 75, 77)
( 80, 84)( 81, 83)( 88, 89)( 95, 99)( 96, 98)(105,109)(106,108)(111,112)
(114,115)(117,118)(120,124)(121,123)(126,130)(127,129)(136,140)(137,139)
(142,146)(143,145)(148,152)(149,151)(154,158)(155,157)(160,161)(163,167)
(164,166)(169,170)(172,176)(173,175)(184,185)(187,188)(190,194)(191,193)
(198,202)(199,201)(204,208)(205,207)(210,214)(211,213)(216,220)(217,219)
(222,223)(225,226)(227,233)(228,238)(229,237)(230,236)(231,235)(232,234)
(242,246)(243,245)(248,252)(249,251)(254,258)(255,257)(260,264)(261,263)
(266,270)(267,269)(272,273)(275,276)(278,282)(279,281)(284,288)(285,287)
(290,294)(291,293)(296,300)(297,299)(302,303)(305,309)(306,308)(317,318)
(320,324)(321,323)(326,327)(329,333)(330,332)(335,336)(338,342)(339,341)
(344,348)(345,347)(350,354)(351,353)(356,360)(357,359)(362,366)(363,365)
(370,371)(377,381)(378,380)(387,391)(388,390)(393,394)(396,397)(399,400)
(402,406)(403,405)(408,412)(409,411)(418,422)(419,421)(424,428)(425,427)
(430,434)(431,433)(436,440)(437,439)(442,443)(445,449)(446,448)(451,452)
(454,458)(455,457)(466,467)(469,470)(472,476)(473,475)(480,484)(481,483)
(486,490)(487,489)(492,496)(493,495)(498,502)(499,501)(504,505)(507,508)
(509,515)(510,520)(511,519)(512,518)(513,517)(514,516)(524,528)(525,527)
(530,534)(531,533)(536,540)(537,539)(542,546)(543,545)(548,552)(549,551)
(554,555)(557,558)(560,564)(561,563)
],
["ConstructDirectProduct",[["Cyclic",2],["6.Fi22"]]]);
ALF("2x6.Fi22","2x3.Fi22",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,
13,14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,25,26,27,
28,29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,40,41,42,
40,41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,53,54,54,
55,56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,81,82,83,
84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,96,97,95,
96,97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,107,108,
109,110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,118,119,
120,121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,127,128,
129,130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,139,140,
141,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,150,148,
149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,159,160,
161,162,163,164,165,163,164,165,166,167,168,166,167,168,169,170,171,169,
170,171,172,173,174,172,173,174,175,176,177,178,179,180,178,179,180,181,
181,182,182,183,183,184,185,186,187,188,189,187,188,189,190,191,192,193,
194,195,193,194,195,196,197,198,199,200,201,199,200,201,202,203,204,202,
203,204,205,206,207,205,206,207,208,209,210,208,209,210,211,212,213,211,
212,213,214,214,215,216,217,218,218,219,219,220,221,222,220,221,222,223,
223,224,224,225,226,227,225,226,227,228,229,230,231,232,233,234,235,236,
237,238,239,237,238,239,240,241,242,240,241,242,243,243,244,244,245,246,
247,245,246,247,248,249,250,248,249,250,251,252,253,251,252,253,254,255,
256,254,255,256,257,258,259,260,261,262,260,261,262,263,264,265,266,267,
268,266,267,268,269,269,270,270,271,271,272,273,274,275,276,277,278,279,
280,278,279,280,281,281,282,283,284,282,283,284,285,286,287,285,286,287,
288,289,290,288,289,290,291,292,293,291,292,293,294,295,296,297,298,299,
300,301,302,300,301,302,303,304,305,303,304,305,306,306,307,308,309,307,
308,309,310,311,312,310,311,312,313,314,315,313,314,315,316,317,318,316,
317,318,319,320,321,319,320,321,322,323,324,325,326,327,328,329,330,328,
329,330]);
ALF("2x6.Fi22","2x2.Fi22",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,7,7,8,9,
8,9,8,9,10,11,12,13,14,15,16,16,16,17,18,17,18,17,18,19,19,19,20,21,20,21,
20,21,22,22,22,23,24,23,24,23,24,25,26,25,26,25,26,27,28,27,28,27,28,29,
30,29,30,29,30,31,32,31,32,31,32,33,34,35,35,35,36,37,38,39,40,41,40,41,
40,41,42,43,44,45,46,47,46,47,46,47,48,48,48,49,49,49,50,50,50,51,52,51,
52,51,52,53,54,53,54,53,54,55,56,57,58,59,60,59,60,59,60,61,62,61,62,61,
62,63,64,63,64,63,64,65,66,65,66,65,66,67,67,67,68,69,68,69,68,69,70,70,
70,71,72,71,72,71,72,73,74,75,76,77,78,79,79,79,80,80,80,81,82,81,82,81,
82,83,84,85,86,85,86,85,86,87,88,87,88,87,88,89,90,89,90,89,90,91,92,91,
92,91,92,93,93,93,94,94,94,95,96,95,96,95,96,97,98,97,98,97,98,99,100,101,
102,101,102,101,102,103,104,103,104,103,104,105,106,105,106,105,106,107,
108,107,108,107,108,109,110,109,110,109,110,111,111,111,112,112,112,113,
114,113,114,113,114,115,116,115,116,115,116,117,118,117,118,117,118,119,
120,119,120,119,120,121,121,121,122,123,122,123,122,123,124,125,126,127,
128,129,130,130,130,131,132,131,132,131,132,133,133,133,134,135,134,135,
134,135,136,136,136,137,138,137,138,137,138,139,140,139,140,139,140,141,
142,141,142,141,142,143,144,143,144,143,144,145,146,145,146,145,146,147,
148,149,149,149,150,151,152,153,154,155,154,155,154,155,156,157,158,159,
160,161,160,161,160,161,162,162,162,163,163,163,164,164,164,165,166,165,
166,165,166,167,168,167,168,167,168,169,170,171,172,173,174,173,174,173,
174,175,176,175,176,175,176,177,178,177,178,177,178,179,180,179,180,179,
180,181,181,181,182,183,182,183,182,183,184,184,184,185,186,185,186,185,
186,187,188,189,190,191,192,193,193,193,194,194,194,195,196,195,196,195,
196,197,198,199,200,199,200,199,200,201,202,201,202,201,202,203,204,203,
204,203,204,205,206,205,206,205,206,207,207,207,208,208,208,209,210,209,
210,209,210,211,212,211,212,211,212,213,214,215,216,215,216,215,216,217,
218,217,218,217,218,219,220,219,220,219,220,221,222,221,222,221,222,223,
224,223,224,223,224,225,225,225,226,226,226,227,228,227,228,227,228]);
ALF("2x6.Fi22","3.Fi22",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,13,
14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,25,26,27,28,
29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,40,41,42,40,
41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,53,54,54,55,
56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,81,82,83,84,
85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,96,97,95,96,
97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,107,108,109,
110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,118,119,120,
121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,127,128,129,
130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,139,140,141,
141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,150,148,149,
150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,159,160,161,
162,163,164,165,163,164,165,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,
13,14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,25,26,27,
28,29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,40,41,42,
40,41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,53,54,54,
55,56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,81,82,83,
84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,96,97,95,
96,97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,107,108,
109,110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,118,119,
120,121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,127,128,
129,130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,139,140,
141,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,150,148,
149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,159,160,
161,162,163,164,165,163,164,165]);
ALF("2x6.Fi22","2xFi22",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,5,5,5,
5,5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,12,12,12,13,
13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,17,17,17,
17,17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,22,23,23,23,23,23,23,24,
24,25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,30,30,30,
31,31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,35,35,35,35,35,35,36,36,
36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,39,39,39,40,40,40,41,41,
41,41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,47,47,47,47,47,47,48,48,
49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,52,52,52,52,
53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,58,58,58,58,
58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,62,62,62,62,
62,62,63,63,63,64,64,64,65,65,65,65,65,65,66,66,66,66,66,66,67,67,67,67,
67,67,68,68,68,68,68,68,69,69,69,70,70,70,70,70,70,71,71,72,72,73,73,74,
74,74,75,75,75,75,75,75,76,76,76,77,77,77,77,77,77,78,78,78,79,79,79,79,
79,79,80,80,80,80,80,80,81,81,81,81,81,81,82,82,82,82,82,82,83,83,83,83,
83,83,84,84,85,85,85,86,86,87,87,88,88,88,88,88,88,89,89,90,90,91,91,91,
91,91,91,92,92,92,93,93,93,94,94,94,95,95,95,95,95,95,96,96,96,96,96,96,
97,97,98,98,99,99,99,99,99,99,100,100,100,100,100,100,101,101,101,101,101,
101,102,102,102,102,102,102,103,103,103,104,104,104,104,104,104,105,105,
105,106,106,106,106,106,106,107,107,108,108,109,109,110,110,110,111,111,
111,112,112,112,112,112,112,113,113,114,114,114,114,114,114,115,115,115,
115,115,115,116,116,116,116,116,116,117,117,117,117,117,117,118,118,118,
119,119,119,120,120,120,120,120,120,121,121,121,121,121,121,122,122,123,
123,123,123,123,123,124,124,124,124,124,124,125,125,125,125,125,125,126,
126,126,126,126,126,127,127,127,127,127,127,128,128,128,129,129,129,130,
130,130,130,130,130]);
ALF("2x6.Fi22","Fi22",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,5,5,5,5,
5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,12,12,12,13,13,
13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,17,17,17,17,
17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,22,23,23,23,23,23,23,24,24,
25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,30,30,30,31,
31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,
36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,39,39,39,40,40,40,41,41,41,
41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,47,47,47,47,47,47,48,48,49,
49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,52,52,52,52,53,
53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,58,58,58,58,58,
58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,62,62,62,62,62,
62,63,63,63,64,64,64,65,65,65,65,65,65,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,
3,4,4,4,5,5,5,5,5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,
12,12,12,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,
17,17,17,17,17,17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,22,23,23,23,
23,23,23,24,24,25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,30,30,
30,30,30,30,31,31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,35,35,35,35,
35,35,36,36,36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,39,39,39,40,
40,40,41,41,41,41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,47,47,47,47,
47,47,48,48,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,
52,52,52,52,53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,
58,58,58,58,58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,
62,62,62,62,62,62,63,63,63,64,64,64,65,65,65,65,65,65]);
ALF("2x6.Fi22","(2^2x3).2E6(2)",[1,10,8,2,9,7,15,24,18,16,23,17,25,34,32,
26,33,31,37,39,38,40,49,47,41,48,46,56,57,52,53,56,57,78,82,81,101,110,
104,102,109,103,111,115,114,129,138,136,130,137,135,141,143,142,150,159,
157,151,158,156,164,173,167,165,172,166,192,201,195,193,200,194,217,226,
224,218,225,223,178,187,185,179,186,184,176,177,214,216,215,235,236,229,
230,202,211,209,203,210,208,231,232,233,234,249,258,256,250,257,255,283,
287,284,282,286,285,303,307,306,339,341,340,339,341,340,354,363,361,355,
362,360,366,367,366,367,372,381,375,373,380,374,382,391,389,383,390,388,
394,403,401,395,402,400,406,415,413,407,414,412,459,463,462,441,445,444,
441,445,444,441,445,444,479,488,482,480,487,481,516,515,520,519,507,508,
523,527,526,489,491,490,497,506,500,498,505,499,511,512,547,556,554,548,
555,553,547,556,554,548,555,553,573,582,576,574,581,575,595,604,602,596,
603,601,616,620,619,616,620,619,678,687,681,679,686,680,690,699,693,691,
698,692,702,703,704,713,711,705,712,710,754,763,757,755,762,756,768,777,
775,769,776,774,782,791,785,783,790,784,794,803,797,795,802,796,815,819,
818,816,820,817,877,886,880,878,885,879,3,12,6,4,11,5,13,22,20,14,21,19,
27,36,30,28,35,29,37,39,38,42,51,45,43,50,44,58,59,54,55,58,59,79,83,80,
99,108,106,100,107,105,112,116,113,131,140,134,132,139,133,141,143,142,
152,161,155,153,160,154,162,171,169,163,170,168,190,199,197,191,198,196,
219,228,222,220,227,221,180,189,183,181,188,182,174,175,214,216,215,233,
234,231,232,204,213,207,205,212,206,229,230,235,236,251,260,254,252,259,
253,282,286,285,283,287,284,304,308,305,339,341,340,339,341,340,356,365,
359,357,364,358,368,369,368,369,370,379,377,371,378,376,384,393,387,385,
392,386,396,405,399,397,404,398,408,417,411,409,416,410,460,464,461,442,
446,443,442,446,443,442,446,443,477,486,484,478,485,483,518,517,522,521,
509,510,524,528,525,489,491,490,495,504,502,496,503,501,513,514,549,558,
552,550,557,551,549,558,552,550,557,551,571,580,578,572,579,577,597,606,
600,598,605,599,617,621,618,617,621,618,676,685,683,677,684,682,688,697,
695,689,696,694,700,701,706,715,709,707,714,708,752,761,759,753,760,758,
770,779,773,771,778,772,780,789,787,781,788,786,792,801,799,793,800,798,
816,820,817,815,819,818,875,884,882,876,883,881],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);
ALN("2x6.Fi22",["(2^2x3).2E6(2)M7"]);

MOT("(2^2x3).2E6(2)M8",
[
"8th maximal subgroup of (2^2x3).2E6(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["2x6.Fi22"]]);
ALF("(2^2x3).2E6(2)M8","6.Fi22",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,
128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,
146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,
164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,
182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,
200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,
218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,
236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,
254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,
272,273,274,275,276,277,278,279,280,281,282,4,5,6,1,2,3,10,11,12,7,8,9,16,
17,18,13,14,15,19,20,21,25,26,27,22,23,24,29,28,31,30,33,32,34,35,36,40,
41,42,37,38,39,43,44,45,49,50,51,46,47,48,52,53,54,58,59,60,55,56,57,64,
65,66,61,62,63,70,71,72,67,68,69,76,77,78,73,74,75,82,83,84,79,80,81,86,
85,87,88,89,91,90,93,92,97,98,99,94,95,96,101,100,103,102,107,108,109,104,
105,106,110,111,112,113,114,115,116,117,118,122,123,124,119,120,121,128,
129,130,125,126,127,132,131,134,133,138,139,140,135,136,137,144,145,146,
141,142,143,150,151,152,147,148,149,156,157,158,153,154,155,159,160,161,
165,166,167,162,163,164,168,169,170,174,175,176,171,172,173,178,177,180,
179,182,181,183,184,185,186,187,188,192,193,194,189,190,191,196,195,200,
201,202,197,198,199,206,207,208,203,204,205,212,213,214,209,210,211,218,
219,220,215,216,217,221,222,223,224,225,226,230,231,232,227,228,229,236,
237,238,233,234,235,240,239,244,245,246,241,242,243,250,251,252,247,248,
249,256,257,258,253,254,255,262,263,264,259,260,261,268,269,270,265,266,
267,271,272,273,274,275,276,280,281,282,277,278,279]);
ALF("(2^2x3).2E6(2)M8","2E6(2)M8",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,
4,4,5,5,5,5,5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,12,
12,12,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,
17,17,17,17,17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,22,23,23,23,23,
23,23,24,24,25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,
30,30,30,31,31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,35,35,35,35,35,
35,36,36,36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,39,39,39,40,40,
40,41,41,41,41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,47,47,47,47,47,
47,48,48,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,52,
52,52,52,53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,58,
58,58,58,58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,62,
62,62,62,62,62,63,63,63,64,64,64,65,65,65,65,65,65,1,1,1,1,1,1,2,2,2,2,2,
2,3,3,3,3,3,3,4,4,4,5,5,5,5,5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,
11,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,
16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,
22,23,23,23,23,23,23,24,24,25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,
29,29,30,30,30,30,30,30,31,31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,
35,35,35,35,35,35,36,36,36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,
39,39,39,40,40,40,41,41,41,41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,
47,47,47,47,47,47,48,48,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,
51,51,52,52,52,52,52,52,53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,
56,56,57,57,58,58,58,58,58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,
61,61,61,61,62,62,62,62,62,62,63,63,63,64,64,64,65,65,65,65,65,65]);
ALF("(2^2x3).2E6(2)M8","2^2.2E6(2)M8",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,
6,7,7,7,8,9,8,9,8,9,10,11,12,13,14,15,16,16,16,17,18,17,18,17,18,19,19,19,
20,21,20,21,20,21,22,22,22,23,24,23,24,23,24,25,26,25,26,25,26,27,28,27,
28,27,28,29,30,29,30,29,30,31,32,31,32,31,32,33,34,35,35,35,36,37,38,39,
40,41,40,41,40,41,42,43,44,45,46,47,46,47,46,47,48,48,48,49,49,49,50,50,
50,51,52,51,52,51,52,53,54,53,54,53,54,55,56,57,58,59,60,59,60,59,60,61,
62,61,62,61,62,63,64,63,64,63,64,65,66,65,66,65,66,67,67,67,68,69,68,69,
68,69,70,70,70,71,72,71,72,71,72,73,74,75,76,77,78,79,79,79,80,80,80,81,
82,81,82,81,82,83,84,85,86,85,86,85,86,87,88,87,88,87,88,89,90,89,90,89,
90,91,92,91,92,91,92,93,93,93,94,94,94,95,96,95,96,95,96,97,98,97,98,97,
98,99,100,101,102,101,102,101,102,103,104,103,104,103,104,105,106,105,106,
105,106,107,108,107,108,107,108,109,110,109,110,109,110,111,111,111,112,
112,112,113,114,113,114,113,114,115,116,115,116,115,116,117,118,117,118,
117,118,119,120,119,120,119,120,121,121,121,122,123,122,123,122,123,124,
125,126,127,128,129,130,130,130,131,132,131,132,131,132,133,133,133,134,
135,134,135,134,135,136,136,136,137,138,137,138,137,138,139,140,139,140,
139,140,141,142,141,142,141,142,143,144,143,144,143,144,145,146,145,146,
145,146,147,148,149,149,149,150,151,152,153,154,155,154,155,154,155,156,
157,158,159,160,161,160,161,160,161,162,162,162,163,163,163,164,164,164,
165,166,165,166,165,166,167,168,167,168,167,168,169,170,171,172,173,174,
173,174,173,174,175,176,175,176,175,176,177,178,177,178,177,178,179,180,
179,180,179,180,181,181,181,182,183,182,183,182,183,184,184,184,185,186,
185,186,185,186,187,188,189,190,191,192,193,193,193,194,194,194,195,196,
195,196,195,196,197,198,199,200,199,200,199,200,201,202,201,202,201,202,
203,204,203,204,203,204,205,206,205,206,205,206,207,207,207,208,208,208,
209,210,209,210,209,210,211,212,211,212,211,212,213,214,215,216,215,216,
215,216,217,218,217,218,217,218,219,220,219,220,219,220,221,222,221,222,
221,222,223,224,223,224,223,224,225,225,225,226,226,226,227,228,227,228,
227,228]);
ALF("(2^2x3).2E6(2)M8","2.Fi22",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,7,
7,8,9,8,9,8,9,10,11,12,13,14,15,16,16,16,17,18,17,18,17,18,19,19,19,20,21,
20,21,20,21,22,22,22,23,24,23,24,23,24,25,26,25,26,25,26,27,28,27,28,27,
28,29,30,29,30,29,30,31,32,31,32,31,32,33,34,35,35,35,36,37,38,39,40,41,
40,41,40,41,42,43,44,45,46,47,46,47,46,47,48,48,48,49,49,49,50,50,50,51,
52,51,52,51,52,53,54,53,54,53,54,55,56,57,58,59,60,59,60,59,60,61,62,61,
62,61,62,63,64,63,64,63,64,65,66,65,66,65,66,67,67,67,68,69,68,69,68,69,
70,70,70,71,72,71,72,71,72,73,74,75,76,77,78,79,79,79,80,80,80,81,82,81,
82,81,82,83,84,85,86,85,86,85,86,87,88,87,88,87,88,89,90,89,90,89,90,91,
92,91,92,91,92,93,93,93,94,94,94,95,96,95,96,95,96,97,98,97,98,97,98,99,
100,101,102,101,102,101,102,103,104,103,104,103,104,105,106,105,106,105,
106,107,108,107,108,107,108,109,110,109,110,109,110,111,111,111,112,112,
112,113,114,113,114,113,114,2,1,2,1,2,1,4,3,4,3,4,3,6,5,6,5,6,5,7,7,7,9,8,
9,8,9,8,11,10,13,12,15,14,16,16,16,18,17,18,17,18,17,19,19,19,21,20,21,20,
21,20,22,22,22,24,23,24,23,24,23,26,25,26,25,26,25,28,27,28,27,28,27,30,
29,30,29,30,29,32,31,32,31,32,31,34,33,35,35,35,37,36,39,38,41,40,41,40,
41,40,43,42,45,44,47,46,47,46,47,46,48,48,48,49,49,49,50,50,50,52,51,52,
51,52,51,54,53,54,53,54,53,56,55,58,57,60,59,60,59,60,59,62,61,62,61,62,
61,64,63,64,63,64,63,66,65,66,65,66,65,67,67,67,69,68,69,68,69,68,70,70,
70,72,71,72,71,72,71,74,73,76,75,78,77,79,79,79,80,80,80,82,81,82,81,82,
81,84,83,86,85,86,85,86,85,88,87,88,87,88,87,90,89,90,89,90,89,92,91,92,
91,92,91,93,93,93,94,94,94,96,95,96,95,96,95,98,97,98,97,98,97,100,99,102,
101,102,101,102,101,104,103,104,103,104,103,106,105,106,105,106,105,108,
107,108,107,108,107,110,109,110,109,110,109,111,111,111,112,112,112,114,
113,114,113,114,113]);
ALF("(2^2x3).2E6(2)M8","3.2E6(2)M8",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,
10,11,12,13,14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,
25,26,27,28,29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,
40,41,42,40,41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,
53,54,54,55,56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,
81,82,83,84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,
96,97,95,96,97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,
107,108,109,110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,
118,119,120,121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,
127,128,129,130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,
139,140,141,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,
150,148,149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,
159,160,161,162,163,164,165,163,164,165,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,
9,10,11,12,13,14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,
25,26,27,28,29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,
40,41,42,40,41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,
53,54,54,55,56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,
81,82,83,84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,
96,97,95,96,97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,
107,108,109,110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,
118,119,120,121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,
127,128,129,130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,
139,140,141,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,
150,148,149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,
159,160,161,162,163,164,165,163,164,165]);
ALF("(2^2x3).2E6(2)M8","(2^2x3).2E6(2)",[1,11,8,3,9,6,16,22,17,14,24,19,
25,35,32,27,33,30,37,39,38,40,50,47,42,48,45,56,58,52,54,56,58,84,88,87,
102,108,103,100,110,105,117,121,120,129,139,136,131,137,134,141,143,142,
150,160,157,152,158,155,165,171,166,163,173,168,193,199,194,191,201,196,
217,227,224,219,225,222,178,188,185,180,186,183,177,175,214,216,215,236,
234,229,231,202,212,209,204,210,207,232,230,233,235,249,259,256,251,257,
254,289,293,290,288,292,291,309,313,312,339,341,340,339,341,340,354,364,
361,356,362,359,366,368,366,368,373,379,374,371,381,376,382,392,389,384,
390,387,394,404,401,396,402,399,406,416,413,408,414,411,465,469,468,447,
451,450,447,451,450,447,451,450,480,486,481,478,488,483,521,519,513,511,
507,509,529,533,532,489,491,490,498,504,499,496,506,501,515,517,547,557,
554,549,555,552,547,557,554,549,555,552,574,580,575,572,582,577,595,605,
602,597,603,600,622,626,625,622,626,625,679,685,680,677,687,682,691,697,
692,689,699,694,703,701,704,714,711,706,712,709,755,761,756,753,763,758,
768,778,775,770,776,773,783,789,784,781,791,786,795,801,796,793,803,798,
821,825,824,822,826,823,878,884,879,876,886,881,4,10,5,2,12,7,13,23,20,15,
21,18,28,34,29,26,36,31,37,39,38,43,49,44,41,51,46,59,57,55,53,59,57,85,
89,86,99,109,106,101,107,104,118,122,119,132,138,133,130,140,135,141,143,
142,153,159,154,151,161,156,162,172,169,164,170,167,190,200,197,192,198,
195,220,226,221,218,228,223,181,187,182,179,189,184,174,176,214,216,215,
233,235,232,230,205,211,206,203,213,208,229,231,236,234,252,258,253,250,
260,255,288,292,291,289,293,290,310,314,311,339,341,340,339,341,340,357,
363,358,355,365,360,369,367,369,367,370,380,377,372,378,375,385,391,386,
383,393,388,397,403,398,395,405,400,409,415,410,407,417,412,466,470,467,
448,452,449,448,452,449,448,452,449,477,487,484,479,485,482,520,522,512,
514,510,508,530,534,531,489,491,490,495,505,502,497,503,500,518,516,550,
556,551,548,558,553,550,556,551,548,558,553,571,581,578,573,579,576,598,
604,599,596,606,601,623,627,624,623,627,624,676,686,683,678,684,681,688,
698,695,690,696,693,700,702,707,713,708,705,715,710,752,762,759,754,760,
757,771,777,772,769,779,774,780,790,787,782,788,785,792,802,799,794,800,
797,822,826,823,821,825,824,875,885,882,877,883,880],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);

MOT("(2^2x3).2E6(2)M9",
[
"9th maximal subgroup of (2^2x3).2E6(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["2x6.Fi22"]]);
ALF("(2^2x3).2E6(2)M9","2E6(2)M9",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,
4,4,5,5,5,5,5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,12,
12,12,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,
17,17,17,17,17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,22,23,23,23,23,
23,23,24,24,25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,
30,30,30,31,31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,35,35,35,35,35,
35,36,36,36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,39,39,39,40,40,
40,41,41,41,41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,47,47,47,47,47,
47,48,48,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,52,
52,52,52,53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,58,
58,58,58,58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,62,
62,62,62,62,62,63,63,63,64,64,64,65,65,65,65,65,65,1,1,1,1,1,1,2,2,2,2,2,
2,3,3,3,3,3,3,4,4,4,5,5,5,5,5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,
11,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,
16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,
22,23,23,23,23,23,23,24,24,25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,
29,29,30,30,30,30,30,30,31,31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,
35,35,35,35,35,35,36,36,36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,
39,39,39,40,40,40,41,41,41,41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,
47,47,47,47,47,47,48,48,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,
51,51,52,52,52,52,52,52,53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,
56,56,57,57,58,58,58,58,58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,
61,61,61,61,62,62,62,62,62,62,63,63,63,64,64,64,65,65,65,65,65,65]);
ALF("(2^2x3).2E6(2)M9","2.2E6(2)M9",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,
7,7,7,8,9,8,9,8,9,10,11,12,13,14,15,16,16,16,17,18,17,18,17,18,19,19,19,
20,21,20,21,20,21,22,22,22,23,24,23,24,23,24,25,26,25,26,25,26,27,28,27,
28,27,28,29,30,29,30,29,30,31,32,31,32,31,32,33,34,35,35,35,36,37,38,39,
40,41,40,41,40,41,42,43,44,45,46,47,46,47,46,47,48,48,48,49,49,49,50,50,
50,51,52,51,52,51,52,53,54,53,54,53,54,55,56,57,58,59,60,59,60,59,60,61,
62,61,62,61,62,63,64,63,64,63,64,65,66,65,66,65,66,67,67,67,68,69,68,69,
68,69,70,70,70,71,72,71,72,71,72,73,74,75,76,77,78,79,79,79,80,80,80,81,
82,81,82,81,82,83,84,85,86,85,86,85,86,87,88,87,88,87,88,89,90,89,90,89,
90,91,92,91,92,91,92,93,93,93,94,94,94,95,96,95,96,95,96,97,98,97,98,97,
98,99,100,101,102,101,102,101,102,103,104,103,104,103,104,105,106,105,106,
105,106,107,108,107,108,107,108,109,110,109,110,109,110,111,111,111,112,
112,112,113,114,113,114,113,114,1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,7,7,
8,9,8,9,8,9,10,11,12,13,14,15,16,16,16,17,18,17,18,17,18,19,19,19,20,21,
20,21,20,21,22,22,22,23,24,23,24,23,24,25,26,25,26,25,26,27,28,27,28,27,
28,29,30,29,30,29,30,31,32,31,32,31,32,33,34,35,35,35,36,37,38,39,40,41,
40,41,40,41,42,43,44,45,46,47,46,47,46,47,48,48,48,49,49,49,50,50,50,51,
52,51,52,51,52,53,54,53,54,53,54,55,56,57,58,59,60,59,60,59,60,61,62,61,
62,61,62,63,64,63,64,63,64,65,66,65,66,65,66,67,67,67,68,69,68,69,68,69,
70,70,70,71,72,71,72,71,72,73,74,75,76,77,78,79,79,79,80,80,80,81,82,81,
82,81,82,83,84,85,86,85,86,85,86,87,88,87,88,87,88,89,90,89,90,89,90,91,
92,91,92,91,92,93,93,93,94,94,94,95,96,95,96,95,96,97,98,97,98,97,98,99,
100,101,102,101,102,101,102,103,104,103,104,103,104,105,106,105,106,105,
106,107,108,107,108,107,108,109,110,109,110,109,110,111,111,111,112,112,
112,113,114,113,114,113,114]);
ALF("(2^2x3).2E6(2)M9","3.2E6(2)M9",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,
10,11,12,13,14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,
25,26,27,28,29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,
40,41,42,40,41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,
53,54,54,55,56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,
81,82,83,84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,
96,97,95,96,97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,
107,108,109,110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,
118,119,120,121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,
127,128,129,130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,
139,140,141,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,
150,148,149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,
159,160,161,162,163,164,165,163,164,165,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,
9,10,11,12,13,14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,
25,26,27,28,29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,
40,41,42,40,41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,
53,54,54,55,56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,
81,82,83,84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,
96,97,95,96,97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,
107,108,109,110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,
118,119,120,121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,
127,128,129,130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,
139,140,141,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,
150,148,149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,
159,160,161,162,163,164,165,163,164,165]);
ALF("(2^2x3).2E6(2)M9","2^2.2E6(2)M9",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,
6,7,7,7,8,9,8,9,8,9,10,11,12,13,14,15,16,16,16,17,18,17,18,17,18,19,19,19,
20,21,20,21,20,21,22,22,22,23,24,23,24,23,24,25,26,25,26,25,26,27,28,27,
28,27,28,29,30,29,30,29,30,31,32,31,32,31,32,33,34,35,35,35,36,37,38,39,
40,41,40,41,40,41,42,43,44,45,46,47,46,47,46,47,48,48,48,49,49,49,50,50,
50,51,52,51,52,51,52,53,54,53,54,53,54,55,56,57,58,59,60,59,60,59,60,61,
62,61,62,61,62,63,64,63,64,63,64,65,66,65,66,65,66,67,67,67,68,69,68,69,
68,69,70,70,70,71,72,71,72,71,72,73,74,75,76,77,78,79,79,79,80,80,80,81,
82,81,82,81,82,83,84,85,86,85,86,85,86,87,88,87,88,87,88,89,90,89,90,89,
90,91,92,91,92,91,92,93,93,93,94,94,94,95,96,95,96,95,96,97,98,97,98,97,
98,99,100,101,102,101,102,101,102,103,104,103,104,103,104,105,106,105,106,
105,106,107,108,107,108,107,108,109,110,109,110,109,110,111,111,111,112,
112,112,113,114,113,114,113,114,115,116,115,116,115,116,117,118,117,118,
117,118,119,120,119,120,119,120,121,121,121,122,123,122,123,122,123,124,
125,126,127,128,129,130,130,130,131,132,131,132,131,132,133,133,133,134,
135,134,135,134,135,136,136,136,137,138,137,138,137,138,139,140,139,140,
139,140,141,142,141,142,141,142,143,144,143,144,143,144,145,146,145,146,
145,146,147,148,149,149,149,150,151,152,153,154,155,154,155,154,155,156,
157,158,159,160,161,160,161,160,161,162,162,162,163,163,163,164,164,164,
165,166,165,166,165,166,167,168,167,168,167,168,169,170,171,172,173,174,
173,174,173,174,175,176,175,176,175,176,177,178,177,178,177,178,179,180,
179,180,179,180,181,181,181,182,183,182,183,182,183,184,184,184,185,186,
185,186,185,186,187,188,189,190,191,192,193,193,193,194,194,194,195,196,
195,196,195,196,197,198,199,200,199,200,199,200,201,202,201,202,201,202,
203,204,203,204,203,204,205,206,205,206,205,206,207,207,207,208,208,208,
209,210,209,210,209,210,211,212,211,212,211,212,213,214,215,216,215,216,
215,216,217,218,217,218,217,218,219,220,219,220,219,220,221,222,221,222,
221,222,223,224,223,224,223,224,225,225,225,226,226,226,227,228,227,228,
227,228]);
ALF("(2^2x3).2E6(2)M9","6.2E6(2)M9",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,
109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,
127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,
145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,
163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,
181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,
199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,
217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,
235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,
253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,
271,272,273,274,275,276,277,278,279,280,281,282,1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,
124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,
142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,
160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,
178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,
196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,
214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,
232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,
250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,
268,269,270,271,272,273,274,275,276,277,278,279,280,281,282]);
ALF("(2^2x3).2E6(2)M9","(2^2x3).2E6(2)",[1,12,8,4,9,5,14,23,19,15,22,18,
25,36,32,28,33,29,37,39,38,40,51,47,43,48,44,56,59,52,55,56,59,90,94,93,
100,109,105,101,108,104,123,127,126,129,140,136,132,137,133,141,143,142,
150,161,157,153,158,154,163,172,168,164,171,167,191,200,196,192,199,195,
217,228,224,220,225,221,178,189,185,181,186,182,175,176,214,216,215,234,
235,229,232,202,213,209,205,210,206,230,231,233,236,249,260,256,252,257,
253,295,299,296,294,298,297,315,319,318,339,341,340,339,341,340,354,365,
361,357,362,358,366,369,366,369,371,380,376,372,379,375,382,393,389,385,
390,386,394,405,401,397,402,398,406,417,413,409,414,410,471,475,474,453,
457,456,453,457,456,453,457,456,478,487,483,479,486,482,514,511,518,515,
507,510,535,539,538,489,491,490,496,505,501,497,504,500,519,522,547,558,
554,550,555,551,547,558,554,550,555,551,572,581,577,573,580,576,595,606,
602,598,603,599,628,632,631,628,632,631,677,686,682,678,685,681,689,698,
694,690,697,693,701,702,704,715,711,707,712,708,753,762,758,754,761,757,
768,779,775,771,776,772,781,790,786,782,789,785,793,802,798,794,801,797,
827,831,830,828,832,829,876,885,881,877,884,880,2,11,7,3,10,6,13,24,20,16,
21,17,26,35,31,27,34,30,37,39,38,41,50,46,42,49,45,57,58,53,54,57,58,91,
95,92,99,110,106,102,107,103,124,128,125,130,139,135,131,138,134,141,143,
142,151,160,156,152,159,155,162,173,169,165,170,166,190,201,197,193,198,
194,218,227,223,219,226,222,179,188,184,180,187,183,174,177,214,216,215,
233,236,230,231,203,212,208,204,211,207,229,232,234,235,250,259,255,251,
258,254,294,298,297,295,299,296,316,320,317,339,341,340,339,341,340,355,
364,360,356,363,359,367,368,367,368,370,381,377,373,378,374,383,392,388,
384,391,387,395,404,400,396,403,399,407,416,412,408,415,411,472,476,473,
454,458,455,454,458,455,454,458,455,477,488,484,480,485,481,513,512,517,
516,508,509,536,540,537,489,491,490,495,506,502,498,503,499,520,521,548,
557,553,549,556,552,548,557,553,549,556,552,571,582,578,574,579,575,596,
605,601,597,604,600,629,633,630,629,633,630,676,687,683,679,684,680,688,
699,695,691,696,692,700,703,705,714,710,706,713,709,752,763,759,755,760,
756,769,778,774,770,777,773,780,791,787,783,788,784,792,803,799,795,800,
796,828,832,829,827,831,830,875,886,882,878,883,879],[
"equals the map from (2^2x3).2E6(2)M8, mapped under an outer autom."
]);

LIBTABLE.LOADSTATUS.ctomax21:="userloaded";

#############################################################################
##
#E