File: ctomaxi4.tbl

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#############################################################################
##
#W  ctomaxi4.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of maximal subgroups
##  (which are neither ATLAS tables nor tables of Ostermann) of the
##  groups Fi22, Fi23, Fi24'.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctomaxi4.tbl,v $
#H  Revision 4.41  2012/05/07 15:26:48  gap
#H  revert three changes:
#H  - use direct product constructions from `[["Symmetric",4],["S6(2)"]]' and
#H    `[["Symmetric",4],["U4(2).2"]]' instead of `[["s4"],["S6(2)"]]' and
#H    `[["s4"],["U4(2).2"]]', respectively
#H  - use the name `"D62x2"' instead of `"D124"'
#H      TB
#H
#H  Revision 4.40  2012/04/23 16:16:12  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 4.39  2012/01/30 08:31:56  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.38  2011/09/28 13:12:51  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added tables of 2.(2x2^(1+8)):U4(2):2, 2.(3^(1+6):2^(3+4):3^2:2),
#H  - added fusions (A4xO8+(2).3).2 -> S4xO8+(2):S3,
#H    S3xU4(3).2_2 -> S3xU4(3).(2^2)_{122}
#H      TB
#H
#H  Revision 4.37  2010/12/01 17:47:56  gap
#H  renamed "Sym(4)" to "Symm(4)";
#H  note that the table constructed with `CharacterTable( "Symmetric", 4 )'
#H  gets the identifier `"Sym(4)"', and this table is sorted differently
#H      TB
#H
#H  Revision 4.36  2010/05/05 13:20:06  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 4.35  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
#H  Revision 4.34  2009/04/22 12:39:04  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.33  2009/01/12 17:33:58  gap
#H  added missing maxes of Fi22.2 and their fusions
#H      TB
#H
#H  Revision 4.32  2009/01/07 09:51:07  gap
#H  added tables of 3xO8+(2):S3, 6xO8+(2):S3, and fusions into 3.Fi22,
#H  6.Fi22, respectively
#H      TB
#H
#H  Revision 4.31  2008/06/24 16:23:05  gap
#H  added several fusions and names
#H      TB
#H
#H  Revision 4.30  2007/07/03 08:50:15  gap
#H  added fusions,
#H  encoded several tables as index two subdirect products
#H      TB
#H
#H  Revision 4.29  2006/06/07 07:54:27  gap
#H  unified ConstructMixed and ConstructMGA (for better programmatic access)
#H      TB
#H
#H  Revision 4.28  2005/08/10 14:34:54  gap
#H  added table of 2^12.M24 < F3+.2 (needed by Bob)
#H      TB
#H
#H  Revision 4.27  2004/08/31 12:33:33  gap
#H  added tables of 4.L2(25).2_3,
#H                  L2(49).2^2,
#H                  L2(81).2^2,
#H                  L2(81).(2x4),
#H                  3.L3(4).3.2_2,
#H                  L3(9).2^2,
#H                  L4(4).2^2,
#H                  2x2^3:L3(2)x2,
#H                  (2xA6).2^2,
#H                  2xL2(11).2,
#H                  S3xTh,
#H                  41:40,
#H                  7^(1+4):(3x2.S7),
#H                  7xL2(8),
#H                  (7xL2(8)).3,
#H                  O7(3)N3A,
#H                  O8+(3).2_1',
#H                  O8+(3).2_1'',
#H                  O8+(3).2_2',
#H                  O8+(3).(2^2)_{122},
#H                  S4(9),
#H                  S4(9).2_i,
#H                  2.U4(3).2_2',
#H                  2.U4(3).(2^2)_{133},
#H                  2.U4(3).D8,
#H                  3.U6(2).S3,
#H  added fusions 3.A6.2_i -> 3.A6.2^2,
#H                L2(49).2_i -> L2(49).2^2,
#H                L3(9).2_i -> L3(9).2^2,
#H                L4(4).2_i -> L4(4).2^2,
#H                G2(3) -> O7(3),
#H                L2(17) -> S8(2),
#H                2.L3(4).2_2 -> 2.M22.2
#H                3.L3(4).2_2 -> 3.L3(4).3.2_2
#H                3.L3(4).3 -> 3.L3(4).3.2_2
#H                2^5:S6 -> 2.M22.2
#H                O8+(3) -> O8+(3).2_1',
#H                O8+(3) -> O8+(3).2_1'',
#H                O8+(3) -> O8+(3).2_2',
#H                O8+(3) -> O8+(3).(2^2)_{122},
#H                O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H                O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H                2.U4(3) -> 2.U4(3).2_2',
#H                2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_2 -> O7(3),
#H                2.U4(3).2_2' -> U4(3).2_2,
#H                2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).4 -> 2.U4(3).D8,
#H                3.U6(2).2 -> 3.U6(2).S3,
#H                3.U6(2).3 -> 3.U6(2).S3,
#H  replaced table of psl(3,4):d12 by L3(4).D12,
#H  changed table of O8+(3).S4 to a construction table,
#H  changed encoding of the table of 12.A6.2_3,
#H  added maxes of Sz(8), Sz(8).3,
#H      TB
#H
#H  Revision 4.26  2004/03/30 08:07:21  gap
#H  changed fusion 2xS3xU4(3).2_2 -> 2xS3xU4(3).(2^2)_{122}
#H      TB
#H
#H  Revision 4.25  2004/03/26 08:07:35  gap
#H  added automorphisms of 2xS3xU4(3).(2^2)_{122},
#H  added fusion (S3x2.U4(3).2_2).2 -> 2.Fi22.2,
#H  changed InfoText of 2^12.3^2.U4(3).2_2',
#H  changed fusion text for 3.2^(1+12).3U4(3).2 -> 3.F3+
#H      TB
#H
#H  Revision 4.24  2004/03/12 09:04:21  gap
#H  added table of 3.2^(1+12).3U4(3).2
#H  and of its factor group 2^12.3^2.U4(3).2_2'
#H  (Eamonn had asked for it)
#H      TB
#H
#H  Revision 4.23  2004/01/20 10:26:13  gap
#H  added several names of the forms `<name>C<class>', `<name>N<class>'
#H      TB
#H
#H  Revision 4.22  2003/11/17 15:49:55  gap
#H  added a few obvious fusions
#H      TB
#H
#H  Revision 4.21  2003/11/14 10:04:58  gap
#H  added a few direct products that are needed to construct other tables
#H      TB
#H
#H  Revision 4.20  2003/10/06 07:09:06  gap
#H  added some tables of maximal subgroups in 2.Fi22, 2.Fi22.2
#H  (for a question of J. An)
#H      TB
#H
#H  Revision 4.19  2003/01/21 16:25:32  gap
#H  further standardizations of `InfoText' strings,
#H  added and corrected `Maxes' infos,
#H  added some fusions
#H      TB
#H
#H  Revision 4.18  2003/01/14 17:28:49  gap
#H  changed `InfoText' values (for a better programmatic access)
#H  and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H  there is only one factor (again better programmatic handling)
#H      TB
#H
#H  Revision 4.17  2002/11/18 16:31:08  gap
#H  added comment for fusion (A4xO8+(2).3).2 -> F3+,
#H  added fusion A6xL2(8):3 -> F3+
#H      TB
#H
#H  Revision 4.16  2002/11/04 16:30:47  gap
#H  fixed info text of a max. subgroup of Fi24'
#H      TB
#H
#H  Revision 4.15  2002/10/22 12:44:08  gap
#H  added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H  (they make it possible to construct <p>-modular Brauer tables
#H  for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H  of <fact> is in the library)
#H      TB
#H
#H  Revision 4.14  2002/09/23 14:54:59  gap
#H  removed trailing blanks
#H      TB
#H
#H  Revision 4.13  2002/09/18 15:22:01  gap
#H  changed the `text' components of many fusions,
#H  in order to use them as a status information (for evaluation)
#H      TB
#H
#H  Revision 4.12  2002/07/12 06:45:55  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.11  2002/07/08 16:06:56  gap
#H  changed `construction' component from function (call) to list of function
#H  name and arguments
#H      TB
#H
#H  Revision 4.10  2002/03/25 18:09:48  gap
#H  F3+M9 is now created automatically
#H      TB
#H
#H  Revision 4.9  2002/03/04 17:08:48  gap
#H  added some fusions and admissible names
#H      TB
#H
#H  Revision 4.8  2001/05/04 16:48:20  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.8 of ctbllib coincides with Rev. 4.7 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctomaxi4.tbl,v
#H  Working file: ctomaxi4.tbl
#H  head: 4.7
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H  	GAP4R2: 4.5.0.4
#H  	GAP4R2PRE2: 4.5.0.2
#H  	GAP4R2PRE1: 4.3.0.2
#H  	GAP4R1: 4.2.0.2
#H  keyword substitution: kv
#H  total revisions: 10;	selected revisions: 10
#H  description:
#H  ----------------------------
#H  revision 4.7
#H  date: 2000/12/11 15:53:03;  author: gap;  state: Exp;  lines: +1502 -2
#H  added the tabel of "3^3.[3^10].GL3(3)" (one of the missing maxes of F3+)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 2000/10/09 17:21:50;  author: gap;  state: Exp;  lines: +549 -2
#H  added tables of 3_1.U4(3).2_2' and F3+M9
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 2000/02/21 12:41:46;  author: gap;  state: Exp;  lines: +5 -5
#H  added tables of Fi22.2M6 and 2.Fi22M5
#H  (Eamonn had asked for them)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 2000/02/17 08:38:28;  author: gap;  state: Exp;  lines: +157 -2
#H  added table of 2^10:M22:2 < Fi22.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 2000/02/02 11:49:07;  author: gap;  state: Exp;  lines: +1109 -593
#H  added table of the preimage of Fi22.2N2B in 3.Fi22
#H  (Eamonn had asked me for this table)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1999/07/14 11:39:39;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:42:51;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.3
#H  date: 1997/04/04 12:20:01;  author: sam;  state: Exp;  lines: +12 -13
#H  added 'ConstructPermuted', 'ConstructSubdirect',
#H  changed table constructions involving 'CharTable', 'RecFields'
#H      'Sort...' up to now
#H  ----------------------------
#H  revision 1.2
#H  date: 1996/10/29 13:54:32;  author: sam;  state: Exp;  lines: +24 -2
#H  added table of O8+(2):S3x2
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:00:07;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("(2^2x2^(1+8)).(3xU4(2)).2",
[
"origin: Dixon's Algorithm,\n",
"10th maximal subgroup of Fi23,\n",
"table is sorted w.r. to normal series 2.2^2.2^8.3.U4(2).2,\n",
"tests:"
],
[318504960,318504960,106168320,106168320,1179648,393216,331776,155520,155520,
1769472,1769472,589824,589824,24576,36864,18432,6144,3456,3456,73728,73728,
24576,24576,2048,2048,1536,576,576,248832,62208,3888,248832,62208,20736,20736,
4608,3888,3456,2592,10368,5184,10368,5184,1728,1728,576,864,41472,1296,41472,
13824,13824,2304,1296,768,3456,1152,216,9216,9216,3072,3072,384,288,288,1536,
1536,512,512,128,128,48,48,240,240,80,80,30,30,6912,6912,6912,6912,2304,2304,
432,432,1152,288,288,3456,3456,864,864,864,864,288,288,192,288,144,3456,3456,
1152,1152,432,432,576,192,72,576,576,288,288,192,192,48,216,216,54,216,216,72,
72,54,36,288,288,288,288,96,96,72,72,48,92160,92160,92160,92160,3072,3072,
3072,6144,6144,6144,6144,3072,512,512,384,384,1536,1536,1536,1536,128,512,512,
512,512,128,64,144,144,144,144,576,576,576,576,96,96,96,192,192,192,192,96,48,
48,64,64,64,64,32,32,40,40,40,40,48,48,48,48],
[,[1,1,1,1,1,1,2,8,8,1,1,1,1,1,2,5,5,8,8,1,1,1,1,6,6,5,8,8,29,30,31,29,30,30,
30,29,31,32,33,40,41,40,41,41,41,40,42,48,49,48,48,48,48,49,48,50,50,54,11,11,
13,13,15,19,19,21,21,21,21,24,24,28,28,74,74,74,74,78,78,30,30,29,29,30,30,31,
31,32,36,33,40,40,41,41,40,40,41,41,40,42,46,48,48,48,48,49,49,53,53,54,41,41,
40,40,41,41,46,118,119,120,118,119,118,118,120,122,80,80,82,82,84,84,87,87,88,
1,1,4,4,5,6,1,6,6,5,5,4,6,5,7,7,21,23,23,21,24,21,21,23,23,24,25,41,41,45,45,
48,48,52,52,53,55,48,53,53,55,55,52,57,56,59,59,62,62,63,63,74,74,76,76,112,
116,116,112],[1,2,3,4,5,6,7,1,2,10,11,12,13,14,15,16,17,10,11,20,21,22,23,24,
25,26,20,21,1,1,1,2,2,3,4,5,2,7,7,1,1,2,2,3,4,5,7,1,1,2,3,4,5,2,6,7,7,7,59,60,
61,62,63,59,60,66,67,68,69,70,71,66,67,74,75,76,77,74,75,11,10,11,10,13,12,10,
11,15,16,15,11,10,11,10,11,10,13,12,14,15,16,10,11,13,12,10,11,16,17,15,20,21,
20,21,22,23,26,30,30,30,33,33,34,35,33,39,60,59,60,59,61,62,60,59,63,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,
157,158,159,160,161,162,136,137,138,139,137,136,139,138,140,141,142,146,145,
144,143,147,150,151,181,182,183,184,185,186,187,188,189,190,155,154,153,
152],,[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,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,1,2,4,3,8,9,80,
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,
181,182,183,184,186,185,137,136,138,139,191,192,193,194]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[10,10,10,10,
10,10,10,10,10,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,
1,1,1,1,-2,-2,-2,-2,-2,-2,-2,-2,4,4,4,4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,-2,-2,-2,
-2,-2,-2,-2,-2,0,0,0,0,0,0,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,6,6,6,6,-2,-2,-2,-2,
-2,-2,-2,-2,-2,-2,2,2,2,2,2,2,2,2,2,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,3,3,3,3,
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[(185,186),(136,137)(138,139)(143,144)(145,146)(152,155)(153,154)(157,158)
(159,160)(163,164)(165,166)(167,168)(169,170)(174,175)(176,177)(181,182)
(183,184)(187,188)(189,190)(191,194)(192,193)]);
ALF("(2^2x2^(1+8)).(3xU4(2)).2","(3xU4(2)):2",[1,1,1,1,1,1,1,2,2,8,8,8,8,
8,8,8,8,9,9,11,11,11,11,11,11,11,10,10,33,32,31,33,32,32,32,33,31,33,32,6,
7,6,7,7,7,6,6,24,23,24,24,24,24,23,24,24,24,23,20,20,20,20,20,19,19,12,12,
12,12,12,12,13,13,39,39,39,39,38,38,28,28,30,30,28,28,29,29,30,30,28,5,5,
3,3,4,4,3,3,5,5,4,44,44,44,44,45,45,44,44,45,18,18,17,17,18,18,17,40,41,
42,40,41,40,40,42,41,36,36,34,34,36,36,35,35,34,27,27,27,27,27,27,25,25,
25,25,25,25,25,25,25,25,15,15,15,15,15,14,14,14,14,14,14,43,43,43,43,26,
26,26,26,26,26,22,22,22,22,22,22,22,22,21,21,21,21,21,21,37,37,37,37,16,
16,16,16]);
ALF("(2^2x2^(1+8)).(3xU4(2)).2","Fi23",[1,4,2,3,3,4,10,7,20,2,4,3,4,4,12,
9,11,18,25,4,3,4,4,10,12,11,26,24,6,6,8,19,21,15,17,17,27,43,46,7,7,25,26,
18,24,24,49,5,8,22,14,16,16,28,22,44,48,54,10,12,12,10,32,49,53,11,9,11,
11,30,31,55,51,13,40,39,38,62,91,19,15,21,15,21,17,23,28,47,45,52,20,18,
25,18,26,18,26,24,26,53,51,14,22,22,16,23,27,42,50,56,20,24,25,24,26,25,
55,35,33,36,68,69,66,71,72,93,47,43,52,46,52,46,56,54,83,3,4,11,9,11,10,4,
10,10,11,9,11,12,11,30,31,11,12,10,9,30,11,11,12,10,31,32,24,26,55,51,22,
16,42,50,50,48,22,42,50,48,44,50,84,82,31,30,31,30,63,64,40,39,75,74,51,
49,53,55],[
"fusion map is unique up to table automorphisms"
]);
ALN("(2^2x2^(1+8)).(3xU4(2)).2",["Fi23C2C","Fi23N2C"]);

MOT("(3xO8+(3):3):2",
[
"origin: constructed in GAP using tables of O8+(3).3, O8+(3).3.2, F3+,\n",
"3rd maximal subgroup of F3+, 3A normalizer in F3+,\n",
"tests: 1.o.r., pow[2,3,5,7,13]"
],
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648,648,120,38211264,52488,5184,648,5832,4374,2187,1458,864,864,108,648,162,
162,63,72,72,81,108,117,117,44569618329600,78382080,2985984,612220032,
56687040,56687040,4251528,1417176,472392,118098,124416,8640,13824,5400,139968,
93312,23328,23328,15552,15552,1944,5832,1944,5832,1944,1458,252,288,288,8748,
8748,6561,2187,729,243,120,5184,1296,1296,1728,972,324,216,216,117,117,84,135,
135,324,324,60,38211264,38211264,52488,52488,5184,5184,648,648,5832,5832,4374,
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63,72,72,72,72,81,81,108,108,117,117,117,117,9170703360,1244160,207360,48384,
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2916,2592,648,324,192,64,240,240,2592,864,864,432,288,288,288,72,72,72,72,28,
648,324,216,54,54,54,54,40,24,26,26,28,30,30,36],
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108,87,89,92,93,89,95,96,90,91,119,118,100,121,122,103,104,109,126,127,128,
129,126,127,128,129,134,135,136,137,138,139,140,141,130,131,130,131,132,133,
134,135,136,137,140,141,154,155,142,143,144,145,160,161,148,149,166,167,164,
165,1,1,2,2,2,3,4,6,5,5,7,8,4,9,5,7,8,10,6,9,10,11,13,14,14,15,18,15,17,18,16,
19,21,21,22,23,27,31,30,31,34,35,32,33,36,39,46,45,47,49,48,50],[1,2,3,1,1,1,
1,1,1,1,11,12,13,14,2,3,2,2,3,3,2,3,3,3,3,3,27,28,29,4,4,4,4,7,8,36,11,11,11,
13,11,11,12,12,45,46,47,14,14,15,15,52,1,1,3,3,7,7,7,7,11,13,13,22,22,22,27,
28,29,32,41,45,46,1,2,3,1,1,1,1,1,1,1,11,12,13,14,2,3,2,2,3,3,2,3,3,3,3,3,27,
28,29,4,4,4,4,7,8,36,11,11,11,13,11,11,12,12,45,46,47,14,14,15,15,52,1,1,1,1,
3,3,3,3,7,7,7,7,7,7,7,7,11,11,13,13,13,13,22,22,22,22,22,22,27,27,28,28,29,29,
32,32,41,41,45,45,46,46,168,169,170,171,172,173,168,168,168,169,168,168,169,
168,169,169,169,168,169,169,169,189,190,191,192,170,170,171,170,172,173,173,
171,172,173,173,204,174,174,180,178,179,180,180,212,189,214,215,216,191,192,
193],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,15,16,17,18,19,20,21,22,23,24,25,26,27,
28,29,30,31,32,33,34,35,2,37,38,39,40,41,42,43,44,46,45,47,5,6,50,51,12,53,54,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,72,74,75,76,77,78,79,80,
81,82,83,84,85,86,74,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,
105,106,107,108,75,110,111,112,113,114,115,116,117,119,118,120,78,79,123,124,
85,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,
163,166,167,164,165,168,169,170,171,172,173,174,175,176,177,178,179,180,181,
182,183,184,185,186,187,188,189,190,168,169,193,194,195,196,197,198,199,200,
201,202,203,204,205,206,207,208,209,210,211,170,213,215,214,216,175,177,
219],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,
28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,46,45,2,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,53,68,69,70,71,73,72,74,75,76,77,78,79,
80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,74,101,102,103,
104,105,106,107,108,109,110,111,112,113,114,115,116,117,119,118,75,121,122,
123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,
142,143,144,145,146,147,148,149,150,151,152,153,126,127,156,157,158,159,160,
161,162,163,166,167,164,165,168,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,
199,200,201,202,203,168,205,206,207,208,209,210,211,212,213,215,214,171,217,
218,219],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,1,1,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,53,53,74,75,76,
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,
102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,74,74,120,121,
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,
160,161,162,163,126,127,126,127,168,169,170,171,172,173,174,175,176,177,178,
179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,
198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,168,168,216,
217,218,219]],
0,
[( 45, 46)( 72, 73)(118,119)(164,166)(165,167)(214,215),(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),( 53,126)( 54,128)( 55,130)( 56,132)( 57,134)
( 58,136)( 59,138)( 60,140)( 61,142)( 62,144)( 63,146)( 64,148)( 65,150)
( 66,152)( 67,154)( 68,156)( 69,158)( 70,160)( 71,162)( 72,164)( 73,166)],
[ "ConstructIndexTwoSubdirectProduct", "C3", "S3", "O8+(3).3", "O8+(3).3.2", 
  [ 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 ], (), 
  (127,178,156,140,184,160,194,166,146,187,203,210,213,215,218,216,219,217,
    177,155,191,204,211,175,153,139,133,181,201,169,149,189,163,196,206,172,
    152,193,165,145,186,202,170,150,138,132,180,200,209,212,214,176,154,190,
    164,197,207,173,198,168,148,188,162,144,136,182,158,142,134,130,128,179,
    157,141,185,161,195,167,147,137,183,159,143,135,131,129)(151,192,205,
    171)(174,199,208) ]);
ALF("(3xO8+(3):3):2","F3+",[1,2,3,5,6,4,5,7,6,7,9,10,9,12,15,17,18,13,21,
16,18,17,22,14,21,20,24,26,26,30,31,29,33,30,34,35,39,42,38,39,39,43,49,
41,51,51,52,56,54,62,60,67,4,7,16,22,29,33,33,31,40,38,43,61,63,59,69,77,
76,84,97,99,100,4,13,16,4,5,6,7,6,7,7,38,41,40,54,13,16,15,18,17,21,19,22,
21,22,20,22,69,76,77,30,31,32,33,33,34,90,38,39,42,40,43,42,44,49,100,99,
103,55,56,62,60,108,8,8,8,8,23,23,23,23,31,31,29,29,32,32,33,33,46,47,47,
46,47,46,59,59,61,61,63,63,70,70,78,79,79,78,84,84,95,96,101,102,102,101,
2,3,10,10,10,11,15,13,18,14,15,19,17,18,21,17,20,19,16,21,22,26,26,35,36,
44,41,44,49,41,45,48,49,49,45,50,52,60,62,59,62,64,61,63,67,76,83,83,87,
90,91,98],[
"fusion map is unique up to table automorphisms"
]);
ALF("(3xO8+(3):3):2","O8+(3).3.2",[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,
65,66,67,68,69,70,71,72,73,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,
60,60,61,61,62,62,63,63,64,64,65,65,66,66,67,67,68,68,69,69,70,70,71,71,
72,72,73,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
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]);
ALF("(3xO8+(3):3):2","S3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3]);
ALN("(3xO8+(3):3):2",["(3xO8+(3).3):2","F3+N3A"]);

MOT("(A4xO8+(2).3).2",
[
"12th maximal subgroup of Fi24'"
],
[12541132800,7962624,1105920,221184,1866240,139968,46656,331776,36864,4608,
4608,7200,41472,6912,15552,5184,1728,1728,504,2304,2304,648,480,3456,2592,576,
360,435456,7776,6912,1728,864,648,3456,1728,1152,144,216,252,288,288,5806080,
18432,15360,9216,1536,1536,512,8640,2592,576,432,288,144,384,128,32,120,576,
192,144,48,48,28,36,40,48,60,4180377600,2654208,368640,73728,622080,46656,
15552,110592,12288,1536,1536,2400,13824,2304,5184,1728,576,576,168,768,768,
216,160,1152,864,192,120,145152,2592,2304,576,288,216,1152,576,384,48,72,84,
96,96,1567641600,995328,138240,27648,233280,17496,5832,41472,4608,576,576,900,
5184,864,1944,648,216,216,63,288,288,81,60,432,324,72,45,108864,108864,1944,
1944,1728,1728,432,432,216,216,162,162,864,864,432,432,288,288,36,36,54,54,63,
63,72,72,72,72,5806080,18432,15360,9216,1536,1536,512,8640,2592,576,432,288,
144,384,128,32,120,576,192,144,48,48,28,36,40,48,60],
[,[1,1,1,1,5,6,7,2,2,3,4,12,5,5,6,7,7,7,19,8,9,22,12,13,15,14,27,28,29,28,28,
29,33,30,30,30,32,33,39,34,36,1,1,3,3,2,3,3,5,6,5,7,6,7,8,9,11,12,14,14,17,17,
15,19,22,23,24,27,1,1,1,1,5,6,7,2,2,3,4,12,5,5,6,7,7,7,19,8,9,22,12,13,15,14,
27,28,29,28,28,29,33,30,30,30,32,33,39,34,36,110,110,110,110,114,115,116,111,
111,112,113,121,114,114,115,116,116,116,128,117,118,131,121,122,124,123,136,
137,138,139,140,137,138,137,138,139,140,147,148,141,142,141,142,141,142,145,
146,147,148,159,160,149,150,153,154,69,69,71,71,70,71,71,73,74,73,75,74,75,76,
77,79,80,82,82,85,85,83,87,90,91,92,95],[1,2,3,4,1,1,1,8,9,10,11,12,2,3,2,2,3,
4,19,20,21,6,23,8,8,10,12,1,1,2,4,4,6,8,8,9,11,15,19,20,21,42,43,44,45,46,47,
48,42,42,43,42,43,43,55,56,57,58,45,44,45,47,46,64,50,66,55,58,69,70,71,72,69,
69,69,76,77,78,79,80,70,71,70,70,71,72,87,88,89,74,91,76,76,78,80,69,69,70,72,
72,74,76,76,77,79,83,87,88,89,1,2,3,4,1,1,1,8,9,10,11,12,2,3,2,2,3,4,19,20,21,
6,23,8,8,10,12,1,1,1,1,2,2,4,4,4,4,6,6,8,8,8,8,9,9,11,11,15,15,19,19,20,20,21,
21,165,166,167,168,169,170,171,165,165,166,165,166,166,178,179,180,181,168,
167,168,170,169,187,173,189,178,181],,[1,2,3,4,5,6,7,8,9,10,11,1,13,14,15,16,
17,18,19,20,21,22,3,24,25,26,5,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,42,59,60,61,62,63,64,65,44,67,49,
69,70,71,72,73,74,75,76,77,78,79,69,81,82,83,84,85,86,87,88,89,90,71,92,93,94,
73,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,110,122,123,124,125,126,127,128,129,130,131,112,133,
134,135,114,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,
172,173,174,175,176,177,178,179,180,165,182,183,184,185,186,187,188,167,190,
172],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,20,21,22,23,24,25,26,27,
28,29,30,31,32,33,34,35,36,37,38,28,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,42,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,
80,81,82,83,84,85,86,69,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,
104,105,106,96,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,125,126,127,110,129,130,131,132,133,134,135,136,137,138,139,140,141,
142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,137,138,
161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,165,188,189,190,191]],
0,
[(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)],
["ConstructIndexTwoSubdirectProduct","a4","Symm(4)","O8+(2).3","O8+(2).3.2",
[246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,
265,266,267,268,269,270,271,272,314,315,316,317,318,319,320,321,322,323,324,
325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340],(42,69,96,
123,150,54,81,108,135,162,66,93,120,147,51,78,105,132,159,63,90,117,144,48,75,
102,129,156,60,87,114,141,45,72,99,126,153,57,84,111,138)(43,70,97,124,151,55,
82,109,136,163,67,94,121,148,52,79,106,133,160,64,91,118,145,49,76,103,130,
157,61,88,115,142,46,73,100,127,154,58,85,112,139)(44,71,98,125,152,56,83,110,
137,164,68,95,122,149,53,80,107,134,161,65,92,119,146,50,77,104,131,158,62,89,
116,143,47,74,101,128,155,59,86,113,140),(70,164,136,108,88,174,146,118,94,80,
74,167,139,111,91,176,148,120,189,161,133,105,182,154,126,98,82,171,143,115,
93,79,73,166,138,110,90,78,169,141,113,184,156,128,100,180,152,124,96,179,151,
123,191,163,135,107,87,77,168,140,112,92,177,149,121,95,178,150,122,190,162,
134,106,183,155,127,99,83,75,71,165,137,109,89,175,147,119,188,160,132,104,86,
173,145,117,187,159,131,103,85,172,144,116,186,158,130,102,84,76,72)(81,170,
142,114,185,157,129,101,181,153,125,97)]);
ALF("(A4xO8+(2).3).2","S4xO8+(2):S3",[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,
40,41,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,
263,264,265,266,267,268,269,270,271,272,69,70,71,72,73,74,75,76,77,78,79,
80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,164,
165,165,166,166,167,167,168,168,169,169,170,170,171,171,172,172,173,173,
174,174,175,175,176,176,177,177,314,315,316,317,318,319,320,321,322,323,
324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340],[
"fusion map is unique"
]);
ALF("(A4xO8+(2).3).2","F3+",[1,3,2,3,4,5,6,9,9,10,9,12,16,13,17,21,18,14,
24,26,26,30,35,38,39,41,54,4,7,16,16,22,31,40,40,38,43,59,69,77,76,2,3,10,
10,11,10,10,13,15,16,18,17,21,26,26,26,35,41,41,49,49,45,52,62,67,76,90,2,
2,3,3,13,15,18,9,9,10,11,35,13,16,15,18,21,21,52,26,26,62,36,40,39,41,90,
13,19,13,16,20,60,38,40,40,50,60,103,77,76,4,16,13,16,6,7,7,38,40,41,40,
54,21,18,22,20,19,22,69,76,77,33,90,42,43,49,56,8,8,8,8,23,23,23,23,23,23,
33,33,46,47,46,47,47,46,47,46,63,63,70,70,78,79,79,78,10,10,9,9,10,11,11,
41,44,41,49,44,49,26,26,28,67,38,40,42,48,44,87,98,68,77,108],[
"determined by the factorization of the fusion of the subgroup 3xO8+(2).3\n",
"through (A4xO8+(2).3).2 and (3xO8+(3):3):2"
]);
ALF("(A4xO8+(2).3).2","Symm(4)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]);
ALF("(A4xO8+(2).3).2","O8+(2).3.2",[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,
64,65,66,67,68,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,28,29,29,30,30,
31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,43,
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]);
ALN("(A4xO8+(2).3).2",["(a4xo8+(2):3):2"]);

MOT("(A5xA9):2",
[
"origin: constructed in GAP using tables of A5, A5.2, A9, A9.2, F3+,\n",
"18th maximal subgroup of F3+,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[21772800,57600,23040,129600,9720,6480,2880,1920,7200,2880,720,840,540,2400,
1440,900,1451520,3840,1536,8640,648,432,192,128,480,192,48,56,36,160,96,60,
1088640,2880,1152,6480,486,324,144,96,360,144,36,42,27,120,72,45,907200,2400,
960,5400,405,270,120,80,300,120,30,35,45,45,100,60,75,75,60480,1728,2880,192,
864,864,216,216,108,48,120,144,84,120,20160,576,960,64,288,288,72,72,36,16,40,
48,28,40,30240,864,1440,96,432,432,108,108,54,24,60,72,42,60],
[,[1,1,1,4,5,6,2,3,9,4,6,12,13,9,10,16,1,1,1,4,5,6,2,3,9,4,6,12,13,9,10,16,33,
33,33,36,37,38,34,35,41,36,38,44,45,41,42,48,49,49,49,52,53,54,50,51,57,52,54,
60,62,61,57,58,66,65,1,1,2,2,4,4,6,6,5,8,9,10,12,14,17,17,18,18,20,20,22,22,
21,24,25,26,28,30,33,33,34,34,36,36,38,38,37,40,41,42,44,46],[1,2,3,1,1,1,7,8,
9,2,3,12,5,14,7,9,17,18,19,17,17,17,23,24,25,18,19,28,21,30,23,25,1,2,3,1,1,1,
7,8,9,2,3,12,5,14,7,9,49,50,51,49,49,49,55,56,57,50,51,60,53,53,63,55,57,57,
67,68,69,70,67,68,67,68,68,76,77,69,79,80,81,82,83,84,81,82,81,82,82,90,91,83,
93,94,67,68,69,70,67,68,67,68,68,76,77,69,79,80],,[1,2,3,4,5,6,7,8,1,10,11,12,
13,2,15,4,17,18,19,20,21,22,23,24,17,26,27,28,29,18,31,20,33,34,35,36,37,38,
39,40,33,42,43,44,45,34,47,36,1,2,3,4,5,6,7,8,1,10,11,12,13,13,2,15,4,4,67,68,
69,70,71,72,73,74,75,76,67,78,79,69,81,82,83,84,85,86,87,88,89,90,81,92,93,83,
95,96,97,98,99,100,101,102,103,104,95,106,107,97],,[1,2,3,4,5,6,7,8,9,10,11,1,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,17,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,33,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,49,62,61,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,67,80,81,82,83,84,85,86,87,88,89,90,
91,92,81,94,95,96,97,98,99,100,101,102,103,104,105,106,95,108]],
0,
[(61,62),(65,66)],
["ConstructIndexTwoSubdirectProduct","A5","A5.2","A9","A9.2",[137,138,139,140,
141,142,143,144,145,146,147,148,149,150,167,168,169,170,171,172,173,174,175,
176,177,178,179,180,197,198,199,200,201,202,203,204,205,206,207,208,209,210],
(),(33,105,101,97,93,89,85,81,77,73,69,65,61,57,53,49,45,41,37,107,103,99,95,
91,87,83,79,75,71,67,63,59,55,51,47,43,39,35)(34,106,102,98,94,90,86,82,78,74,
70,66,62,58,54,50,46,42,38,108,104,100,96,92,88,84,80,76,72,68,64,60,56,52,48,
44,40,36)]);
ALF("(A5xA9):2","A5.2",[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,
2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,
7,7,7,7,7,7,7,7,7]);
ALF("(A5xA9):2","A9.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,
4,5,6,7,8,9,10,11,12,13,13,14,15,16,16,17,18,19,20,21,22,23,24,25,26,27,
28,29,30,17,18,19,20,21,22,23,24,25,26,27,28,29,30,17,18,19,20,21,22,23,
24,25,26,27,28,29,30]);
ALF("(A5xA9):2","A14",[1,2,3,5,7,6,9,10,15,17,18,27,32,34,39,51,2,3,4,17,
22,21,12,14,34,19,23,50,55,35,42,64,5,17,19,6,8,7,39,41,51,21,24,59,33,64,
44,53,15,34,35,51,52,53,56,57,16,64,65,68,70,71,36,72,54,54,2,3,9,12,17,
19,21,18,24,29,34,39,50,56,9,12,10,14,39,42,44,40,46,31,56,41,63,57,17,19,
39,42,21,20,22,24,25,61,64,44,69,72],[
"fusion map is unique up to table aut."
]);
ALF("(A5xA9):2","F3+",[1,2,3,4,5,6,10,9,12,13,14,24,30,35,41,54,2,3,3,13,
15,18,10,11,35,16,21,52,62,36,41,90,4,13,16,6,7,7,41,40,54,18,22,69,33,90,
49,56,12,35,36,54,55,56,67,68,12,90,91,94,106,107,35,108,54,54,2,3,10,10,
13,16,18,21,17,26,35,41,52,67,10,10,9,11,41,41,49,49,44,28,67,40,87,68,13,
16,41,41,18,21,19,20,22,77,90,49,103,108],[
"fusion map is unique up to table automorphisms"
]);
ALN("(A5xA9):2",["A14M6","(A5xA9).2"]);

MOT("29:14",
[
"25th maximal subgroup of F3+"
],
0,
0,
0,
[( 4, 6,12,16,14, 8)( 5, 9, 7,15,11,13),(2,3)],
["ConstructPermuted",["P:Q",[29,14]]]);
ALF("29:14","frob",[1,2,2,10,4,12,6,14,8,9,3,11,5,13,7,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("29:14","L2(29)",[1,16,17,10,8,9,6,11,7,2,7,11,6,9,8,10]);
ALF("29:14","F3+",[1,88,89,53,25,53,25,53,25,3,25,53,25,53,25,53],[
"fusion map is unique up to table automorphisms"
]);
ALF("29:14","Ru",[1,35,36,21,12,22,12,23,12,3,12,23,12,22,12,21],[
"fusion map is unique up to table automorphisms"
]);
ALN("29:14",["F3+N29","RuN29"]);

MOT("2^(5+8):(S3xA6)",
[
"origin: Dixon's Algorithm,\n",
"10th maximal subgroup of Fi22,\n",
"table sorted w.r. to normal series given by 2^4.2.2^8.3.2.A6,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[17694720,1179648,2949120,1769472,49152,16384,12288,12288,4608,34560,5760,
3456,2304,368640,61440,36864,24576,3072,1024,6144,6144,1024,6144,6144,3072,
3072,1024,1024,1024,1024,1024,1024,1024,512,512,512,512,256,256,256,192,192,
128,128,128,32,192,192,96,96,3456,432,3456,1152,1152,432,144,144,144,144,48,
48,144,144,96,96,1728,216,1728,216,144,144,96,144,36,24,384,384,128,128,384,
384,128,128,64,64,64,64,48,48,32,32,48,48,60,60,20,20,30,30,60,60,20,20,30,
30],
[,[1,1,1,1,1,1,2,2,4,10,10,10,10,1,1,1,1,5,5,1,1,1,2,2,2,2,5,5,2,5,5,5,5,5,5,
5,2,6,6,5,10,10,8,7,7,9,13,13,13,13,51,52,51,51,51,52,52,52,52,52,52,52,53,53,
54,54,67,68,67,68,67,67,67,69,70,73,20,20,20,20,24,24,24,24,27,28,27,28,42,42,
43,43,47,47,101,101,101,101,105,105,95,95,95,95,99,99],[1,2,3,4,5,6,7,8,9,1,3,
4,2,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,21,20,43,44,45,46,24,23,26,25,1,1,4,2,3,4,2,3,16,14,17,15,9,9,8,7,1,
1,4,4,14,16,5,9,9,18,77,78,79,80,81,82,83,84,85,86,87,88,78,77,91,92,82,81,
101,102,103,104,101,102,95,96,97,98,95,96],,[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,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,92,91,
93,94,1,3,14,15,10,11,1,3,14,15,10,11]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[5,5,5,5,5,5,5,5,5,
5,5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[5,5,5,5,5,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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,-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],[8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(5)-E(5)^4,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,
-E(5)^2-E(5)^3],
[GALOIS,[4,2]],[9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,1,1,1,1,1,1,1,1,1,1,1,1,
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,
0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1],[10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,-2,-2,-2,-2,
-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-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],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,1,1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,-1,1,1,-1,-1,1,1,
-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,[2,8]],
[TENSOR,[3,8]],
[TENSOR,[5,8]],
[TENSOR,[4,8]],
[TENSOR,[6,8]],
[TENSOR,[7,8]],[2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,0,0,0,0,0,0,2,2,0,2,2,2,2,2,2,0,
0,0,0,0,2,0,0,0,0,2,2,-1,-1,2,0,0,0,-1,-1,-1,-1,-1,2,-1,-1,-1,2,2,2,0,0,0,0,
-1,-1,-1,-1,2,-1,2,-1,0,0,2,2,-1,0,2,2,0,0,2,2,0,0,0,0,2,2,-1,-1,0,0,-1,-1,2,
2,0,0,-1,-1,2,2,0,0,-1,-1],[10,10,10,10,10,10,10,10,10,-5,-5,-5,-5,0,0,0,0,0,
0,2,2,0,2,2,2,2,2,2,0,0,0,0,0,2,0,0,0,0,2,2,-1,-1,2,0,0,0,-1,-1,-1,-1,-2,4,-2,
-2,-2,4,4,4,0,0,0,0,-2,-2,-2,-2,-2,1,-2,1,0,0,-2,-2,1,0,-2,-2,0,0,-2,-2,0,0,0,
0,-2,-2,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[10,10,10,10,10,10,10,10,10,-5,
-5,-5,-5,0,0,0,0,0,0,2,2,0,2,2,2,2,2,2,0,0,0,0,0,2,0,0,0,0,2,2,-1,-1,2,0,0,0,
-1,-1,-1,-1,1,-2,1,1,1,-2,-2,-2,0,0,0,0,1,1,1,1,4,-2,4,-2,0,0,4,4,-2,0,-2,-2,
0,0,-2,-2,0,0,0,0,-2,-2,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,16,16,
16,16,16,16,-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,
0,0,0,0,0,0,0,0,0,0,1,-2,1,1,1,-2,-2,-2,0,0,0,0,1,1,1,1,-2,1,-2,1,0,0,-2,-2,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(5)^2-2*E(5)^3,-2*E(5)^2-2*E(5)^3,0,
0,E(5)^2+E(5)^3,E(5)^2+E(5)^3,-2*E(5)-2*E(5)^4,-2*E(5)-2*E(5)^4,0,0,
E(5)+E(5)^4,E(5)+E(5)^4],
[GALOIS,[18,2]],[18,18,18,18,18,18,18,18,18,-9,-9,-9,-9,0,0,0,0,0,0,2,2,0,2,2,
2,2,2,2,0,0,0,0,0,2,0,0,0,0,2,2,-1,-1,2,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,2,2,0,0,0,0,2,2,-1,-1,0,0,-1,-1,-2,-2,
0,0,1,1,-2,-2,0,0,1,1],[20,20,20,20,20,20,20,20,20,-10,-10,-10,-10,0,0,0,0,0,
0,-4,-4,0,-4,-4,-4,-4,-4,-4,0,0,0,0,0,-4,0,0,0,0,-4,-4,2,2,-4,0,0,0,2,2,2,2,
-1,2,-1,-1,-1,2,2,2,0,0,0,0,-1,-1,-1,-1,2,-1,2,-1,0,0,2,2,-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],[45,45,45,45,13,13,-3,-3,-3,0,
0,0,0,15,15,15,15,-1,-1,9,9,3,9,9,9,9,1,1,3,3,3,3,3,1,3,3,3,3,1,1,0,0,-3,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,0,9,0,3,3,1,-3,0,-1,3,3,1,1,3,
3,1,1,1,1,-1,-1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
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0,0,0,0,0,-16,0,0,-16,0,8,8,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,3,-1,0,0,0,0,3,-1,-1,
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0,0,1,1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[480,-32,160,-96,0,0,0,0,0,-15,-5,
3,1,0,0,0,0,0,0,-8,-24,0,8,24,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,1,0,0,0,0,-3,
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-4,0,0,0,0,0,0,-1,1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0],[480,-32,160,-96,0,0,0,
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[TENSOR,[84,8]],[480,-32,160,-96,0,0,0,0,0,-15,-5,3,1,0,0,0,0,0,0,24,8,0,-24,
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-1,0,0,0,0,0,0,0,0,0,0,0,0],[540,-36,-180,108,12,-4,-12,12,0,0,0,0,0,90,-30,
18,-6,-6,2,12,-12,2,12,-12,0,0,8,0,2,6,-6,6,-6,-4,-2,6,-2,-2,-4,4,0,0,0,-2,2,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,-2,
-2,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,-36,-180,108,12,-4,-12,
12,0,0,0,0,0,90,-30,18,-6,-6,2,12,-12,-6,12,-12,0,0,8,0,-6,-2,2,-2,2,-4,-2,6,
6,-2,4,-4,0,0,0,-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,
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[TENSOR,[87,8]],
[TENSOR,[88,8]],[540,-36,-180,108,12,-4,-12,12,0,0,0,0,0,90,-30,18,-6,-6,2,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,-36,-180,108,12,-4,-12,12,0,0,0,0,0,
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0,0,-2,-2,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[91,8]],
[TENSOR,[92,8]],[720,-48,240,-144,0,0,0,0,0,45,15,-9,-3,-180,-60,36,12,0,0,
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-1,1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[95,8]],[720,-48,240,-144,0,0,0,0,0,45,15,-9,-3,-180,-60,36,12,0,0,4,
12,-8,-4,-12,-4,4,0,0,8,4,4,-4,-4,0,0,0,0,0,0,0,3,1,0,0,0,0,-3,-1,1,-1,0,0,0,
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-1,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[97,8]],[720,-48,-240,144,-48,16,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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-2*E(8)-2*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[99,8]],[960,-64,320,-192,0,0,0,0,0,-30,-10,6,2,0,0,0,0,0,0,16,-16,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1080,-72,-360,216,24,-8,-24,24,0,0,0,0,0,180,
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0,0,0,0,0,0,0,0,0,0,0,0],[1440,-96,480,-288,0,0,0,0,0,-45,-15,9,3,0,0,0,0,0,0,
8,24,0,-8,-24,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-1,0,0,0,0,3,1,-1,1,0,0,0,0,
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0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0],[1440,-96,-480,288,-96,32,32,-32,0,0,0,0,0,0,
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18,6,-6,0,0,0,0,0,0,0,0,0,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 95,101)( 96,102)( 97,103)( 98,104)( 99,105)(100,106),(91,92),(63,64)]);
ALF("2^(5+8):(S3xA6)","Fi22",[1,3,2,4,3,4,9,11,12,5,15,20,18,2,3,4,4,10,
13,3,4,4,9,9,10,13,11,9,11,9,10,11,13,13,13,10,13,12,12,13,20,18,29,28,27,
30,39,40,46,41,6,7,21,17,16,24,23,19,22,19,24,23,42,43,45,38,7,8,22,25,19,
24,23,44,48,47,13,9,11,13,27,28,27,28,29,28,29,27,40,46,53,54,63,64,14,34,
34,35,52,65,14,34,34,35,52,65],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(5+8):(S3xA6)","2^(5+8):(S3xS6)",[1,2,3,4,5,6,7,8,9,71,72,73,74,
120,121,122,123,124,125,10,11,126,12,13,15,14,17,16,127,130,131,129,128,
18,132,133,134,135,19,20,75,76,21,136,137,138,77,78,80,79,84,26,85,86,87,
27,29,28,142,143,145,144,90,90,88,89,22,81,23,82,140,139,24,25,83,141,30,
31,147,146,32,33,149,148,150,151,35,34,92,91,152,152,94,93,36,37,153,154,
95,96,36,37,153,154,95,96],[
"fusion map is unique"
]);

MOT("2^(1+5+8).(S3xA6)",
[
"origin: Dixon's Algorithm"
],
[35389440,35389440,2359296,2359296,5898240,5898240,1769472,98304,98304,16384,
12288,12288,9216,9216,69120,69120,11520,11520,3456,4608,4608,737280,737280,
122880,122880,36864,49152,49152,6144,6144,1024,12288,12288,6144,1024,6144,
12288,12288,6144,6144,3072,1024,1024,1024,1024,2048,2048,1024,1024,512,1024,
1024,1024,1024,512,512,512,512,512,256,192,384,384,128,128,128,64,64,384,384,
192,96,192,192,6912,6912,864,864,6912,6912,2304,2304,2304,2304,864,864,288,288
,288,288,288,288,288,288,96,96,96,96,288,288,288,288,96,96,3456,3456,432,432,
3456,3456,432,432,288,288,288,288,192,192,288,288,72,72,48,48,384,384,128,128,
384,384,128,128,64,64,64,64,48,48,32,32,48,48,120,120,120,120,40,40,40,40,60,
60,60,60,120,120,120,120,40,40,40,40,60,60,60,60],
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13,20,20,20,21,21,21,75,75,77,77,75,75,75,75,75,75,77,77,77,77,77,77,77,77,77,
77,77,77,77,77,79,79,80,80,81,81,105,105,107,107,105,105,107,107,105,105,105,
105,105,105,109,109,111,111,117,117,33,32,32,33,37,38,38,37,42,43,42,43,63,62,
64,64,69,70,155,155,155,155,155,155,155,155,163,163,163,163,143,143,143,143,
143,143,143,143,151,151,151,151],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,6,5,7,3
,4,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,34,33,32,64,65,66,67,68,38,37,36,41,
40,39,1,2,1,2,7,7,3,4,5,6,7,7,4,3,6,5,26,26,22,23,27,28,24,25,13,14,14,13,12,
11,1,2,1,2,7,7,7,7,22,23,26,26,8,9,13,14,14,13,29,30,125,126,127,128,129,130,
131,132,133,134,135,136,126,125,139,140,130,129,155,156,157,158,159,160,161,
162,155,156,157,158,143,144,145,146,147,148,149,150,143,144,145,146],,[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,
126,127,128,129,130,131,132,133,134,135,136,137,138,140,139,141,142,1,2,5,6,22
,23,25,24,15,16,18,17,1,2,5,6,22,23,25,24,15,16,18,17]],
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1,1,1,1,1,1,1,1,1,1,1],[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
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,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0
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[GALOIS,[4,2]],[9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
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,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[10,10,10,10,10,
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,0,0,0,0,0,0,0,0,0,-12,12,6,-6,12,-12,-4,4,-4,4,6,-6,-2,2,-2,2,0,0,0,0,0,0,0,0
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,0,0,0,0,0,-2,2,2,-2,0,0,0,0,1,-1,-1,1,-2,2,2,-2,0,0,0,0,1,-1,-1,1],[960,-960,
-320,320,-640,640,0,0,0,0,0,0,0,0,-30,30,-20,20,0,10,-10,0,0,0,0,0,0,0,0,0,0,
-16,16,0,0,0,16,-16,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,
0,0,0,2,-2,0,0,2,-2,12,-12,-6,6,12,-12,4,-4,-4,4,6,-6,2,-2,-2,2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[960,-960,-320,
320,640,-640,0,0,0,0,0,0,0,0,-30,30,20,-20,0,10,-10,0,0,0,0,0,0,0,0,0,0,-16,16
,0,0,0,16,-16,-16,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,
2,-2,0,0,-2,2,12,-12,-6,6,-12,12,4,-4,4,-4,-6,6,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[960,-960,192,-192,0,0,
0,-64,64,0,0,0,16,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,-12,0,0,0,0
,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,-2,0,0,-6,6,6,-6,-6,6,6,-6,0,0,
0,0,2,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[960,-960,192,-192,0,0,0,-64,64,0,0,0,16,-16,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,-12,0,0,0,0,-12,12,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,-2,2,2,-2,0,0,12,-12,-3,3,12,-12,-3,3,0,0,0,0,-4,4,4,-4,-1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[960,-960,192,-192,0,0,0,-64,64,0,0,0,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-6,6,0,0,18,-18,6,-6,18,-18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2
,-4,4,0,0,-6,6,-3,3,-6,6,-3,3,0,0,0,0,2,-2,-2,2,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[960,-960,192,
-192,0,0,0,-64,64,0,0,0,16,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,
0,0,-18,18,6,-6,-18,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,2,-2,0,0,-6,6,-3,3,-6,
6,-3,3,0,0,0,0,2,-2,-2,2,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1440,-1440,288,-288,0,0,0,32,-32,0,0
,0,-24,24,0,0,0,0,0,0,0,240,-240,0,0,0,-48,48,-16,16,0,0,0,0,0,0,0,0,0,0,0,0,0
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3,-3,0,0,-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,
0,0,0,0,0,0,0,0,0,0],
[TENSOR,[165,8]]],
[(139,140),
(143,155)(144,156)(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)
(151,163)(152,164)(153,165)(154,166)
,
( 22, 23)( 24, 25)( 27, 28)( 29, 30)( 46, 47)( 51, 52)( 53, 54)( 56, 57)
( 67, 68)( 91, 92)( 93, 94)( 95, 96)( 97, 98)(113,114)(115,116)(123,124)
(147,148)(149,150)(159,160)(161,162)
,
(  5,  6)( 17, 18)( 24, 25)( 39, 40)( 56, 57)( 73, 74)( 79, 80)( 83, 84)
( 85, 86)( 89, 90)( 91, 92)( 97, 98)( 99,102)(100,101)(145,146)(149,150)
(153,154)(157,158)(161,162)(165,166)
]);
ALF("2^(1+5+8).(S3xA6)","2^(5+8):(S3xA6)",[1,1,2,2,3,3,4,5,5,6,7,8,9,9,10,
10,11,11,12,13,13,14,14,15,15,16,17,17,18,18,19,20,20,21,22,23,24,24,25,
25,26,27,28,29,30,31,31,32,33,34,35,35,36,36,37,38,38,39,39,40,41,42,42,
43,44,45,46,46,47,47,48,49,50,50,51,51,52,52,53,53,54,54,55,55,56,56,57,
57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,66,67,67,68,68,69,69,70,
70,71,71,72,72,73,73,74,74,75,75,76,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,
102,103,103,104,104,105,105,106,106]);
ALF("2^(1+5+8).(S3xA6)","2.Fi22",[1,2,6,5,3,4,7,5,6,7,16,19,20,21,8,9,26,
25,35,32,31,3,4,6,5,7,7,7,17,18,22,6,5,7,7,16,16,16,18,17,22,19,16,19,16,
17,18,19,22,22,22,22,17,18,22,21,20,20,21,22,35,31,32,50,49,48,52,51,69,
68,70,80,71,72,10,11,12,13,36,37,30,29,27,28,43,42,40,41,34,33,39,38,33,
34,42,43,41,40,74,73,75,76,79,67,12,13,14,15,38,39,45,44,33,34,42,43,40,
41,77,78,84,83,81,82,22,16,19,22,48,49,48,49,50,49,50,48,70,80,93,94,111,
112,23,24,59,60,59,60,61,62,91,92,113,114,23,24,59,60,59,60,61,62,91,92,
113,114],[
"fusion map is unique up to table aut."
]);

MOT("2x2F4(2)'",
[
"maximal subgroup of 2.Fi22",
],
0,
0,
0,
[(37,41)(38,42)(39,43)(40,44),(29,31)(30,32),(23,25)(24,26),(19,21)(20,22)(37,
39)(38,40)(41,43)(42,44),(33,35)(34,36)],
["ConstructDirectProduct",[["2F4(2)'"],["Cyclic",2]]]);
ALF("2x2F4(2)'","2.Fi22",[1,2,6,5,7,7,14,15,21,20,19,19,20,21,23,24,45,44,
50,50,50,50,51,52,52,51,62,61,84,83,84,83,85,86,87,88,93,93,94,94,94,94,
93,93]);

MOT("2^(6+8):(A7xS3)",
[
"origin: Dixon's Algorithm,\n",
"11th maximal subgroup of Fi23,\n",
"table is sorted w.r. to normal series given by 2^6.2^8.A7.3.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[247726080,35389440,11796480,7077888,688128,98304,36864,36864,36864,12288,
3456,3456,36864,18432,12288,6144,1024,1024,512,384,384,120,3456,3456,3456,
3456,864,864,576,288,192,192,168,168,384,384,384,64,64,120,120,120,288,288,
288,144,56,56,483840,27648,432,69120,27648,23040,13824,6912,6912,4608,1152,
576,432,432,432,384,1152,1152,1152,576,576,384,288,288,288,192,72,72,48,48,60,
21,21,48,48,48,60,60,60,5160960,737280,245760,147456,3072,43008,6144,3072,
2048,2048,1536,1024,1024,1024,128,128,1152,1152,288,288,288,288,288,288,192,
96,128,128,128,128,64,64,40,40,40,40,96,48,48,48,28,28,32,32,28,28],
[,[1,1,1,1,1,1,4,4,1,1,11,12,4,3,4,3,6,6,5,9,10,22,11,12,12,12,11,11,11,11,12,
12,33,34,7,13,15,18,17,22,22,22,26,26,23,29,33,34,49,50,51,49,50,49,49,50,50,
50,49,50,51,51,51,49,53,53,55,54,53,55,57,57,58,54,63,63,59,64,79,80,81,66,67,
70,79,79,79,1,1,1,1,1,5,5,4,5,5,3,6,5,6,10,9,11,11,12,12,12,12,11,11,11,11,8,
8,15,13,18,17,22,22,22,22,23,29,31,31,33,34,35,35,47,48],[1,2,3,4,5,6,7,8,9,
10,1,1,13,14,15,16,17,18,19,20,21,22,4,4,2,4,2,4,3,9,5,6,34,33,35,36,37,38,39,
40,42,41,8,7,13,14,48,47,1,1,1,2,4,3,4,2,4,3,9,9,4,2,4,10,8,7,13,14,13,15,7,8,
14,16,7,8,20,21,22,34,33,35,36,37,42,41,40,88,89,90,91,92,93,94,95,96,97,98,
99,100,101,102,103,91,88,89,91,88,91,91,89,90,92,114,115,116,117,118,119,121,
120,122,123,95,98,93,94,129,128,130,131,133,132],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,1,23,24,25,26,27,28,29,30,31,32,34,33,35,36,37,38,
39,3,2,2,43,44,45,46,48,47,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,49,81,80,82,83,84,52,52,54,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,114,115,116,117,118,119,89,89,90,88,124,125,126,127,129,128,131,130,133,
132],,[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,
27,28,29,30,31,32,1,1,35,36,37,38,39,40,42,41,43,44,45,46,5,5,49,50,51,52,53,
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,
49,49,82,83,84,86,85,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,
104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,121,120,122,
123,124,125,126,127,88,88,131,130,93,93]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-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,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,6,6,6,2,2,3,0,2,2,2,2,2,2,2,0,0,1,
3,0,0,0,3,3,3,-1,0,0,-1,-1,2,0,0,0,0,1,1,1,0,0,-1,-1,-1,-1,6,3,0,6,3,6,6,3,3,
3,2,-1,0,0,0,2,3,3,2,2,-1,2,3,3,-1,2,0,0,0,0,1,-1,-1,-1,0,0,1,1,1,-6,-6,-6,-6,
-2,-6,-6,-2,-2,-2,-2,-2,-2,-2,0,0,-3,-3,0,0,0,0,-3,-3,-3,1,-2,-2,0,0,0,0,-1,
-1,-1,-1,1,1,0,0,1,1,0,0,1,1],
[TENSOR,[4,2]],[10,10,10,10,10,10,10,10,-2,-2,1,1,-2,-2,-2,-2,-2,-2,-2,0,0,0,
1,1,1,1,1,1,1,1,1,1,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,-2,0,0,0,0,0,0,0,
1,1,1,1,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,10,1,1,10,1,10,10,1,1,1,-2,1,
1,1,1,-2,1,1,-2,-2,1,-2,1,1,1,-2,1,1,0,0,0,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,1,0,0,0,0,0,-10,-10,-10,-10,2,-10,-10,2,2,2,2,2,2,2,0,0,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,
-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6],
[GALOIS,[6,3]],
[TENSOR,[6,2]],
[TENSOR,[7,2]],[12,12,12,12,12,12,12,12,4,4,6,0,4,4,4,4,4,4,4,0,0,2,6,0,0,0,6,
6,6,-2,0,0,-2,-2,4,0,0,0,0,2,2,2,0,0,-2,-2,-2,-2,-6,-3,0,-6,-3,-6,-6,-3,-3,-3,
-2,1,0,0,0,-2,-3,-3,-2,-2,1,-2,-3,-3,1,-2,0,0,0,0,-1,1,1,1,0,0,-1,-1,-1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[14,14,14,14,14,14,14,14,2,2,-1,2,2,2,2,2,2,2,2,0,0,-1,-1,2,2,2,-1,
-1,-1,-1,2,2,0,0,2,0,0,0,0,-1,-1,-1,2,2,-1,-1,0,0,14,-1,2,14,-1,14,14,-1,-1,
-1,2,-1,2,2,2,2,-1,-1,2,2,-1,2,-1,-1,-1,2,2,2,0,0,-1,0,0,-1,0,0,-1,-1,-1,-14,
-14,-14,-14,-2,-14,-14,-2,-2,-2,-2,-2,-2,-2,0,0,1,1,-2,-2,-2,-2,1,1,1,1,-2,-2,
0,0,0,0,1,1,1,1,1,1,-2,-2,0,0,0,0,0,0],[14,14,14,14,14,14,14,14,2,2,2,-1,2,2,
2,2,2,2,2,0,0,-1,2,-1,-1,-1,2,2,2,2,-1,-1,0,0,2,0,0,0,0,-1,-1,-1,-1,-1,2,2,0,
0,14,2,-1,14,2,14,14,2,2,2,2,2,-1,-1,-1,2,2,2,2,2,2,2,2,2,2,2,-1,-1,0,0,-1,0,
0,2,0,0,-1,-1,-1,-14,-14,-14,-14,-2,-14,-14,-2,-2,-2,-2,-2,-2,-2,0,0,-2,-2,1,
1,1,1,-2,-2,-2,-2,-2,-2,0,0,0,0,1,1,1,1,-2,-2,1,1,0,0,0,0,0,0],
[TENSOR,[11,2]],
[TENSOR,[12,2]],[15,15,15,15,15,15,15,15,-1,-1,3,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,
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[TENSOR,[107,2]],[1680,720,80,-240,0,0,0,0,4,-12,-6,0,20,12,4,-4,0,0,0,-2,2,0,
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[TENSOR,[109,2]],[1680,-240,-240,144,-112,16,-16,16,0,0,0,-6,0,0,0,0,0,0,0,0,
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[TENSOR,[111,2]],[1792,-1280,768,-256,0,0,0,0,0,0,-8,-8,0,0,0,0,0,0,0,0,0,2,8,
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0,0,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,-E(5)+E(5)^2+E(5)^3
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[GALOIS,[113,2]],[2016,-1440,864,-288,0,0,0,0,24,-8,0,0,24,-24,-8,8,0,0,0,-4,
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0,0,0],[2016,864,96,-288,0,0,0,0,-24,8,0,0,-24,-24,8,8,0,0,0,0,0,1,0,0,0,0,0,
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0,0],
[TENSOR,[116,2]],[2240,-1600,960,-320,0,0,0,0,-48,16,8,8,-48,48,16,-16,0,0,0,
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0,0,0,0,0,0,0],[2520,-360,-360,216,56,-8,24,-24,0,0,0,-9,0,0,0,0,8,8,-8,0,0,0,
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[TENSOR,[119,2]],[2688,1152,128,-384,0,0,0,0,32,32,12,0,-32,0,-32,0,0,0,0,0,0,
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0,0,0,0,0,0],[2688,1152,128,-384,0,0,0,0,-32,-32,12,0,32,0,32,0,0,0,0,0,0,-2,
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0,0,0,0],[3360,1440,160,-480,0,0,0,0,40,8,-12,0,8,24,-24,-8,0,0,0,4,-4,0,-12,
0,0,0,0,0,4,4,0,0,0,0,0,4,-4,0,0,0,0,0,0,0,-4,0,0,0,-105,24,0,-45,24,-5,15,0,
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0,0,0],[3360,1440,160,-480,0,0,0,0,8,-24,-12,0,40,24,8,-8,0,0,0,-4,4,0,-12,0,
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0,0],[3360,-480,-480,288,-224,32,-32,32,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,-6,-6,6,
0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,-48,3,0,0,0,0,12,36,-24,0,0,
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3360,-480,-480,288,-224,32,-32,32,0,0,0,-12,0,0,0,0,0,0,0,0,0,0,0,12,12,-12,0,
0,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,-4,4,0,0,0,0,0,-12,3,0,36,0,0,-24,0,12,0,0,-3,
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-480,-480,288,-224,32,-32,32,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,-6,-6,6,0,0,0,0,-2,
2,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,-12,-6,0,36,0,0,-24,0,12,0,0,6,6,-6,0,-4,
4,0,0,0,0,-2,2,0,0,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3360,-480,-480,
288,-224,32,-32,32,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,-6,-6,6,0,0,0,0,-2,2,0,0,0,0,
0,0,0,0,0,0,2,-2,0,0,0,0,0,60,3,0,-36,0,0,12,-36,12,0,0,-3,-3,3,0,-4,4,0,0,0,
0,4,-4,0,0,1,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3780,-540,-540,324,84,
-12,36,-36,36,-12,0,0,-36,0,12,0,-8,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,630,-90,-90,54,6,-42,6,6,-10,6,-6,2,-2,2,2,2,0,0,0,0,
0,0,0,0,0,0,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[129,2]],[3780,-540,-540,324,84,-12,36,-36,-36,12,0,0,36,0,-12,0,0,-8,
4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,630,-90,-90,54,
6,-42,6,6,6,-10,-6,2,-2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,-2,2,2,2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],
[TENSOR,[131,2]],[4032,1728,192,-576,0,0,0,0,-48,16,0,0,-48,-48,16,16,0,0,0,0,
0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,0,0,0,0,0,0,-126,0,0,-54,0,-6,
18,0,0,0,6,0,0,0,0,-2,0,0,6,6,0,-2,0,0,0,-2,0,0,0,0,-1,0,0,0,0,0,1,1,-1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0]],
[(130,131),( 41, 42)( 85, 86)(120,121),( 33, 34)( 47, 48)( 80, 81)(128,129)
(132,133)]);
ALF("2^(6+8):(A7xS3)","A7xS3",[1,1,1,1,1,1,1,1,4,4,7,10,4,4,4,4,4,4,4,13,
13,16,7,10,10,10,7,7,7,19,10,10,22,25,4,13,13,13,13,16,16,16,10,10,19,19,
22,25,2,8,11,2,8,2,2,8,8,8,5,20,11,11,11,5,8,8,5,5,20,5,8,8,20,5,11,11,14,
14,17,23,26,20,14,14,17,17,17,3,3,3,3,6,3,3,6,6,6,6,6,6,6,15,15,9,9,12,12,
12,12,9,9,9,21,6,6,15,15,15,15,18,18,18,18,21,21,12,12,24,27,15,15,24,27]);
ALF("2^(6+8):(A7xS3)","Fi23",[1,2,3,4,3,4,12,10,3,4,7,7,10,9,10,11,10,12,
11,11,10,13,25,20,18,25,18,26,24,24,24,26,29,29,32,31,30,32,31,39,38,38,
49,53,49,51,60,60,5,6,8,14,19,16,22,15,21,17,16,17,27,23,28,22,43,47,44,
42,43,48,52,46,45,50,56,54,50,48,61,76,76,83,82,84,90,90,89,2,3,4,4,4,9,
11,12,11,9,11,12,11,10,12,11,20,18,24,26,18,25,25,24,26,26,31,30,31,30,32,
30,39,39,40,38,53,55,51,55,59,59,63,64,88,88],[
"fusion map is unique up to table automorphisms"
]);

MOT("2x3.O7(3)",
[
"2nd maximal subgroup of 6.Fi22"
],
0,
0,
0,
[(102,105)(103,106)(104,107)(228,231)(229,232)(230,233),( 18, 19)( 60, 61)
( 62, 63)( 78, 79)( 97, 98)(144,145)(186,187)(188,189)(204,205)(223,224),
(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 15, 16)( 23, 24)( 26, 27)( 29, 30)
( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 56, 57)
( 66, 67)( 69, 70)( 72, 73)( 75, 76)( 81, 82)( 84, 85)( 89, 90)( 92, 93)
( 95, 96)(100,101)(103,104)(106,107)(109,110)(112,113)(114,117)(115,119)
(116,118)(122,123)(125,126)(128,129)(131,132)(134,135)(137,138)(141,142)
(149,150)(152,153)(155,156)(158,159)(161,162)(164,165)(167,168)(171,172)
(175,176)(179,180)(182,183)(192,193)(195,196)(198,199)(201,202)(207,208)
(210,211)(215,216)(218,219)(221,222)(226,227)(229,230)(232,233)(235,236)
(238,239)(240,243)(241,245)(242,244)(248,249)(251,252)],
["ConstructDirectProduct",[["Cyclic",2],["3.O7(3)"]]]);
ALF("2x3.O7(3)","6.Fi22",[1,5,3,7,11,9,13,17,15,19,20,21,28,22,26,24,30,
32,28,30,32,37,41,39,46,50,48,46,50,48,52,53,54,55,59,57,67,71,69,61,65,
63,85,73,77,75,92,94,98,96,90,79,83,81,87,88,89,100,85,103,91,93,101,102,
104,108,106,122,120,124,119,123,121,125,129,127,131,133,131,141,145,143,
135,139,137,181,178,189,193,191,171,175,173,178,178,178,195,180,186,187,
188,197,201,199,203,207,205,209,213,211,215,219,217,227,231,229,233,237,
235,239,241,245,243,247,251,249,4,2,6,10,8,12,16,14,18,19,20,21,29,25,23,
27,31,33,29,31,33,40,38,42,49,47,51,49,47,51,52,53,54,58,56,60,70,68,72,
64,62,66,86,76,74,78,93,97,95,99,91,82,80,84,87,88,89,101,86,102,90,92,
100,103,107,105,109,119,123,121,122,120,124,128,126,130,132,134,132,144,
142,146,138,136,140,182,177,192,190,194,174,172,176,177,177,177,196,179,
186,187,188,200,198,202,206,204,208,212,210,214,218,216,220,230,228,232,
236,234,238,240,244,242,246,250,248,252],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2x3.O7(3)","2xO7(3)",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,6,6,7,8,9,10,11,12,
12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,20,20,20,
21,22,22,22,23,24,24,24,25,25,25,26,27,28,29,30,31,32,33,33,33,34,34,34,
35,35,35,36,36,36,37,38,39,40,40,40,41,41,41,42,43,44,44,44,45,45,45,46,
46,46,47,48,49,49,49,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,
55,56,57,57,57,58,58,58,59,59,59,60,60,60,61,61,61,62,62,62,63,64,64,64,
65,66,67,68,69,70,70,70,71,71,71,72,72,72,73,73,73,74,74,74,75,75,75,76,
76,76,77,78,78,78,79,80,80,80,81,82,82,82,83,83,83,84,85,86,87,88,89,90,
91,91,91,92,92,92,93,93,93,94,94,94,95,96,97,98,98,98,99,99,99,100,101,
102,102,102,103,103,103,104,104,104,105,106,107,107,107,108,108,108,109,
109,109,110,110,110,111,111,111,112,112,112,113,113,113,114,115,115,115,
116,116,116]);
ALN("2x3.O7(3)",["6.Fi22M2"]);

MOT("6.Fi22M3",
[
"3rd maximal subgroup of 6.Fi22"
],
0,
0,
0,
0,
["ConstructPermuted",["2x3.O7(3)"]]);
ALF("6.Fi22M3","6.Fi22",[1,3,5,10,12,8,13,15,17,19,21,20,28,22,24,26,30,
32,28,30,32,40,42,38,46,48,50,46,48,50,52,54,53,55,57,59,70,72,68,64,66,
62,86,73,75,77,92,94,96,98,91,79,81,83,87,89,88,101,86,103,90,93,100,102,
104,106,108,119,121,123,122,124,120,125,127,129,131,133,131,141,143,145,
138,140,136,181,180,192,194,190,174,176,172,180,180,180,195,178,186,188,
187,203,205,207,197,199,201,212,214,210,215,217,219,236,238,234,230,232,
228,240,241,243,245,250,252,248,4,6,2,7,9,11,16,18,14,19,21,20,29,25,27,
23,31,33,29,31,33,37,39,41,49,51,47,49,51,47,52,54,53,58,60,56,67,69,71,
61,63,65,85,76,78,74,93,97,99,95,90,82,84,80,87,89,88,100,85,102,91,92,
101,103,107,109,105,122,124,120,119,121,123,128,130,126,132,134,132,144,
146,142,135,137,139,182,179,189,191,193,171,173,175,179,179,179,196,177,
186,188,187,206,208,204,200,202,198,209,211,213,218,220,216,233,235,237,
227,229,231,239,244,246,242,247,249,251],[
"fusion 2x3.O7(3) -> 6.Fi22 mapped under 6.Fi22.2"
]);

MOT("2xO7(3)",
[
"2nd maximal subgroup of 2.Fi22"
],
0,
0,
0,
[( 54, 55)(112,113),( 50, 51)(108,109),(  8,  9)( 28, 29)( 30, 31)( 38, 39)
( 47, 48)( 66, 67)( 86, 87)( 88, 89)( 96, 97)(105,106)],
["ConstructDirectProduct",[["Cyclic",2],["O7(3)"]]]);
ALF("2xO7(3)","2.Fi22",[1,3,5,7,10,8,12,14,10,12,14,17,20,20,22,23,27,25,
33,29,38,40,36,31,35,42,33,45,37,39,43,44,46,52,51,53,55,57,55,61,59,77,
74,81,71,74,83,76,80,85,87,89,91,95,97,99,101,103,2,4,6,7,11,9,13,15,11,
13,15,18,21,21,22,24,28,26,34,30,39,41,37,32,35,43,34,44,36,38,42,45,47,
51,52,54,56,58,56,62,60,78,73,82,72,73,84,75,80,86,88,90,92,96,98,100,102,
104],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("2.Fi22M3",
[
"3rd maximal subgroup of 2.Fi22"
],
0,
0,
0,
0,
["ConstructPermuted",["2xO7(3)"]]);
ALF("2.Fi22M3","2.Fi22",[1,4,5,7,10,8,12,14,10,12,14,18,20,20,22,23,28,26,
34,29,38,40,37,31,35,43,34,45,36,39,42,44,46,51,52,53,55,57,55,61,60,77,
76,82,72,76,83,74,80,87,85,90,91,98,96,100,101,104,2,3,6,7,11,9,13,15,11,
13,15,17,21,21,22,24,27,25,33,30,39,41,36,32,35,42,33,44,37,38,43,45,47,
52,51,54,56,58,56,62,59,78,75,81,71,75,84,73,80,88,86,89,92,97,95,99,102,
103],[
"fusion 2xO7(3) -> 2.Fi22 mapped under 2.Fi22.2"
]);

MOT("3^(1+8).2^(1+6).3^(1+2).2S4",
[
"origin: Dixon's Algorithm,\n",
"maximal subgroup of Fi23,\n",
"characters and classes are sorted w.r. to normal series given by\n",
"3.3^8.2.2^6.3.3^2.2.2^2.3.2,\n",
"tests: 1.o.r., pow[2,3]"
],
[3265173504,1632586752,944784,3779136,236196,2125764,248832,497664,3456,6912,
15552,373248,746496,3888,17496,1458,104976,104976,104976,3888,3888,3888,1458,
1458,1458,4374,52488,104976,648,1296,108,216,62208,124416,5184,17496,139968,
10077696,5038848,8748,26244,2304,1152,216,2592,5184,216,1296,1296,1296,162,
3888,3888,3888,5184,2592,864,288,288,576,48,96,36,216,216,216,72,72,72,5832,
5832,419904,419904,419904,4374,5184,5184,5184,2592,2592,2592,216,216,432,432,
432,216,216,216,729,1458,4374,104976,104976,104976,1296,1296,1296,324,324,324,
162,729,1458,1458,8748,8748,8748,162,162,162,27,54,54,54,1296,1296,1296,216,
648,324,11664,11664,11664,486,36,216,216,216,72,72,72,162,3888,3888,3888,162,
3888,3888,3888,54,972,972,972,162,54,324,324,324,7776,648,3888,1296,972,972,
324,972,648,32,192,192,288,72,72,54,54,54,54,108,24,24,96,48,96,48,16,96,48,
96,48,16],
[,[1,2,3,4,5,6,2,1,7,8,4,2,1,3,15,16,17,18,19,19,17,18,23,24,25,26,27,28,27,
28,29,30,2,1,4,3,4,1,2,5,6,8,7,14,12,13,15,18,19,17,16,19,17,18,34,33,35,35,
33,34,43,42,47,48,49,50,48,49,50,70,71,72,73,74,75,73,74,72,72,73,74,71,70,78,
76,77,97,98,96,90,91,92,93,94,95,93,94,95,107,108,106,102,103,104,105,106,107,
108,109,110,111,112,110,111,109,73,74,72,71,71,70,72,73,74,75,83,80,81,79,98,
96,97,92,93,94,95,91,95,93,94,102,106,107,108,105,104,106,107,108,1,3,3,3,6,5,
5,6,4,10,10,10,13,11,14,25,26,23,24,28,32,32,55,57,55,58,62,55,57,55,58,62],[
1,1,1,1,1,1,8,8,10,10,13,13,13,13,2,6,1,1,1,8,8,8,6,6,6,1,1,1,8,8,10,10,34,34,
34,38,38,38,38,38,38,42,42,46,46,46,33,34,34,34,41,38,38,38,55,55,55,55,60,60,
62,62,56,55,55,55,60,60,60,2,2,1,1,1,1,8,8,8,13,13,13,12,12,10,10,10,10,10,10,
6,6,1,1,1,1,8,8,8,8,8,8,5,6,2,6,1,1,1,18,18,18,15,22,22,22,34,34,34,33,39,39,
38,38,38,38,45,46,46,46,42,42,42,34,34,34,34,41,38,38,38,40,38,38,38,41,33,34,
34,34,150,150,150,150,150,150,150,150,150,159,160,161,162,162,162,154,150,154,
154,150,160,161,172,172,174,174,176,177,177,179,179,181]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-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,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-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],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[4,2]],[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,-2,0,0,0,0,0,
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,-1,-1,-1,-1,-1,-1,
-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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,E(8)+E(8)^3,
E(8)+E(8)^3],
[TENSOR,[6,2]],[4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,0,0,0,0,0,
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,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-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],[8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[9,2]],[16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,
16,16,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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,-2,1,1,1,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,6,6,
6,6,6,6,6,6,6,-3,-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,
-2,-2,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,-3,-3,-3,
-3,-3,-3,-3,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-2,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[6,6,6,6,6,6,6,6,6,6,6,6,6,6,-3,-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,
0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,2,2,2,2,2,
2,2,2,-1,-1,-1,-1,-1,-1,-1,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,
3,3,3,3,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-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],[6,6,6,6,6,6,6,6,6,6,6,6,6,6,-3,
-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,
-2,-2,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,3,3,3,3,3,3,3,3,3,3,0,0,0,
0,0,0,0,-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,
1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
12,12,12,12,12,12,12,12,12,12,12,12,12,12,-6,-6,-6,-6,-6,-6,-6,-6,0,0,0,0,0,0,
0,0,0,0,4,4,4,4,4,4,4,4,4,4,4,4,4,4,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,3,3,3,3,3,3,3,-3,-3,
-3,-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,12,12,12,12,12,12,12,12,12,12,12,-6,
-6,-6,-6,-6,-6,-6,-6,0,0,0,0,0,0,0,0,0,0,4,4,4,4,4,4,4,4,4,4,4,4,4,4,-2,-2,-2,
-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,
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,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,12,12,12,
12,12,12,12,12,12,12,12,-6,-6,-6,-6,-6,-6,-6,-6,0,0,0,0,0,0,0,0,0,0,4,4,4,4,4,
4,4,4,4,4,4,4,4,4,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,
-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,
3,3,3,3,3,3,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-2,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[18,18,18,18,18,18,18,18,18,18,18,18,18,18,-9,-9,-9,-9,-9,-9,
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0,0,0,0,0,0,0,0,0,0,0,0,-9,0,9,0,0,0,-27,27,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,
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],[10368,-5184,0,0,0,0,64,-128,0,0,0,0,0,0,0,0,72,0,-72,-8,-8,16,0,0,0,0,
18,-36,-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,72,-144,72,0,16,-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-36,-36,72,
4,4,-8,-2,4,-2,0,0,0,0,-18,18,0,0,3,-3,0,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[10368,-5184,0,0,0,0,64,-128,0,0,0,0,0,0,0,0,72,0,
-72,-8,-8,16,0,0,0,0,18,-36,-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,72,72,-144,0,-8,16,-8,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,72,-36,-36,-8,4,4,-2,-2,4,0,0,0,0,0,-18,18,-3,0,3,0,-2,1,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10368,-5184,0,0,0,0,64,-128,0,
0,0,0,0,0,0,0,72,0,-72,-8,-8,16,0,0,0,0,18,-36,-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-144,72,72,0,-8,-8,16,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-36,72,-36,4,-8,4,4,-2,-2,0,0,0,0,18,0,-18,3,-3,0,
0,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[11664,-5832,
0,0,0,0,-72,144,8,-16,0,-72,144,0,0,0,0,0,0,0,0,0,0,0,0,0,27,-54,3,-6,-1,2,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-108,54,54,0,6,6,-12,-12,6,6,0,0,-4,2,2,-4,2,2,0,0,0,-54,108,-54,-6,12,-6,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[11664,-5832,0,0,0,0,-72,144,8,-16,0,-72,144,0,0,0,0,0,0,0,0,0,0,0,0,0,
27,-54,3,-6,-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,
0,0,0,0,0,0,0,0,0,54,-108,54,0,-12,6,6,6,-12,6,0,0,2,-4,2,2,-4,2,0,0,0,-54,
-54,108,-6,-6,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[11664,-5832,0,0,0,0,-72,144,8,-16,0,-72,144,0,0,
0,0,0,0,0,0,0,0,0,0,0,27,-54,3,-6,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,54,54,-108,0,6,-12,6,6,6,-12,0,0,2,2,
-4,2,2,-4,0,0,0,108,-54,-54,12,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[11664,-5832,0,0,0,0,72,-144,
0,0,0,0,0,0,0,0,0,-81,81,-9,18,-9,0,0,0,0,0,0,0,0,0,0,36,-72,0,0,0,648,-324,0,
0,0,0,0,0,0,0,-9,9,0,0,-9,18,-9,-12,6,0,0,2,-4,0,0,0,3,-3,0,-1,-1,2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[11664,-5832,0,0,0,
0,72,-144,0,0,0,0,0,0,0,0,-81,81,0,18,-9,-9,0,0,0,0,0,0,0,0,0,0,36,-72,0,0,0,
648,-324,0,0,0,0,0,0,0,0,9,0,-9,0,18,-9,-9,-12,6,0,0,2,-4,0,0,0,-3,0,3,-1,2,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
13122,-6561,0,0,0,0,-81,162,-9,18,0,135,-270,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,27,-54,0,0,0,-486,243,0,0,18,-9,0,-9,18,0,0,0,0,0,0,0,0,-18,9,0,0,-3,6,
-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0]],
[(160,161)(170,171)(172,177)(173,178)(174,179)(175,180)(176,181),( 72, 73, 74)
( 76, 77, 78)( 79, 80, 81)( 84, 85, 86)( 87, 88, 89)( 93, 94, 95)( 96, 97, 98)
( 99,100,101)(106,107,108)(109,110,111)(113,114,115)(116,117,118)(122,123,124)
(127,128,129)(130,131,132)(134,135,136)(138,139,140)(142,143,144)
(147,148,149)]);
ALF("3^(1+8).2^(1+6).3^(1+2).2S4","2^(1+6).3^(1+2).2S4",[1,1,1,1,1,1,2,2,
3,3,4,4,4,4,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,9,9,10,10,10,11,11,11,11,11,
11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,16,16,16,17,17,18,18,19,19,
19,19,20,20,20,21,21,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,25,25,
25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,29,29,29,29,30,30,30,30,
31,31,31,32,32,32,32,33,33,33,33,33,33,34,34,34,34,35,35,35,36,36,36,36,
37,37,37,37,38,38,38,38,38,39,39,39,39,40,40,40,40,40,40,40,40,40,41,42,
43,44,44,44,45,45,45,45,45,46,47,48,48,49,49,50,51,51,52,52,53]);
ALF("3^(1+8).2^(1+6).3^(1+2).2S4","Fi23",[1,6,7,5,8,6,19,4,43,10,16,17,3,
24,33,34,7,6,8,27,20,21,35,33,36,8,8,5,28,22,54,44,21,4,22,18,14,2,15,23,
15,12,47,51,45,9,69,19,28,25,67,23,18,15,10,46,44,48,52,12,83,32,93,43,54,
49,47,56,53,34,35,5,6,7,8,19,25,22,16,17,24,71,70,44,43,49,46,49,54,36,34,
8,8,6,7,28,21,25,26,28,27,37,35,36,34,8,7,8,33,36,35,87,72,68,69,21,26,22,
68,66,67,14,15,18,23,94,45,51,42,53,56,52,28,27,19,20,67,18,23,15,73,23,
18,23,67,72,28,25,27,4,25,20,26,21,27,28,19,22,30,31,31,11,50,55,72,28,68,
69,22,82,82,31,82,30,84,63,31,82,30,84,64],[
"fusion map is unique up to table automorphisms"
]);
ALN("3^(1+8).2^(1+6).3^(1+2).2S4",["Fi23N3B"]);

MOT("7:6xA7",
[
"19th maximal subgroup of F3+"
],
0,
0,
0,
[(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,46)(29,47)
(30,48)(31,49)(32,50)(33,51)(34,52)(35,53)(36,54),( 8, 9)(17,18)(26,27)(35,36)
(44,45)(53,54)(62,63)],
["ConstructDirectProduct",[["P:Q",[7,6]],["A7"]]]);
ALF("7:6xA7","F3+",[1,2,4,8,10,12,13,25,25,24,52,69,70,87,94,103,24,24,14,
21,22,23,49,91,20,104,105,6,18,7,8,49,56,19,72,71,3,3,16,23,10,36,16,53,
53,6,18,7,8,49,56,19,71,72,14,21,22,23,49,91,20,105,104],[
"fusion map is unique up to table automorphisms"
]);

MOT("A6xL2(8):3",
[
"20th maximal subgroup of F3+"
],
0,
0,
0,
[(56,67)(57,68)(58,69)(59,70)(60,71)(61,72)(62,73)(63,74)(64,75)(65,76)
(66,77),(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)
(33,44),( 6, 7)( 8, 9)(10,11)(17,18)(19,20)(21,22)(28,29)(30,31)(32,33)(39,40)
(41,42)(43,44)(50,51)(52,53)(54,55)(61,62)(63,64)(65,66)(72,73)(74,75)
(76,77)],
["ConstructDirectProduct",[["A6"],["L2(8).3"]]]);
ALF("A6xL2(8):3","F3+",[1,3,5,24,30,6,6,14,14,30,30,2,3,15,52,62,18,18,21,
21,62,62,4,16,7,69,33,7,7,22,22,33,33,8,23,8,70,29,8,8,23,23,32,32,10,10,
44,87,98,49,49,49,49,98,98,12,36,55,94,106,56,56,91,91,106,106,12,36,55,
94,107,56,56,91,91,107,107],[
"determined by the factorization of the fusion of the subgroup\n",
"3^2:2xL2(8).3 through A6xL2(8):3 and (3xO8+(3):3):2"
]);

MOT("Fi23M8",
[
"origin: Dixon's Algorithm,\n",
"8th maximal subgroup of Fi23,\n",
"table is sorted w.r. to normal series 3^3.3^7.2.L3(3),\n",
"tests: 1.o.r."
],
[663238368,25509168,12282192,944784,944784,944784,314928,39366,17496,8188128,
314928,34992,34992,34992,7776,7776,3888,3888,3888,3888,3888,1296,1296,1296,
1296,432,324,162,216,78732,78732,78732,78732,78732,78732,26244,26244,26244,
13122,13122,1458,8748,8748,8748,2916,2916,2916,2916,2916,2916,1458,1458,1458,
1458,486,486,486,162,486,162,486,486,486,243,162,162,162,54,54,27,1296,144,
648,216,216,216,216,72,72,72,72,72,36,972,972,972,324,324,324,324,324,324,324,
324,324,324,324,324,324,324,324,162,54,54,54,54,54,54,48,48,24,24,48,48,24,24,
78,26,39,78,26,39,78,26,39,78,26,39],
[,[1,2,3,4,5,6,7,8,9,1,2,5,4,6,1,1,5,4,6,2,2,3,4,5,6,7,7,8,9,30,31,32,33,34,
35,36,37,38,39,40,41,35,34,33,37,38,36,31,30,32,40,52,53,54,55,56,57,53,59,59,
61,62,63,64,65,61,62,63,65,70,16,16,21,22,23,25,24,26,25,24,23,21,29,32,30,31,
36,37,38,37,38,36,33,35,34,35,33,34,32,31,30,39,41,55,57,56,52,54,71,71,78,74,
71,71,78,74,123,123,125,126,126,128,120,120,122,117,117,119],[1,1,1,1,1,1,1,1,
2,10,10,10,10,10,15,16,15,15,15,15,16,16,16,16,16,16,15,15,21,1,1,1,1,1,1,1,1,
1,1,1,1,10,10,10,10,10,10,10,10,10,10,2,2,2,6,6,6,11,1,10,2,2,6,6,4,11,11,14,
13,9,71,72,71,71,71,71,71,71,72,72,72,72,73,16,16,16,16,16,16,15,15,15,16,16,
16,15,15,15,15,15,15,16,16,19,19,19,21,21,109,110,110,109,113,114,114,113,117,
118,117,120,121,120,123,124,123,126,127,126],,,,,,,,,,[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,
89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,113,114,
115,116,109,110,111,112,1,10,3,1,10,3,1,10,3,1,10,3]],
[[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,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1],[12,12,12,12,12,12,12,12,12,12,12,12,12,12,4,4,4,4,4,
4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[
13,13,13,13,13,13,13,13,13,13,13,13,13,13,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,
-3,-3,-3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,16,16,
16,16,16,16,16,16,16,16,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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,-2,1,1,1,1,1,1,
1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,E(13)+E(13)^3+E(13)^9,E(13)+E(13)^3+E(13)^9,
E(13)+E(13)^3+E(13)^9,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)^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)^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],
[GALOIS,[4,4]],
[GALOIS,[4,7]],
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-6,12,-6,3,0,0,0,0,0,0,0,-6,0,3,3,0,0,0,3,-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],
[TENSOR,[115,13]],[5616,-216,0,-216,0,216,0,0,0,624,-24,48,-24,-24,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-54,54,0,-72,36,-18,-18,36,-18,0,9,0,-6,-24,12,12,-6,-6,
-6,-6,12,3,0,0,0,0,0,0,0,3,-3,-6,3,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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],
[TENSOR,[117,13]],[5616,-216,0,216,-216,0,-72,9,0,0,0,0,0,0,16,0,-8,-8,16,-8,
0,0,0,0,0,0,-2,1,0,54,0,-54,0,-54,54,-18,36,-18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-6,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2,
-2,0,0,0,-2,4,-2,-2,4,-2,0,0,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],
[TENSOR,[119,13]],[5616,-216,0,216,-216,0,-72,9,0,0,0,0,0,0,16,0,-8,-8,16,-8,
0,0,0,0,0,0,-2,1,0,0,-54,54,-54,54,0,36,-18,-18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,3,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
-2,4,0,0,0,4,-2,-2,-2,-2,4,0,0,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],
[TENSOR,[121,13]],[5616,-216,0,216,-216,0,-72,9,0,0,0,0,0,0,16,0,-8,-8,16,-8,
0,0,0,0,0,0,-2,1,0,-54,54,0,54,0,-54,-18,-18,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,3,3,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,4,
-2,0,0,0,-2,-2,4,4,-2,-2,0,0,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],
[TENSOR,[123,13]],[5616,-216,0,-216,0,216,0,0,0,624,-24,48,-24,-24,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,54,0,-54,36,-18,-72,36,-18,-18,0,9,0,12,-6,-24,-6,-6,12,
12,-6,-6,3,0,0,0,0,0,0,0,3,3,3,-6,0,0,0,-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],
[TENSOR,[125,13]],[6318,-243,0,0,243,-243,0,0,0,702,-27,-27,54,-27,-18,-18,9,
-18,9,9,9,0,0,-9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,2,3,0,0,3,-3,0,-1,-1,2,-1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[127,13]]],
[(117,123,120,126)(118,124,121,127)(119,125,122,128),(109,113)(110,114)
(111,115)(112,116)]);
ALF("Fi23M8","L3(3)x2",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,4,3,4,4,4,4,3,3,3,3,3,
3,4,4,3,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,6,7,8,7,7,
7,7,7,8,8,8,8,7,9,10,9,9,9,9,9,9,10,10,10,10,9,11,11,11,11,11,11,12,12,12,
11,11,11,12,12,12,12,12,12,11,11,12,12,12,11,11,13,14,14,13,15,16,16,15,
17,18,17,19,20,19,21,22,21,23,24,23]);
ALF("Fi23M8","Fi23",[1,6,5,8,7,6,5,8,33,2,15,18,23,15,4,4,20,27,21,19,21,
22,28,25,19,22,22,28,69,6,7,8,6,7,5,7,8,8,8,8,8,14,18,15,23,23,18,18,15,
23,23,36,34,35,33,35,36,67,8,23,35,34,34,36,37,66,67,67,73,87,10,12,46,44,
54,43,49,48,47,53,56,52,93,27,19,20,25,27,28,28,27,26,21,22,26,22,19,25,
28,25,21,28,28,69,72,68,72,68,31,30,84,82,31,30,84,82,57,85,95,57,85,95,
58,86,96,58,86,96],[
"fusion map is unique up to table automorphisms"
]);

MOT("S3xO7(3)",
[
"5th maximal subgroup of Fi23"
],
0,
0,
0,
[( 54, 55)(112,113)(170,171),( 50, 51)(108,109)(166,167),(  8,  9)( 28, 29)
( 30, 31)( 38, 39)( 47, 48)( 66, 67)( 86, 87)( 88, 89)( 96, 97)(105,106)
(124,125)(144,145)(146,147)(154,155)(163,164)],
["ConstructDirectProduct",[["Dihedral",6],["O7(3)"]]]);
ALF("S3xO7(3)","Fi23",[1,2,3,4,6,5,7,6,8,7,8,9,10,10,11,13,15,14,18,17,25,
24,21,16,22,26,18,19,28,25,20,27,29,31,30,35,34,34,37,39,38,49,46,51,42,
46,43,54,50,58,57,59,61,66,66,67,71,74,5,14,16,22,5,7,6,8,7,8,8,42,44,48,
50,61,14,18,15,16,19,17,22,24,26,21,23,28,25,27,28,28,76,82,84,35,34,36,
37,89,90,43,44,45,51,48,54,49,55,96,95,97,62,66,66,67,71,98,2,3,4,4,15,14,
18,15,23,18,23,11,12,12,11,38,17,16,24,21,20,26,19,22,22,25,24,21,27,26,
25,28,59,30,31,66,67,67,73,40,39,53,52,55,50,52,47,56,50,86,85,60,90,71,
71,70,68,75],[
"fusion map is unique up to table automorphisms,\n",
"compatible with Brauer tables"
]);
ALF("S3xO7(3)","2xO7(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,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,1,2,3,4,5,6,7,8,9,10,11,12,
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]);

MOT("S3xU4(3).(2^2)_{122}",
[
"7th maximal subgroup of Fi22.2"
],
0,
0,
0,
[(  4,  5)( 11, 12)( 15, 16)( 23, 24)( 29, 30)( 32, 46)( 33, 47)( 34, 48)
( 35, 49)( 36, 50)( 37, 51)( 38, 52)( 39, 53)( 40, 54)( 41, 55)( 42, 56)
( 43, 57)( 44, 58)( 45, 59)( 63, 64)( 70, 71)( 74, 75)( 82, 83)( 88, 89)
( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)
( 99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(122,123)(129,130)
(133,134)(141,142)(147,148)(150,164)(151,165)(152,166)(153,167)(154,168)
(155,169)(156,170)(157,171)(158,172)(159,173)(160,174)(161,175)(162,176)
(163,177)],
["ConstructDirectProduct",[["Symmetric",3],["U4(3).(2^2)_{122}"]]]);
ALF("S3xU4(3).(2^2)_{122}","Fi22.2",[1,3,6,5,7,7,9,13,14,17,18,23,26,28,
31,32,37,60,62,63,64,70,71,78,72,79,84,87,86,89,96,2,4,9,10,16,19,15,24,
22,27,34,37,40,51,60,61,63,65,70,68,72,73,77,80,83,87,93,100,2,4,16,15,19,
19,11,13,34,21,20,24,48,27,51,52,43,62,61,65,65,74,73,77,78,79,85,92,91,
93,97,3,4,11,13,17,23,18,22,24,28,35,43,44,53,62,62,65,66,74,71,78,71,78,
80,84,92,94,101,5,18,5,7,6,8,38,44,49,18,23,17,55,57,31,32,38,69,71,86,90,
69,78,74,75,104,110,86,89,87,112,15,20,39,40,15,16,19,21,25,58,59,39,45,
51,68,73,88,91,68,72,70,77,76,105,109,88,92,100],[
"fusion map is unique up to table automorphisms"
]);
ALN("S3xU4(3).(2^2)_{122}",["Fi22.2N3A"]);

MOT("2xS3xU4(3).(2^2)_{122}",
[
"intermediate table, needed to construct 2.(S3x2.U4(3).2_2).2"
],
0,
0,
0,
[(60,237)(61,238)(62,239)(63,240)(64,241)(65,242)(66,243)(67,244)(68,245)(69,
246)(70,247)(71,248)(72,249)(73,250)(74,251)(75,252)(76,253)(77,254)(78,255)
(79,256)(80,257)(81,258)(82,259)(83,260)(84,261)(85,262)(86,263)(87,264)(88,
265)(89,266)(90,267)(91,268)(92,269)(93,270)(94,271)(95,272)(96,273)(97,274)
(98,275)(99,276)(100,277)(101,278)(102,279)(103,280)(104,281)(105,282)(106,
283)(107,284)(108,285)(109,286)(110,287)(111,288)(112,289)(113,290)(114,291)
(115,292)(116,293)(117,294)(118,295),(32,209)(33,210)(34,211)(35,212)(36,213)
(37,214)(38,215)(39,216)(40,217)(41,218)(42,219)(43,220)(44,221)(45,222)(46,
223)(47,224)(48,225)(49,226)(50,227)(51,228)(52,229)(53,230)(54,231)(55,232)
(56,233)(57,234)(58,235)(59,236)(91,268)(92,269)(93,270)(94,271)(95,272)(96,
273)(97,274)(98,275)(99,276)(100,277)(101,278)(102,279)(103,280)(104,281)(105,
282)(106,283)(107,284)(108,285)(109,286)(110,287)(111,288)(112,289)(113,290)
(114,291)(115,292)(116,293)(117,294)(118,295)(150,327)(151,328)(152,329)(153,
330)(154,331)(155,332)(156,333)(157,334)(158,335)(159,336)(160,337)(161,338)
(162,339)(163,340)(164,341)(165,342)(166,343)(167,344)(168,345)(169,346)(170,
347)(171,348)(172,349)(173,350)(174,351)(175,352)(176,353)(177,354),(18,195)
(19,196)(20,197)(21,198)(22,199)(23,200)(24,201)(25,202)(26,203)(27,204)(28,
205)(29,206)(30,207)(31,208)(46,223)(47,224)(48,225)(49,226)(50,227)(51,228)
(52,229)(53,230)(54,231)(55,232)(56,233)(57,234)(58,235)(59,236)(77,254)(78,
255)(79,256)(80,257)(81,258)(82,259)(83,260)(84,261)(85,262)(86,263)(87,264)
(88,265)(89,266)(90,267)(105,282)(106,283)(107,284)(108,285)(109,286)(110,287)
(111,288)(112,289)(113,290)(114,291)(115,292)(116,293)(117,294)(118,295)(136,
313)(137,314)(138,315)(139,316)(140,317)(141,318)(142,319)(143,320)(144,321)
(145,322)(146,323)(147,324)(148,325)(149,326)(164,341)(165,342)(166,343)(167,
344)(168,345)(169,346)(170,347)(171,348)(172,349)(173,350)(174,351)(175,352)
(176,353)(177,354),(4,5)(11,12)(15,16)(23,24)(29,30)(32,46)(33,47)(34,48)(35,
49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)(45,59)(63,
64)(70,71)(74,75)(82,83)(88,89)(91,105)(92,106)(93,107)(94,108)(95,109)(96,
110)(97,111)(98,112)(99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(122,
123)(129,130)(133,134)(141,142)(147,148)(150,164)(151,165)(152,166)(153,167)
(154,168)(155,169)(156,170)(157,171)(158,172)(159,173)(160,174)(161,175)(162,
176)(163,177)(181,182)(188,189)(192,193)(200,201)(206,207)(209,223)(210,224)
(211,225)(212,226)(213,227)(214,228)(215,229)(216,230)(217,231)(218,232)(219,
233)(220,234)(221,235)(222,236)(240,241)(247,248)(251,252)(259,260)(265,266)
(268,282)(269,283)(270,284)(271,285)(272,286)(273,287)(274,288)(275,289)(276,
290)(277,291)(278,292)(279,293)(280,294)(281,295)(299,300)(306,307)(310,311)
(318,319)(324,325)(327,341)(328,342)(329,343)(330,344)(331,345)(332,346)(333,
347)(334,348)(335,349)(336,350)(337,351)(338,352)(339,353)(340,354)],
["ConstructDirectProduct",[["Cyclic",2],["S3xU4(3).(2^2)_{122}"]]]);

MOT("S3x2.U4(3).2_2",
[
"8th maximal subgroup of 2.Fi22"
],
0,
0,
0,
[( 51, 52)(114,115)(177,178),(127,128)(129,130)(131,132)(133,134)(135,136)
(137,138)(139,140)(142,143)(144,145)(146,147)(148,149)(150,151)(153,154)(155,
156)(157,158)(159,160)(161,162)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(180,181)(182,183)(184,185)(186,187)(188,189),( 35, 36)( 39,
 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 54, 55)( 56, 57)( 58, 59)
( 60, 61)( 62, 63)( 98, 99)(102,103)(104,105)(106,107)(108,109)(110,111)(112,
113)(117,118)(119,120)(121,122)(123,124)(125,126)(161,162)(165,166)(167,168)
(169,170)(171,172)(173,174)(175,176)(180,181)(182,183)(184,185)(186,187)(188,
189),( 27, 29)( 28, 30)( 41, 43)( 42, 44)( 56, 57)( 60, 62)( 61, 63)( 90, 92)
( 91, 93)(104,106)(105,107)(119,120)(123,125)(124,126)(153,155)(154,156)(167,
169)(168,170)(182,183)(186,188)(187,189)],
["ConstructDirectProduct",[["Dihedral",6],["2.U4(3).2_2"]]]);
ALF("S3x2.U4(3).2_2","S3xU4(3).2_2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,
10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,19,20,21,22,22,23,23,
24,24,25,25,26,26,27,27,28,28,29,30,30,31,31,32,32,33,33,34,34,35,35,36,
36,37,37,38,38,39,39,40,40,41,41,42,43,43,44,44,45,45,46,46,47,47,48,49,
49,50,50,51,51,52,52,53,53,54,55,56,56,57,57,58,58,59,59,60,60,61,61,62,
62,63,64,64,65,65,66,66,67,67,68,68,69,69,70,70,71,71,72,72,73,73,74,74,
75,75,76,77,77,78,78,79,79,80,80,81,81,82,83,83,84,84,85,85,86,86,87,87,
88,89,90,90,91,91,92,92,93,93,94,94,95,95,96,96,97,98,98,99,99,100,100,
101,101,102,102]);
ALF("S3x2.U4(3).2_2","2.Fi22",[1,2,6,5,10,11,8,9,12,13,12,13,16,
16,22,23,24,30,29,32,31,41,40,46,47,49,53,54,53,54,55,56,67,67,3,4,7,16,
17,18,27,28,27,28,33,34,25,26,43,42,38,39,48,59,60,67,67,71,72,95,96,97,
98,8,9,32,31,8,9,12,13,10,11,14,15,68,69,80,91,92,32,31,41,40,30,29,105,
106,111,53,54,53,54,55,56,68,69,25,26,35,70,71,72,25,26,25,26,27,28,33,34,
37,36,44,45,112,113,114,70,70,81,82,95,96,97,98,3,4,7,7,27,28,25,26,33,34,
33,34,19,19,22,59,60,37,36,35,35,43,42,89,90,48,97,98,95,96,99,100,79,79,
5,6,7,19,22,22,29,30,29,30,40,41,31,32,39,38,42,43,49,61,62,79,79,80,80,
101,102,101,102],[
"fusion map is unique up to table automorphisms"
]);

MOT("2xS3x2.U4(3).2_2",
[
"intermediate table, needed to construct 2.(S3x2.U4(3).2_2).2"
],
0,
0,
0,
[( 51, 52)(114,115)(177,178)(240,241)(303,304)(366,367),
(190,191)(192,193)(194,195)(196,197)(198,199)(200,201)(202,203)(205,206)
(207,208)(209,210)(211,212)(213,214)(216,217)(218,219)(220,221)(222,223)
(224,225)(228,229)(230,231)(232,233)(234,235)(236,237)(238,239)(240,241)
(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)
(259,260)(261,262)(263,264)(265,266)(268,269)(270,271)(272,273)(274,275)
(276,277)(279,280)(281,282)(283,284)(285,286)(287,288)(291,292)(293,294)
(295,296)(297,298)(299,300)(301,302)(303,304)(306,307)(308,309)(310,311)
(312,313)(314,315)(316,317)(318,319)(320,321)(322,323)(324,325)(326,327)
(328,329)(331,332)(333,334)(335,336)(337,338)(339,340)(342,343)(344,345)
(346,347)(348,349)(350,351)(354,355)(356,357)(358,359)(360,361)(362,363)
(364,365)(366,367)(369,370)(371,372)(373,374)(375,376)(377,378),
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(142,143)
(144,145)(146,147)(148,149)(150,151)(153,154)(155,156)(157,158)(159,160)
(161,162)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)
(180,181)(182,183)(184,185)(186,187)(188,189)(316,317)(318,319)(320,321)
(322,323)(324,325)(326,327)(328,329)(331,332)(333,334)(335,336)(337,338)
(339,340)(342,343)(344,345)(346,347)(348,349)(350,351)(354,355)(356,357)
(358,359)(360,361)(362,363)(364,365)(366,367)(369,370)(371,372)(373,374)
(375,376)(377,378), (127,316)(128,317)(129,318)(130,319)(131,320)(132,321)
(133,322)(134,323)(135,324)(136,325)(137,326)(138,327)(139,328)(140,329)
(141,330)(142,331)(143,332)(144,333)(145,334)(146,335)(147,336)(148,337)
(149,338)(150,339)(151,340)(152,341)(153,342)(154,343)(155,344)(156,345)
(157,346)(158,347)(159,348)(160,349)(161,350)(162,351)(163,352)(164,353)
(165,354)(166,355)(167,356)(168,357)(169,358)(170,359)(171,360)(172,361)
(173,362)(174,363)(175,364)(176,365)(177,366)(178,367)(179,368)(180,369)
(181,370)(182,371)(183,372)(184,373)(185,374)(186,375)(187,376)(188,377)
(189,378), ( 35, 36)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)
( 54, 55)( 56, 57)( 58, 59)( 60, 61)( 62, 63)( 98, 99)(102,103)(104,105)
(106,107)(108,109)(110,111)(112,113)(117,118)(119,120)(121,122)(123,124)
(125,126)(161,162)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(180,181)(182,183)(184,185)(186,187)(188,189)(224,225)(228,229)(230,231)
(232,233)(234,235)(236,237)(238,239)(243,244)(245,246)(247,248)(249,250)
(251,252)(287,288)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(306,307)(308,309)(310,311)(312,313)(314,315)(350,351)(354,355)(356,357)
(358,359)(360,361)(362,363)(364,365)(369,370)(371,372)(373,374)(375,376)
(377,378), ( 35,224)( 36,225)( 37,226)( 38,227)( 39,228)( 40,229)( 41,230)
( 42,231)( 43,232)( 44,233)( 45,234)( 46,235)( 47,236)( 48,237)( 49,238)
( 50,239)( 51,240)( 52,241)( 53,242)( 54,243)( 55,244)( 56,245)( 57,246)
( 58,247)( 59,248)( 60,249)( 61,250)( 62,251)( 63,252)( 98,287)( 99,288)
(100,289)(101,290)(102,291)(103,292)(104,293)(105,294)(106,295)(107,296)
(108,297)(109,298)(110,299)(111,300)(112,301)(113,302)(114,303)(115,304)
(116,305)(117,306)(118,307)(119,308)(120,309)(121,310)(122,311)(123,312)
(124,313)(125,314)(126,315)(161,350)(162,351)(163,352)(164,353)(165,354)
(166,355)(167,356)(168,357)(169,358)(170,359)(171,360)(172,361)(173,362)
(174,363)(175,364)(176,365)(177,366)(178,367)(179,368)(180,369)(181,370)
(182,371)(183,372)(184,373)(185,374)(186,375)(187,376)(188,377)(189,378),
( 27, 29)( 28, 30)( 41, 43)( 42, 44)( 56, 57)( 60, 62)( 61, 63)( 90, 92)
( 91, 93)(104,106)(105,107)(119,120)(123,125)(124,126)(153,155)(154,156)
(167,169)(168,170)(182,183)(186,188)(187,189)(216,218)(217,219)(230,232)
(231,233)(245,246)(249,251)(250,252)(279,281)(280,282)(293,295)(294,296)
(308,309)(312,314)(313,315)(342,344)(343,345)(356,358)(357,359)(371,372)
(375,377)(376,378) ],
["ConstructDirectProduct",[["Cyclic",2],["S3x2.U4(3).2_2"]]]);
ALF("2xS3x2.U4(3).2_2","2xS3xU4(3).2_2",[1,1,2,2,3,3,
4,4,5,5,6,6,7,7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,
19,19,20,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,30,30,31,31,32,
32,33,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,43,43,44,44,
45,45,46,46,47,47,48,49,49,50,50,51,51,52,52,53,53,54,55,56,56,57,57,58,
58,59,59,60,60,61,61,62,62,63,64,64,65,65,66,66,67,67,68,68,69,69,70,70,
71,71,72,72,73,73,74,74,75,75,76,77,77,78,78,79,79,80,80,81,81,82,83,83,
84,84,85,85,86,86,87,87,88,89,90,90,91,91,92,92,93,93,94,94,95,95,96,96,
97,98,98,99,99,100,100,101,101,102,102,103,103,104,104,105,105,106,106,
107,107,108,108,109,109,110,111,111,112,112,113,113,114,114,115,115,116,
117,117,118,118,119,119,120,120,121,121,122,123,124,124,125,125,126,126,
127,127,128,128,129,129,130,130,131,132,132,133,133,134,134,135,135,136,
136,137,137,138,138,139,139,140,140,141,141,142,142,143,143,144,145,145,
146,146,147,147,148,148,149,149,150,151,151,152,152,153,153,154,154,155,
155,156,157,158,158,159,159,160,160,161,161,162,162,163,163,164,164,165,
166,166,167,167,168,168,169,169,170,170,171,171,172,172,173,173,174,174,
175,175,176,176,177,177,178,179,179,180,180,181,181,182,182,183,183,184,
185,185,186,186,187,187,188,188,189,189,190,191,192,192,193,193,194,194,
195,195,196,196,197,197,198,198,199,200,200,201,201,202,202,203,203,204,
204]);

MOT("S3xU4(3).2_2",
[
"8th maximal subgroup of Fi22"
],
0,
0,
0,
[( 15, 16)( 23, 24)( 33, 34)( 49, 50)( 57, 58)( 67, 68)( 83, 84)( 91, 92)
(101,102)],
["ConstructDirectProduct",[["Dihedral",6],["U4(3).2_2"]]]);
ALF("S3xU4(3).2_2","Fi22",[1,3,6,5,7,7,9,13,14,17,18,23,26,28,31,31,32,38,
2,4,9,10,16,16,19,15,24,22,27,34,38,41,55,56,5,18,5,7,6,8,39,46,52,18,23,
17,60,63,31,31,32,39,15,20,40,41,15,15,16,19,21,25,64,65,40,47,55,56,2,4,
16,15,19,19,11,13,34,21,20,24,51,27,56,55,57,45,3,4,11,13,17,17,23,18,22,
24,28,35,45,46,58,58],[
"fusion map is unique up to table automorphisms"
]);
ALF("S3xU4(3).2_2","S3xU4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,15,16,17,32,33,34,35,36,36,37,38,39,40,41,42,43,44,45,45,119,120,
121,122,123,124,125,126,127,128,129,130,131,132,133,133,134,135,150,151,
152,153,154,154,155,156,157,158,159,160,161,162,163,163,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,74,75,76,91,92,93,94,95,95,96,97,98,99,100,101,
102,103,104,104]);
ALN("S3xU4(3).2_2",["S3xU4(3):2_2"]);

MOT("2xS3xU4(3).2_2",
[
"intermediate table, needed to construct 2.(S3x2.U4(3).2_2).2"
],
0,
0,
0,
[ ( 69,171)( 70,172)( 71,173)( 72,174)( 73,175)( 74,176)( 75,177)
( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,183)( 82,184)( 83,185)
( 84,186)( 85,187)( 86,188)( 87,189)( 88,190)( 89,191)( 90,192)( 91,193)
( 92,194)( 93,195)( 94,196)( 95,197)( 96,198)( 97,199)( 98,200)( 99,201)
(100,202)(101,203)(102,204), ( 19,121)( 20,122)( 21,123)( 22,124)( 23,125)
( 24,126)( 25,127)( 26,128)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)
( 32,134)( 33,135)( 34,136)( 53,155)( 54,156)( 55,157)( 56,158)( 57,159)
( 58,160)( 59,161)( 60,162)( 61,163)( 62,164)( 63,165)( 64,166)( 65,167)
( 66,168)( 67,169)( 68,170)( 87,189)( 88,190)( 89,191)( 90,192)( 91,193)
( 92,194)( 93,195)( 94,196)( 95,197)( 96,198)( 97,199)( 98,200)( 99,201)
(100,202)(101,203)(102,204), ( 15, 16)( 23, 24)( 33, 34)( 49, 50)( 57, 58)
( 67, 68)( 83, 84)( 91, 92)(101,102)(117,118)(125,126)(135,136)(151,152)
(159,160)(169,170)(185,186)(193,194)(203,204) ],
["ConstructDirectProduct",[["Cyclic",2],["S3xU4(3).2_2"]]]);
ALF("2xS3xU4(3).2_2","2xS3xU4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,15,16,17,32,33,34,35,36,36,37,38,39,40,41,42,43,44,45,45,119,120,
121,122,123,124,125,126,127,128,129,130,131,132,133,133,134,135,150,151,
152,153,154,154,155,156,157,158,159,160,161,162,163,163,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,74,75,76,91,92,93,94,95,95,96,97,98,99,100,101,
102,103,104,104,178,179,180,181,182,183,184,185,186,187,188,189,190,191,
192,192,193,194,209,210,211,212,213,213,214,215,216,217,218,219,220,221,
222,222,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,310,
311,312,327,328,329,330,331,331,332,333,334,335,336,337,338,339,340,340,
237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,251,252,253,
268,269,270,271,272,272,273,274,275,276,277,278,279,280,281,281],[
"fusion map is unique up to table automorphisms"
]);

MOT("S4xS6(2)",
[
"12th maximal subgroup of Fi23"
],
0,
0,
0,
[],
["ConstructDirectProduct",[["Symmetric",4],["S6(2)"]],(),
(  1, 31, 91,121)(  2, 32, 92,122)(  3, 33, 93,123)(  4, 34, 94,124)
(  5, 35, 95,125)(  6, 36, 96,126)(  7, 37, 97,127)(  8, 38, 98,128)
(  9, 39, 99,129)( 10, 40,100,130)( 11, 41,101,131)( 12, 42,102,132)
( 13, 43,103,133)( 14, 44,104,134)( 15, 45,105,135)( 16, 46,106,136)
( 17, 47,107,137)( 18, 48,108,138)( 19, 49,109,139)( 20, 50,110,140)
( 21, 51,111,141)( 22, 52,112,142)( 23, 53,113,143)( 24, 54,114,144)
( 25, 55,115,145)( 26, 56,116,146)( 27, 57,117,147)( 28, 58,118,148)
( 29, 59,119,149)( 30, 60,120,150)]);
ALF("S4xS6(2)","Fi23",[1,2,4,3,4,5,6,7,10,11,9,10,11,13,14,22,19,16,18,25,20,
29,31,30,34,38,50,42,43,61,2,3,4,4,4,14,15,18,12,11,11,12,11,38,16,22,21,22,
24,26,25,59,30,31,67,39,50,50,47,90,3,4,3,4,4,16,17,24,10,9,11,10,11,39,22,
16,17,22,26,24,26,60,31,30,70,40,42,50,43,89,5,14,22,16,22,7,8,8,44,50,42,48,
50,61,18,26,28,24,23,27,28,76,82,84,36,90,55,51,54,62,9,11,9,11,11,42,45,51,
9,10,10,11,12,74,50,42,45,50,55,51,55,88,31,30,94,75,44,48,45,98],[
"fusion map is unique"
]);

MOT("O8+(2):S3x2",
[
"4th maximal subgroup of 2.Fi22,\n",
"3rd maximal subgroup of Fi22.2"
],
0,
0,
0,
[( 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)],
["ConstructDirectProduct",[["O8+(2).3.2"],["Cyclic",2]]]);
ALF("O8+(2):S3x2","2.Fi22",[1,2,6,5,5,6,7,7,8,9,10,11,12,13,16,16,16,16,
22,22,20,21,23,24,32,31,31,32,30,29,41,40,40,41,39,38,46,47,49,49,48,48,
55,56,61,62,68,69,67,67,80,80,91,92,8,9,14,15,32,31,35,35,45,44,53,54,69,
68,70,70,68,69,83,84,102,101,105,106,111,111,112,112,3,4,7,7,17,18,18,17,
19,19,17,18,22,22,25,26,27,28,35,35,33,34,37,36,43,42,48,48,49,49,51,52,
59,60,72,71,71,72,82,81,81,82,79,79,89,90,99,100,103,104,112,112,113,114],[
"fusion map is unique up to table automorphisms"
]);
ALF("O8+(2):S3x2","Fi22.2",[1,60,3,60,3,61,4,61,5,68,6,70,7,72,9,63,9,64,
13,65,12,67,14,83,18,68,18,73,17,70,23,72,23,77,22,77,26,96,28,79,27,80,
32,100,35,85,38,88,37,87,44,91,49,109,5,69,8,75,18,69,20,73,25,76,31,99,
38,86,39,88,38,90,46,95,53,99,55,112,57,104,58,105,2,62,4,62,10,64,10,63,
11,65,10,66,13,66,15,71,16,74,20,71,19,78,21,74,24,78,27,79,28,80,30,82,
34,84,40,86,40,90,45,89,45,94,43,92,48,97,52,101,54,103,58,104,59,110],[
"fusion map is unique up to table automorphisms"
]);
ALN("O8+(2):S3x2",["2xO8+(2):S3"]);

MOT("3xO8+(2):S3",
[
"4th maximal subgroup of 3.Fi22"
],
0,
0,
0,
[
(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)
( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)( 71, 72)
( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 86, 87)( 89, 90)( 92, 93)( 95, 96)
( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114)(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)(161,162)(164,165)(167,168)
(170,171)(173,174)(176,177)(179,180)(182,183)(185,186)(188,189)(191,192)
(194,195)(197,198)(200,201)(203,204)
],
["ConstructDirectProduct",[["O8+(2).3.2"],["Cyclic",3]]]);
ALF("3xO8+(2):S3","3.Fi22",[1,2,3,7,8,9,7,8,9,10,11,12,13,14,15,16,16,16,
17,17,17,19,20,21,19,20,21,31,32,33,28,29,30,34,35,36,46,47,48,46,47,48,
43,44,45,55,56,57,55,56,57,54,54,54,60,61,62,66,67,68,63,64,65,78,78,78,
83,84,85,95,96,97,92,93,94,110,111,112,126,127,128,13,14,15,18,18,18,46,
47,48,50,51,52,59,59,59,75,76,77,95,96,97,98,99,100,95,96,97,116,116,116,
142,143,144,148,149,150,157,158,159,160,161,162,4,5,6,10,11,12,22,23,24,
22,23,24,25,26,27,22,23,24,31,32,33,37,38,39,40,41,42,50,51,52,49,49,49,
53,53,53,58,58,58,63,64,65,66,67,68,72,73,74,80,81,82,101,102,103,101,102,
103,113,114,115,113,114,115,107,108,109,123,124,125,141,141,141,145,146,
147,160,161,162,163,164,165],[
"fusion map is unique up to table automorphisms"
]);

MOT("6xO8+(2):S3",
[
"4th maximal subgroup of 6.Fi22"
],
0,
0,
0,
[
(247,250)(248,251)(249,252)(253,256)(254,257)(255,258)(259,262)(260,263)
(261,264)(265,268)(266,269)(267,270)(271,274)(272,275)(273,276)(277,280)
(278,281)(279,282)(283,286)(284,287)(285,288)(289,292)(290,293)(291,294)
(295,298)(296,299)(297,300)(301,304)(302,305)(303,306)(307,310)(308,311)
(309,312)(313,316)(314,317)(315,318)(319,322)(320,323)(321,324)(325,328)
(326,329)(327,330)(331,334)(332,335)(333,336)(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)(367,370)(368,371)(369,372)(373,376)
(374,377)(375,378)(379,382)(380,383)(381,384)(385,388)(386,389)(387,390)
(391,394)(392,395)(393,396)(397,400)(398,401)(399,402)(403,406)(404,407)
(405,408)
,
(  2,  6)(  3,  5)(  8, 12)(  9, 11)( 14, 18)( 15, 17)( 20, 24)( 21, 23)
( 26, 30)( 27, 29)( 32, 36)( 33, 35)( 38, 42)( 39, 41)( 44, 48)( 45, 47)
( 50, 54)( 51, 53)( 56, 60)( 57, 59)( 62, 66)( 63, 65)( 68, 72)( 69, 71)
( 74, 78)( 75, 77)( 80, 84)( 81, 83)( 86, 90)( 87, 89)( 92, 96)( 93, 95)
( 98,102)( 99,101)(104,108)(105,107)(110,114)(111,113)(116,120)(117,119)
(122,126)(123,125)(128,132)(129,131)(134,138)(135,137)(140,144)(141,143)
(146,150)(147,149)(152,156)(153,155)(158,162)(159,161)(164,168)(165,167)
(170,174)(171,173)(176,180)(177,179)(182,186)(183,185)(188,192)(189,191)
(194,198)(195,197)(200,204)(201,203)(206,210)(207,209)(212,216)(213,215)
(218,222)(219,221)(224,228)(225,227)(230,234)(231,233)(236,240)(237,239)
(242,246)(243,245)(248,252)(249,251)(254,258)(255,257)(260,264)(261,263)
(266,270)(267,269)(272,276)(273,275)(278,282)(279,281)(284,288)(285,287)
(290,294)(291,293)(296,300)(297,299)(302,306)(303,305)(308,312)(309,311)
(314,318)(315,317)(320,324)(321,323)(326,330)(327,329)(332,336)(333,335)
(338,342)(339,341)(344,348)(345,347)(350,354)(351,353)(356,360)(357,359)
(362,366)(363,365)(368,372)(369,371)(374,378)(375,377)(380,384)(381,383)
(386,390)(387,389)(392,396)(393,395)(398,402)(399,401)(404,408)(405,407)
],
["ConstructDirectProduct",[["O8+(2).3.2"],["Cyclic",6]]]);
ALF("6xO8+(2):S3","O8+(2):S3x2",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,8,
7,8,7,8,9,10,9,10,9,10,11,12,11,12,11,12,13,14,13,14,13,14,15,16,15,16,15,
16,17,18,17,18,17,18,19,20,19,20,19,20,21,22,21,22,21,22,23,24,23,24,23,
24,25,26,25,26,25,26,27,28,27,28,27,28,29,30,29,30,29,30,31,32,31,32,31,
32,33,34,33,34,33,34,35,36,35,36,35,36,37,38,37,38,37,38,39,40,39,40,39,
40,41,42,41,42,41,42,43,44,43,44,43,44,45,46,45,46,45,46,47,48,47,48,47,
48,49,50,49,50,49,50,51,52,51,52,51,52,53,54,53,54,53,54,55,56,55,56,55,
56,57,58,57,58,57,58,59,60,59,60,59,60,61,62,61,62,61,62,63,64,63,64,63,
64,65,66,65,66,65,66,67,68,67,68,67,68,69,70,69,70,69,70,71,72,71,72,71,
72,73,74,73,74,73,74,75,76,75,76,75,76,77,78,77,78,77,78,79,80,79,80,79,
80,81,82,81,82,81,82,83,84,83,84,83,84,85,86,85,86,85,86,87,88,87,88,87,
88,89,90,89,90,89,90,91,92,91,92,91,92,93,94,93,94,93,94,95,96,95,96,95,
96,97,98,97,98,97,98,99,100,99,100,99,100,101,102,101,102,101,102,103,104,
103,104,103,104,105,106,105,106,105,106,107,108,107,108,107,108,109,110,
109,110,109,110,111,112,111,112,111,112,113,114,113,114,113,114,115,116,
115,116,115,116,117,118,117,118,117,118,119,120,119,120,119,120,121,122,
121,122,121,122,123,124,123,124,123,124,125,126,125,126,125,126,127,128,
127,128,127,128,129,130,129,130,129,130,131,132,131,132,131,132,133,134,
133,134,133,134,135,136,135,136,135,136]);
ALF("6xO8+(2):S3","3xO8+(2):S3",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,
11,12,10,11,12,13,14,15,13,14,15,16,17,18,16,17,18,19,20,21,19,20,21,22,
23,24,22,23,24,25,26,27,25,26,27,28,29,30,28,29,30,31,32,33,31,32,33,34,
35,36,34,35,36,37,38,39,37,38,39,40,41,42,40,41,42,43,44,45,43,44,45,46,
47,48,46,47,48,49,50,51,49,50,51,52,53,54,52,53,54,55,56,57,55,56,57,58,
59,60,58,59,60,61,62,63,61,62,63,64,65,66,64,65,66,67,68,69,67,68,69,70,
71,72,70,71,72,73,74,75,73,74,75,76,77,78,76,77,78,79,80,81,79,80,81,82,
83,84,82,83,84,85,86,87,85,86,87,88,89,90,88,89,90,91,92,93,91,92,93,94,
95,96,94,95,96,97,98,99,97,98,99,100,101,102,100,101,102,103,104,105,103,
104,105,106,107,108,106,107,108,109,110,111,109,110,111,112,113,114,112,
113,114,115,116,117,115,116,117,118,119,120,118,119,120,121,122,123,121,
122,123,124,125,126,124,125,126,127,128,129,127,128,129,130,131,132,130,
131,132,133,134,135,133,134,135,136,137,138,136,137,138,139,140,141,139,
140,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,150,148,
149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,159,157,
158,159,160,161,162,160,161,162,163,164,165,163,164,165,166,167,168,166,
167,168,169,170,171,169,170,171,172,173,174,172,173,174,175,176,177,175,
176,177,178,179,180,178,179,180,181,182,183,181,182,183,184,185,186,184,
185,186,187,188,189,187,188,189,190,191,192,190,191,192,193,194,195,193,
194,195,196,197,198,196,197,198,199,200,201,199,200,201,202,203,204,202,
203,204]);
ALF("6xO8+(2):S3","6.Fi22",[1,2,3,4,5,6,16,17,18,13,14,15,13,14,15,16,17,
18,19,20,21,19,20,21,22,23,24,25,26,27,28,29,28,29,28,29,30,31,30,31,30,
31,34,35,36,34,35,36,34,35,36,34,35,36,52,53,54,52,53,54,46,47,48,49,50,
51,55,56,57,58,59,60,82,83,84,79,80,81,79,80,81,82,83,84,76,77,78,73,74,
75,97,98,99,94,95,96,94,95,96,97,98,99,93,92,93,92,93,92,104,105,106,107,
108,109,113,114,115,113,114,115,110,111,112,110,111,112,131,132,131,132,
131,132,141,142,143,144,145,146,162,163,164,165,166,167,159,160,161,159,
160,161,186,187,188,186,187,188,215,216,217,218,219,220,22,23,24,25,26,27,
32,33,32,33,32,33,82,83,84,79,80,81,87,88,89,87,88,89,103,102,103,102,103,
102,125,126,127,128,129,130,165,166,167,162,163,164,168,169,170,168,169,
170,162,163,164,165,166,167,195,196,195,196,195,196,244,245,246,241,242,
243,253,254,255,256,257,258,271,272,273,271,272,273,274,275,276,274,275,
276,7,8,9,10,11,12,19,20,21,19,20,21,37,38,39,40,41,42,40,41,42,37,38,39,
43,44,45,43,44,45,37,38,39,40,41,42,52,53,54,52,53,54,61,62,63,64,65,66,
67,68,69,70,71,72,87,88,89,87,88,89,85,86,85,86,85,86,91,90,91,90,91,90,
101,100,101,100,101,100,110,111,112,110,111,112,113,114,115,113,114,115,
119,120,121,122,123,124,135,136,137,138,139,140,174,175,176,171,172,173,
171,172,173,174,175,176,192,193,194,189,190,191,189,190,191,192,193,194,
183,184,185,183,184,185,209,210,211,212,213,214,239,240,239,240,239,240,
247,248,249,250,251,252,274,275,276,274,275,276,277,278,279,280,281,282],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("6xO8+(2):S3",["6.Fi22M4"]);

MOT("2x2.U4(3).2_2",
0,
0,
0,
0,
[(51,52)(114,115),(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(79,80)(81,
82)(83,84)(85,86)(87,88)(90,91)(92,93)(94,95)(96,97)(98,99)(102,103)(104,105)
(106,107)(108,109)(110,111)(112,113)(114,115)(117,118)(119,120)(121,122)(123,
124)(125,126),(35,36)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(54,55)(56,57)
(58,59)(60,61)(62,63)(98,99)(102,103)(104,105)(106,107)(108,109)(110,111)(112,
113)(117,118)(119,120)(121,122)(123,124)(125,126),(35,98)(36,99)(37,100)(38,
101)(39,102)(40,103)(41,104)(42,105)(43,106)(44,107)(45,108)(46,109)(47,110)
(48,111)(49,112)(50,113)(51,114)(52,115)(53,116)(54,117)(55,118)(56,119)(57,
120)(58,121)(59,122)(60,123)(61,124)(62,125)(63,126),(27,29)(28,30)(41,43)(42,
44)(56,57)(60,62)(61,63)(90,92)(91,93)(104,106)(105,107)(119,120)(123,125)
(124,126)],
["ConstructDirectProduct",[["Cyclic",2],["2.U4(3).2_2"]]]);
ALF("2x2.U4(3).2_2","2^2.U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,27,28,29,30,31,32,33,34,
35,36,37,38,39,40,39,40,41,42,43,44,45,46,47,47,48,49,50,51,51,52,53,54,
55,54,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,64,64,65,65,66,66,
67,67,68,68,69,70,71,71,70,72,72,73,73,74,74,75,76,77,77,78,79,79,78,80,
80,81,81,82,82,83,84,85,86,86,87,88,89,89,90,91,91,90],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2x2.U4(3).2_2","2xU4(3).2_2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,
10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,19,20,21,22,22,23,23,
24,24,25,25,26,26,27,27,28,28,29,30,30,31,31,32,32,33,33,34,34,35,35,36,
36,37,37,38,38,39,39,40,40,41,41,42,43,43,44,44,45,45,46,46,47,47,48,49,
49,50,50,51,51,52,52,53,53,54,55,56,56,57,57,58,58,59,59,60,60,61,61,62,
62,63,64,64,65,65,66,66,67,67,68,68]);
ALF("2x2.U4(3).2_2","U4(3).2_2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,10,
11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,19,20,21,22,22,23,23,24,
24,25,25,26,26,27,27,28,28,29,30,30,31,31,32,32,33,33,34,34,1,1,2,2,3,3,4,
4,5,5,6,6,7,7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,
19,20,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,30,30,31,31,32,32,
33,33,34,34]);
ALF("2x2.U4(3).2_2","2^2.U6(2)",[1,2,10,9,18,19,14,15,22,23,22,23,28,28,
38,39,40,56,55,60,59,68,67,75,76,81,86,87,90,91,94,95,118,118,5,6,13,29,
34,35,43,44,47,48,63,64,51,52,72,71,73,74,81,98,99,119,119,124,125,132,
133,136,137,3,4,12,11,20,21,16,17,24,25,24,25,29,29,38,41,42,58,57,62,61,
70,69,77,78,80,88,89,92,93,96,97,119,119,7,8,13,28,36,37,45,46,49,50,65,
66,53,54,74,73,71,72,80,100,101,118,118,126,127,134,135,138,139],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2x2.U4(3).2_2",["2^2.U6(2)M4"]);

MOT("2^2.U4(3).(2^2)_{122}",
0,
[52254720,52254720,18432,18432,93312,93312,15552,15552,15552,15552,1296,1296,
1536,1536,128,80,80,1152,1152,576,576,576,576,56,56,64,216,216,216,216,192,192
,414720,414720,4608,768,768,768,5184,5184,1728,1728,864,864,576,576,72,64,80,
80,96,96,96,72,72,26127360,9216,46656,7776,7776,648,768,128,40,576,288,288,28,
64,216,216,108,96,207360,4608,768,384,5184,5184,864,432,288,144,144,64,40,192,
192,48,72,72,48384,5760,4608,512,864,144,144,72,64,40,288,144,144,28,207360,
4608,768,384,2592,864,432,288,72,64,40,96,48,36,48384,5760,4608,512,864,144,
144,72,64,40,288,144,144,28,207360,4608,768,384,2592,864,432,288,72,64,40,96,
48,36],
[,[1,1,1,1,5,5,7,7,9,9,11,11,3,3,4,16,16,5,5,7,7,9,9,24,24,14,27,27,29,29,18,
18,1,1,1,3,4,4,5,5,9,9,7,7,9,9,11,13,16,16,18,21,21,27,27,1,1,5,7,9,11,3,4,16,
5,7,9,24,14,27,27,29,18,1,1,3,4,5,5,9,7,9,11,11,13,16,18,18,21,27,27,1,2,3,3,5
,8,10,11,14,17,18,20,22,24,2,2,4,3,6,8,10,8,12,14,17,19,22,30,2,1,4,4,6,7,9,12
,13,16,19,21,23,25,1,1,3,4,5,7,9,7,11,13,16,18,23,29],[1,2,3,4,1,2,1,2,1,2,1,2
,13,14,15,16,17,3,4,3,4,3,4,24,25,26,5,6,5,6,13,14,33,34,35,36,37,38,33,34,33,
34,33,34,35,35,35,48,49,50,36,37,38,39,40,56,57,56,56,56,56,62,63,64,57,57,57,
68,69,58,58,58,62,74,75,76,77,74,74,74,74,75,75,75,85,86,76,76,77,78,79,92,93,
94,95,92,93,93,92,100,101,94,94,94,105,106,107,108,109,106,106,106,107,107,115
,116,108,109,110,120,121,122,123,120,121,121,120,128,129,122,122,122,133,134,
135,136,137,134,134,134,135,135,143,144,136,137,138],,[1,2,3,4,5,6,7,8,9,10,11
,12,13,14,15,1,2,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,33,34,51,52,53,54,55,56,57,58,59,60,61,62,63,
56,65,66,67,68,69,71,70,72,73,74,75,76,77,79,78,80,81,82,83,84,85,74,88,87,89,
91,90,92,93,94,95,96,97,98,99,100,93,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,106,117,118,119,120,121,122,123,124,125,126,127,128,121,130,
131,132,133,134,135,136,137,138,139,140,141,142,143,134,145,146,147],,[1,2,3,4
,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,2,26,27,28,29,30,31,32,
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,
59,60,61,62,63,64,65,66,67,56,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,92,106,107,
108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,
127,128,129,130,131,132,120,134,135,136,137,138,139,140,141,142,143,144,145,
146,147]],
0,
[(83,84),(70,71)(78,79)(87,88)(90,91),(33,34)(37,38)(39,40)(41,42)(43,44)(45,
46)(49,50)(52,53)(54,55)(78,79)(87,88)(90,91)],
["ConstructMGA","2x2.U4(3).2_2","2xU4(3).(2^2)_{122}",[[35,99],[36,98],[37,
100],[38,101],[39,102],[40,103],[41,104],[42,105],[43,108],[44,109],[45,106],
[46,107],[47,110],[48,112],[49,111],[50,113],[51,114],[52,115],[53,116],[54,
117],[55,119],[56,118],[57,120],[58,121],[59,122],[60,123],[61,124],[62,125],
[63,126]],()]);
ALF("2^2.U4(3).(2^2)_{122}","2xU4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,
6,7,7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,32,32,33,34,35,
35,36,36,37,37,38,38,39,39,40,41,42,42,43,44,44,45,45,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,74,75,76,91,92,93,94,95,95,96,97,98,99,99,100,
101,102,102,103,104,104,18,19,20,21,22,23,24,25,26,27,28,29,30,31,46,47,
48,49,50,51,52,53,54,55,56,57,58,59,77,78,79,80,81,82,83,84,85,86,87,88,
89,90,105,106,107,108,109,110,111,112,113,114,115,116,117,118]);
ALF("2^2.U4(3).(2^2)_{122}","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,
7,7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,32,32,33,34,35,35,
36,36,37,37,38,38,39,39,40,41,42,42,43,44,44,45,45,1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,15,16,17,32,33,34,35,36,36,37,38,39,40,40,41,42,43,43,44,
45,45,18,19,20,21,22,23,24,25,26,27,28,29,30,31,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,18,19,20,21,22,23,24,25,26,27,28,29,30,31,46,47,48,49,
50,51,52,53,54,55,56,57,58,59]);

MOT("2xU4(3).(2^2)_{122}",
0,
0,
0,
0,
[(18,77)(19,78)(20,79)(21,80)(22,81)(23,82)(24,83)(25,84)(26,85)(27,86)(28,87)
(29,88)(30,89)(31,90)(46,105)(47,106)(48,107)(49,108)(50,109)(51,110)(52,111)
(53,112)(54,113)(55,114)(56,115)(57,116)(58,117)(59,118),(18,77)(19,78)(20,79)
(21,80)(22,81)(23,82)(24,83)(25,84)(26,85)(27,86)(28,87)(29,88)(30,89)(31,90)
(32,91)(33,92)(34,93)(35,94)(36,95)(37,96)(38,97)(39,98)(40,99)(41,100)(42,
101)(43,102)(44,103)(45,104),(4,5)(11,12)(15,16)(23,24)(29,30)(32,46)(33,47)
(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)
(45,59)(63,64)(70,71)(74,75)(82,83)(88,89)(91,105)(92,106)(93,107)(94,108)(95,
109)(96,110)(97,111)(98,112)(99,113)(100,114)(101,115)(102,116)(103,117)(104,
118)],
["ConstructDirectProduct",[["Cyclic",2],["U4(3).(2^2)_{122}"]]]);

MOT("3x2.U4(3).(2^2)_{122}",
0,
0,
0,
0,
[(61,62)(79,80)(148,149)(166,167)(235,236)(253,254),(88,175)(89,176)(90,177)
(91,178)(92,179)(93,180)(94,181)(95,182)(96,183)(97,184)(98,185)(99,186)(100,
187)(101,188)(102,189)(103,190)(104,191)(105,192)(106,193)(107,194)(108,195)
(109,196)(110,197)(111,198)(112,199)(113,200)(114,201)(115,202)(116,203)(117,
204)(118,205)(119,206)(120,207)(121,208)(122,209)(123,210)(124,211)(125,212)
(126,213)(127,214)(128,215)(129,216)(130,217)(131,218)(132,219)(133,220)(134,
221)(135,222)(136,223)(137,224)(138,225)(139,226)(140,227)(141,228)(142,229)
(143,230)(144,231)(145,232)(146,233)(147,234)(148,235)(149,236)(150,237)(151,
238)(152,239)(153,240)(154,241)(155,242)(156,243)(157,244)(158,245)(159,246)
(160,247)(161,248)(162,249)(163,250)(164,251)(165,252)(166,253)(167,254)(168,
255)(169,256)(170,257)(171,258)(172,259)(173,260)(174,261),(56,57)(65,66)(68,
69)(74,75)(83,84)(86,87)(143,144)(152,153)(155,156)(161,162)(170,171)(173,174)
(230,231)(239,240)(242,243)(248,249)(257,258)(260,261),(33,34)(38,39)(42,43)
(46,47)(50,51)(74,75)(79,80)(83,84)(86,87)(120,121)(125,126)(129,130)(133,134)
(137,138)(161,162)(166,167)(170,171)(173,174)(207,208)(212,213)(216,217)(220,
221)(224,225)(248,249)(253,254)(257,258)(260,261),(7,9)(8,10)(20,22)(21,23)
(27,29)(28,30)(40,41)(48,49)(52,70)(53,71)(54,72)(55,73)(56,74)(57,75)(58,76)
(59,77)(60,78)(61,79)(62,80)(63,81)(64,82)(65,83)(66,84)(67,85)(68,86)(69,87)
(94,96)(95,97)(107,109)(108,110)(114,116)(115,117)(127,128)(135,136)(139,157)
(140,158)(141,159)(142,160)(143,161)(144,162)(145,163)(146,164)(147,165)(148,
166)(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)(156,174)
(181,183)(182,184)(194,196)(195,197)(201,203)(202,204)(214,215)(222,223)(226,
244)(227,245)(228,246)(229,247)(230,248)(231,249)(232,250)(233,251)(234,252)
(235,253)(236,254)(237,255)(238,256)(239,257)(240,258)(241,259)(242,260)(243,
261)],
["ConstructDirectProduct",[["Cyclic",3],["2.U4(3).(2^2)_{122}"]]]);
ALF("3x2.U4(3).(2^2)_{122}","(S3x2.U4(3).2_2).2",[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,33,34,
35,36,37,37,38,39,40,40,41,42,43,43,44,45,46,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,69,70,71,72,73,73,74,75,76,
76,77,78,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,
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,
153,154,155,156,157,158,159,160,161,162,163,164,165,79,80,81,82,83,84,85,
86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,112,111,113,114,115,117,116,118,119,121,120,122,123,125,124,
126,127,129,128,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,147,148,149,150,151,153,152,154,155,156,158,157,159,160,162,
161,163,165,164],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("(S3x2.U4(3).2_2).2",
[
"7th maximal subgroup of 2.Fi22.2,\n",
"origin: constructed in August 2003 by Thomas Breuer,\n",
"using the M.G.A structure,\n",
"(independently computed using Dixon's Algorithm)"
],
[156764160,156764160,55296,55296,279936,279936,46656,46656,46656,46656,3888,
3888,4608,4608,384,240,240,3456,3456,1728,1728,1728,1728,168,168,192,648,648,
648,648,576,576,145152,17280,13824,1536,2592,432,432,216,192,120,864,432,432,
84,622080,13824,2304,1152,15552,15552,2592,1296,864,432,432,192,120,576,576,
144,216,216,622080,13824,2304,1152,7776,2592,1296,864,216,192,120,288,144,108,
78382080,78382080,27648,27648,139968,139968,23328,23328,23328,23328,1944,1944,
2304,2304,192,120,120,1728,1728,864,864,864,864,84,84,96,324,324,324,324,288,
288,145152,145152,8640,6912,768,2592,2592,216,216,216,216,96,60,864,864,216,
216,84,84,311040,6912,1152,576,7776,7776,1296,648,432,216,216,96,60,288,288,72
,108,108,311040,6912,1152,576,7776,7776,1296,648,432,216,216,96,60,288,288,72,
108,108,414720,414720,4608,768,768,768,5184,5184,1728,1728,864,864,576,576,72,
64,80,80,96,96,96,72,72,26127360,9216,46656,7776,7776,648,768,128,40,576,288,
288,28,64,216,216,108,96,207360,4608,768,384,2592,864,432,288,72,64,40,96,48,
36,48384,5760,4608,512,864,144,144,72,64,40,288,144,144,28],
[,[1,1,1,1,5,5,7,7,9,9,11,11,3,3,4,16,16,5,5,7,7,9,9,24,24,14,27,27,29,29,18,
18,1,2,3,3,5,8,10,11,14,17,18,20,22,24,1,1,3,4,5,5,9,7,9,11,11,13,16,18,18,21,
27,27,1,1,3,4,5,7,9,7,11,13,16,18,23,29,79,79,79,79,83,83,85,85,87,87,89,89,81
,81,82,94,94,83,83,85,85,87,87,102,102,92,105,105,107,107,96,96,79,79,80,81,81
,83,83,86,88,89,89,92,95,96,96,98,100,102,102,79,79,81,82,83,83,87,85,87,89,89
,91,94,96,96,99,105,105,79,79,81,82,83,83,85,87,85,89,89,91,94,96,96,101,107,
107,1,1,1,3,4,4,5,5,9,9,7,7,9,9,11,13,16,16,18,21,21,27,27,1,1,5,7,9,11,3,4,16
,5,7,9,24,14,27,27,29,18,2,2,4,3,6,8,10,8,12,14,17,19,22,30,2,1,4,4,6,7,9,12,
13,16,19,21,23,25],[1,2,3,4,1,2,1,2,1,2,1,2,13,14,15,16,17,3,4,3,4,3,4,24,25,
26,5,6,5,6,13,14,33,34,35,36,33,34,34,33,41,42,35,35,35,46,47,48,49,50,47,47,
47,47,48,48,48,58,59,49,49,50,51,52,65,66,67,68,65,65,65,66,66,74,75,67,68,69,
1,2,3,4,1,2,1,2,1,2,1,2,13,14,15,16,17,3,4,3,4,3,4,24,25,26,5,6,5,6,13,14,33,
33,34,35,36,33,33,34,34,33,33,41,42,35,35,35,35,46,46,47,48,49,50,47,47,47,47,
48,48,48,58,59,49,49,50,51,52,65,66,67,68,65,65,65,65,66,66,66,74,75,67,67,68,
69,69,166,167,168,169,170,171,166,167,166,167,166,167,168,168,168,181,182,183,
169,170,171,172,173,189,190,189,189,189,189,195,196,197,190,190,190,201,202,
191,191,191,195,207,208,209,210,207,207,207,208,208,216,217,209,210,211,221,
222,223,224,221,222,222,221,229,230,223,223,223,234],,[1,2,3,4,5,6,7,8,9,10,11
,12,13,14,15,1,2,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,34,43,44,45,46,47,48,49,50,52,51,53,54,55,56,57,58,47,61,60,62,64,
63,65,66,67,68,69,70,71,72,73,74,65,76,77,78,79,80,81,82,83,84,85,86,87,88,89,
90,91,92,93,79,80,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,112,
111,113,114,115,117,116,118,119,121,120,122,113,125,124,126,127,129,128,130,
131,132,133,135,134,136,137,138,139,140,141,130,144,143,145,147,146,148,149,
150,151,152,153,154,155,156,158,157,159,148,161,162,163,164,165,166,167,168,
169,170,171,172,173,174,175,176,177,178,179,180,181,166,167,184,185,186,187,
188,189,190,191,192,193,194,195,196,189,198,199,200,201,202,204,203,205,206,
207,208,209,210,211,212,213,214,215,216,207,218,219,220,221,222,223,224,225,
226,227,228,229,222,231,232,233,234],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,1,2,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43
,44,45,33,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69
,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
,96,97,98,99,100,101,79,80,104,105,106,107,108,109,110,111,112,113,114,115,116
,117,118,119,120,121,122,123,124,125,126,127,111,112,130,131,132,133,134,135,
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,
193,194,195,196,197,198,199,200,189,202,203,204,205,206,207,208,209,210,211,
212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,
231,232,233,221]],
0,
[(111,112)(116,117)(120,121)(124,125)(128,129)(152,153)(157,158)(161,162)(164,
165),( 56, 57)(139,140)(157,158),(166,167)(170,171)(172,173)(174,175)(176,177)
(178,179)(182,183)(185,186)(187,188)(203,204),( 51, 52)( 60, 61)( 63, 64)(134,
135)(143,144)(146,147)(152,153)(161,162)(164,165)(203,204)],
["ConstructMGA","3x2.U4(3).(2^2)_{122}","2^2.U4(3).(2^2)_{122}",[[88,175],
[89,176],[90,177],[91,178],[92,179],[93,180],[94,181],[95,182],[96,183],[97,
184],[98,185],[99,186],[100,187],[101,188],[102,189],[103,190],[104,191],[105,
192],[106,193],[107,194],[108,195],[109,196],[110,197],[111,198],[112,199],
[113,200],[114,201],[115,202],[116,203],[117,204],[118,205],[119,206],[120,
207],[121,208],[122,209],[123,210],[124,211],[125,212],[126,213],[127,214],
[128,215],[129,216],[130,217],[131,218],[132,219],[133,220],[134,221],[135,
222],[136,223],[137,224],[138,225],[139,226],[140,227],[141,228],[142,229],
[143,230],[144,231],[145,232],[146,233],[147,236],[148,237],[149,234],[150,
235],[151,238],[152,239],[153,240],[154,241],[155,242],[156,244],[157,243],
[158,248],[159,247],[160,246],[161,245],[162,250],[163,249],[164,251],[165,
252],[166,256],[167,255],[168,254],[169,253],[170,257],[171,258],[172,260],
[173,259],[174,261]],()]);
ALF("(S3x2.U4(3).2_2).2","2^2.U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,92,93,94,
95,96,97,98,99,100,101,102,103,104,105,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,134,135,136,137,138,139,140,141,142,143,144,145,146,
147,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,92,92,93,94,95,96,96,97,98,99,99,100,101,102,102,103,
104,105,105,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,134,135,
136,137,138,138,139,140,141,142,142,143,144,145,145,146,147,147,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
60,61,62,63,64,65,66,67,68,69,70,71,72,73,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,
132,133]);
ALF("(S3x2.U4(3).2_2).2","S3xU4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,
7,7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,36,37,38,39,40,40,41,42,43,43,44,
45,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,119,119,120,120,121,121,
122,122,123,123,124,124,125,125,126,127,127,128,128,129,129,130,130,131,
131,132,133,133,134,134,135,135,136,136,137,138,139,140,140,141,142,143,
143,144,145,146,146,147,148,149,149,150,151,152,153,154,154,155,156,157,
158,158,159,160,161,161,162,163,163,164,165,166,167,168,168,169,170,171,
172,172,173,174,175,175,176,177,177,91,91,92,93,94,94,95,95,96,96,97,97,
98,98,99,100,101,101,102,103,103,104,104,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,74,75,76,105,106,107,108,109,110,111,112,113,114,115,116,117,
118,77,78,79,80,81,82,83,84,85,86,87,88,89,90]);
ALF("(S3x2.U4(3).2_2).2","2.Fi22.2",[1,2,5,4,9,10,7,8,11,12,11,12,15,15,
20,21,22,26,25,28,27,35,34,39,40,42,45,46,47,48,56,56,89,91,92,93,100,101,
110,102,111,116,119,118,121,129,3,6,15,16,24,24,29,23,36,32,33,41,51,56,
56,60,76,77,89,90,92,94,100,97,102,103,109,112,115,119,125,134,7,8,28,27,
7,8,11,12,9,10,13,14,57,58,66,73,74,28,27,35,34,26,25,82,83,86,45,46,47,
48,57,58,98,99,101,118,122,98,99,110,104,105,106,139,146,118,118,121,119,
149,150,23,30,59,60,23,23,24,29,31,37,38,87,88,59,59,67,76,77,97,103,120,
123,97,97,102,100,109,108,107,140,145,120,120,124,134,134,4,5,6,17,20,20,
25,26,34,35,27,28,33,32,36,42,52,53,65,66,66,79,80,3,6,24,23,29,29,17,20,
51,31,30,36,72,41,77,76,78,65,91,91,94,95,104,101,110,101,110,112,116,124,
126,135,91,90,94,94,104,103,109,110,111,117,124,123,125,130],[
"fusion map is unique up to table automorphisms"
]);
ALF("(S3x2.U4(3).2_2).2","S3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]);

MOT("(2x2^(1+8)):U4(2):2",
[
"origin: Dixon's Algorithm,\n",
"7th maximal subgroup of Fi22,\n",
"table is sorted w.r.t. normal series 2.2.2^8.U4(2).2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[53084160,53084160,26542080,196608,196608,110592,294912,294912,147456,8192,
12288,3072,3072,12288,12288,6144,2048,2048,512,512,10368,10368,10368,10368,
864,864,864,432,6912,6912,3456,384,384,576,576,1536,1536,1536,1536,128,256,
256,128,128,128,32,40,40,20,1152,1152,1152,1152,96,144,144,144,144,576,576,
288,96,96,96,96,48,36,36,36,36,96,96,96,96,48,48,46080,46080,3072,3072,3072,
3072,3072,3072,512,512,384,384,768,768,128,256,256,128,64,72,72,288,288,96,96,
96,96,96,96,48,48,32,32,32,32,20,20,24,24],
[,[1,1,1,1,1,2,1,1,1,1,2,4,4,1,1,1,4,4,4,5,21,21,21,21,24,26,26,26,29,29,29,
29,29,30,30,8,9,8,9,11,14,14,14,17,17,20,47,47,47,21,21,21,21,24,26,26,26,26,
29,29,29,33,33,26,26,26,67,67,67,67,53,52,52,53,51,51,1,2,4,4,1,4,4,2,4,4,6,6,
15,14,17,15,14,17,18,26,27,29,30,33,33,29,33,33,30,34,34,36,38,40,40,47,48,64,
65],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,3,3,2,6,1,2,3,1,2,3,
5,4,6,6,36,37,38,39,40,41,42,43,44,45,46,47,48,49,7,8,9,9,11,9,7,9,8,8,7,9,12,
13,14,15,16,21,22,24,23,37,37,39,39,38,36,77,78,79,80,81,82,83,84,85,86,87,88,
89,90,91,92,93,94,95,77,78,77,78,79,80,81,83,82,84,88,87,108,109,110,111,112,
113,90,89],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,22,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,1,2,3,50,51,
53,52,54,57,56,55,58,59,60,61,62,63,64,65,66,67,70,69,68,72,71,74,73,75,76,77,
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,
103,104,105,106,107,108,109,111,110,77,78,114,115]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[10,10,10,10,10,10,-6,-6,-6,-6,-6,-6,-6,
2,2,2,2,2,2,2,1,1,1,1,1,-2,-2,-2,4,4,4,4,4,4,4,2,2,2,2,2,-2,-2,-2,-2,-2,-2,0,
0,0,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,2,2,2,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,
6,6,6,-2,-2,-2,-2,-2,-2,-2,2,2,2,2,2,2,2,-3,-3,-3,-3,-3,3,3,3,0,0,0,0,0,0,0,2,
2,2,2,2,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,-1,-1,-1,0,0,0,0,
-1,-1,-1,-1,-1,-1,4,4,4,4,0,0,0,0,0,0,0,0,-2,-2,-2,2,2,2,2,1,1,-2,-2,-2,-2,0,
0,0,0,0,0,0,0,0,0,-1,-1,1,1],
[TENSOR,[4,2]],[20,20,20,20,20,20,4,4,4,4,4,4,4,-4,-4,-4,-4,-4,-4,-4,-7,-7,-7,
-7,-7,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,0,0,0,0,0,0,0,0,0,1,1,1,1,1,-2,-2,-2,-2,
-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[15,15,15,15,15,15,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,6,6,6,6,6,3,3,3,0,0,0,0,0,0,0,3,3,3,3,3,-1,-1,
-1,-1,-1,-1,0,0,0,2,2,2,2,2,-1,-1,-1,-1,2,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,0,
0,5,5,5,5,-3,-3,-3,-3,-3,-3,-3,-3,1,1,1,1,1,1,1,-1,-1,2,2,2,2,0,0,0,0,0,0,-1,
-1,-1,-1,0,0,1,1],
[TENSOR,[7,2]],[15,15,15,15,15,15,7,7,7,7,7,7,7,3,3,3,3,3,3,3,-3,-3,-3,-3,-3,
0,0,0,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,-2,-2,-2,-2,1,
1,1,1,1,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,5,5,5,5,1,1,1,1,1,1,1,1,3,3,3,-1,-1,
-1,-1,2,2,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
[TENSOR,[9,2]],[20,20,20,20,20,20,4,4,4,4,4,4,4,4,4,4,4,4,4,4,2,2,2,2,2,5,5,5,
-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,
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(108,109)]);
ALF("(2x2^(1+8)):U4(2):2","Fi22",[1,3,2,3,4,9,2,4,3,4,11,10,13,3,4,4,9,11,
13,12,6,16,16,17,38,7,23,19,5,18,15,20,18,39,40,12,11,12,9,29,13,10,13,28,
27,30,14,35,34,16,21,17,17,45,23,19,23,24,20,15,18,41,46,23,22,24,31,55,
58,56,45,45,38,38,42,43,3,10,9,13,4,10,9,13,13,11,28,27,12,10,28,12,13,27,
29,23,47,18,41,40,46,20,39,41,46,64,63,30,30,53,54,35,59,47,44],[
"fusion is unique up to table automorphisms"
]);
ALF("(2x2^(1+8)):U4(2):2","(2x2^(1+8)):(U4(2):2x2)",[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,50,51,52,53,52,54,
55,56,57,58,59,60,61,62,63,64,65,64,66,66,67,67,68,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,
99,100,100,101,101,102,103,104,105],[
"fusion map is unique"
]);
ALF("(2x2^(1+8)):U4(2):2","U4(2).2",[1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,
3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,9,9,9,10,10,10,10,
10,11,11,11,11,12,12,12,12,12,13,13,13,14,14,14,14,15,15,15,15,15,15,16,
16,16,16,17,17,17,17,17,17,17,17,18,18,18,19,19,19,19,20,20,21,21,21,21,
22,22,22,22,22,22,23,23,23,23,24,24,25,25]);
ALN("(2x2^(1+8)):U4(2):2",["Fi22C2B","Fi22N2B"]);

MOT("(2x2^(1+8)):(U4(2):2x2)",
[
"6th maximal subgroup of Fi22.2,\n",
"origin: Dixon's Algorithm"
],
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24576,6144,6144,24576,24576,12288,4096,4096,1024,1024,20736,10368,20736,1728,
1728,1728,864,13824,13824,6912,768,768,1152,1152,1536,3072,3072,256,512,512,
256,256,256,64,80,80,40,2304,2304,1152,192,144,288,288,1152,1152,576,192,192,
192,192,96,72,36,72,96,96,48,92160,92160,6144,6144,6144,6144,6144,6144,1024,
1024,768,768,1536,1536,256,512,512,256,128,144,144,576,576,192,192,192,192,192
,192,96,96,32,32,40,40,48,48,1327104,245760,1327104,245760,18432,24576,24576,
18432,4096,12288,12288,4096,4096,1024,1024,2592,2592,864,864,6912,1152,768,
6912,1152,768,256,768,256,256,256,256,64,40,40,288,288,144,144,576,576,192,192
,96,96,36,36,48,48,184320,184320,92160,6144,6144,6144,6144,12288,12288,6144,
1024,1024,768,768,3072,3072,1536,256,1024,1024,512,256,128,288,288,144,1152,
1152,576,192,192,192,192,384,384,192,96,96,64,64,32,80,80,40,96,96,48],
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70,71,72,73,75,74,76,80,79,100,101,102,103,82,81,106,107,108,109,110,111,112,
113,114,115,116,117,118,119,120,106,108,106,108,106,106,107,108,108,109,131,
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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],[2592,-2592,0,0,0,0,
-144,144,0,0,0,0,0,-24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,-12,0,-4,
4,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-72,
72,0,0,0,0,0,-24,24,0,0,0,0,0,12,-12,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,2,-2,0,2,-2,0,0,0,0],
[TENSOR,[198,2]],[2880,-2880,0,0,0,0,96,-96,0,0,0,0,0,-48,48,0,0,0,0,0,-36,0,
36,0,0,0,0,0,0,0,0,0,0,0,0,-8,8,0,8,-8,0,0,0,0,0,0,0,12,-12,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(154,155)(161,162)(168,169)(172,173)(177,178)(180,181)(187,188)(192,193)
(195,196)(198,199),(152,153)]);
ALF("(2x2^(1+8)):(U4(2):2x2)","Fi22.2",[1,3,2,3,4,9,2,4,3,4,11,10,13,3,4,4,
9,11,13,12,6,16,17,37,7,23,19,5,18,15,20,18,38,39,12,11,9,29,13,10,13,28,27,
30,14,35,34,16,21,17,43,23,19,24,20,15,18,40,44,23,22,24,31,51,53,43,37,41,3,
10,9,13,4,10,9,13,13,11,28,27,12,10,28,12,13,27,29,23,45,18,40,39,44,20,38,40,
44,58,57,30,50,35,54,45,42,60,61,63,64,62,63,64,65,66,61,66,66,64,67,65,
70,87,72,89,68,69,73,86,88,90,67,81,67,66,80,79,82,85,103,74,92,78,93,71,
91,88,90,77,94,99,111,106,107,60,61,62,64,65,61,62,63,64,65,66,65,80,79,
63,66,65,80,66,64,65,79,81,77,72,78,68,73,71,90,91,73,71,86,90,91,105,104,
80,79,98,85,83,84,89,94,93],[
"fusion is unique up to table automorphisms"
]);
ALF("(2x2^(1+8)):(U4(2):2x2)","U4(2).2",[1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,
3,3,3,3,4,4,4,4,5,5,5,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,10,10,10,10,
11,11,11,12,12,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,16,17,17,17,
17,17,17,17,17,18,18,18,19,19,19,19,20,20,21,21,21,21,22,22,22,22,22,22,
23,23,24,24,25,25,1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,4,4,5,5,6,6,6,6,6,6,7,7,8,
8,8,8,8,9,9,10,10,11,11,12,12,12,12,13,13,14,14,15,15,16,16,16,16,16,17,
17,17,17,17,17,17,17,17,18,18,18,18,19,19,19,19,19,20,20,20,21,21,21,21,
21,22,22,22,22,22,22,22,23,23,23,24,24,24,25,25,25]);
ALN("(2x2^(1+8)):(U4(2):2x2)",["Fi22.2C2B","Fi22.2N2B"]);

MOT("2.(2x2^(1+8)):U4(2):2",
[
"7th maximal subgroup of 2.Fi22,\n",
"origin: Dixon's Algorithm"
],
[106168320,106168320,106168320,106168320,53084160,53084160,393216,393216,
196608,110592,589824,589824,589824,589824,294912,294912,8192,12288,6144,6144,
3072,24576,24576,24576,24576,12288,12288,2048,2048,512,1024,1024,20736,20736,
20736,20736,20736,20736,20736,20736,864,1728,1728,1728,1728,864,864,13824,
13824,13824,13824,6912,6912,384,768,768,1152,1152,576,3072,3072,1536,3072,3072
,1536,128,512,512,512,512,256,256,128,128,64,64,80,80,80,80,40,40,2304,2304,
2304,2304,2304,2304,2304,2304,96,288,288,288,288,288,288,288,288,1152,1152,
1152,1152,576,576,192,192,96,192,192,192,192,96,96,72,72,72,72,72,72,72,72,96,
96,96,96,96,96,96,96,92160,92160,92160,92160,3072,3072,3072,6144,6144,6144,
6144,3072,512,512,384,384,1536,1536,1536,1536,128,512,512,512,512,128,64,144,
144,144,144,576,576,576,576,96,96,96,192,192,192,192,96,48,48,64,64,64,64,32,
32,40,40,40,40,48,48,48,48],
[,[1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,3,7,7,7,1,1,1,1,1,1,8,8,7,9,9,33,33,33,33
,33,33,33,33,39,43,43,43,43,43,43,48,48,48,48,48,48,48,48,48,50,50,50,14,14,15
,13,13,15,18,23,23,23,23,23,23,28,28,32,32,78,78,78,78,78,78,33,33,33,33,33,33
,33,33,39,43,43,43,43,43,43,43,43,48,48,48,48,48,48,55,55,55,43,43,43,43,43,43
,115,115,115,115,115,115,115,115,90,87,87,90,85,85,86,86,1,1,4,4,8,7,1,7,7,8,8
,4,7,8,10,10,24,24,23,23,28,24,24,23,23,28,29,43,43,44,44,48,48,51,51,56,55,48
,56,56,55,55,51,57,58,61,61,64,64,66,66,78,78,79,79,110,110,111,111],[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
,1,2,5,6,6,5,3,4,10,2,1,4,3,6,5,1,2,3,4,6,5,9,7,8,10,10,10,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,11,12,13,14,15,16,16,15,18,
15,16,12,11,16,15,14,13,14,13,12,11,15,16,20,19,21,22,23,24,25,27,26,33,34,35,
36,39,40,37,38,62,62,65,65,63,64,61,60,131,132,133,134,135,136,137,138,139,140
,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,131,132,
133,134,131,132,133,134,135,136,137,141,140,139,138,142,146,145,176,177,178,
179,180,181,182,183,184,185,150,149,148,147],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,38,37,36,35,39,
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,
66,67,68,69,70,71,72,73,74,75,76,2,1,4,3,5,6,83,84,85,86,90,89,88,87,91,97,96,
94,95,93,92,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,122,121,119,120,118,117,124,123,126,125,127,128,129,130,131,132,133,
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,
172,173,174,175,176,177,178,179,181,180,131,132,133,134,186,187,188,189]],
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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,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-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,-2,-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,-3,3,3,3,3,3,3,0
,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1
,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,-2,-2,-2,-2,-1,-1,-1,-1,-1,-1,0,0,0,0,
0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2
,2,2,2,2,2,2,1,1,1,1,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1
,1,1,1,1],
[TENSOR,[3,2]],[10,10,10,10,10,10,10,10,10,10,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,
-6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,-2,4,4,4,4,4,4,4,4,4
,4,4,4,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,-3,-3,-3,-3,-3,
-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,1,1,1,1,1,1,1,1,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[15,15,15,15,15,
15,15,15,15,15,7,7,7,7,7,7,7,7,7,7,7,3,3,3,3,3,3,3,3,3,3,3,-3,-3,-3,-3,-3,-3,
-3,-3,-3,0,0,0,0,0,0,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,
1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-5,-5,-5,-5,-5,-5,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-3,-3,-3,-3,-3,1,1,1,1,1,1,-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],
[TENSOR,[6,2]],[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,-1,6,6,6,6,6,6,6,6,6,3,3,3,3,3,3,0,0,0,0,0,0,
0,0,0,0,0,0,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,2,2,2,2,2,
2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,5,5,5,5,5,5,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,1,1,1,1,1,1,1,
1,1,1,1,-1,-1,-1,-1,2,2,2,2,2,2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,
1,1],
[TENSOR,[8,2]],[20,20,20,20,20,20,20,20,20,20,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4
,4,4,4,4,4,4,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
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,1,1,1,1],
[TENSOR,[10,2]],[20,20,20,20,20,20,20,20,20,20,4,4,4,4,4,4,4,4,4,4,4,-4,-4,-4
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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],[24,24,24,24,24
,24,24,24,24,24,8,8,8,8,8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,6,6,6,6,6,6,6,6,6,
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,0,0,0],
[TENSOR,[13,2]],[30,30,30,30,30,30,30,30,30,30,-10,-10,-10,-10,-10,-10,-10,
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0,0,0,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[15,2]],[32,32,-32,-32,0,0,0,0,0,0,-16,-16,16,16,0,0,0,0,0,0,0,8,8,-8
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[TENSOR,[173,2]],[1024,-1024,-1024,1024,1024,-1024,0,0,0,0,0,0,0,0,0,0,0,0,0,
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2,-2,4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0],
[TENSOR,[175,2]],[1280,-1280,-1280,1280,1280,-1280,0,0,0,0,128,-128,-128,128,
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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],[
1280,-1280,-1280,1280,-1280,1280,0,0,0,0,-128,128,128,-128,-128,128,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,20,-20,-20,20,20,-20,-20,20,0,4,-4,-4,4,-4,4,8,-8,-8,8,8
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-4,4,0,-2,2,2,-2,2,-2,-2,2,4,-4,-4,4,4,-4,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,-1,-1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1296,-1296,-1296,
1296,-1296,1296,0,0,0,0,72,-72,-72,72,72,-72,0,0,0,0,0,12,-12,-12,12,12,-12,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,-12,0,0
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-12,12,-12,12,0,0,0,0,0,-6,6,-6,6,0,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-2,2,0,0,0,0,-1,1,-1,1,0,0,0,0],
[TENSOR,[179,2]],[1296,-1296,-1296,1296,1296,-1296,0,0,0,0,-72,72,72,-72,72,
-72,0,0,0,0,0,12,-12,-12,12,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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0,0,0,0,0,0,0,0,-36,36,36,-36,0,0,0,12,-12,-12,12,0,0,0,0,0,-6,6,6,-6,0,-2,2,2
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[TENSOR,[181,2]],[1440,-1440,-1440,1440,1440,-1440,0,0,0,0,48,-48,-48,48,-48,
48,0,0,0,0,0,24,-24,-24,24,-24,24,0,0,0,0,0,-18,18,-18,18,18,-18,18,-18,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,8,0,0,0,0,0,-4,4,4,-4,-4,4,0,0,0,0,0,0,0,0,
0,0,6,-6,-6,6,-6,6,6,-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,
0,0,0,0,0,0,0,0,0,0,0,2,-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
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-1440,-1440,1440,-1440,1440,0,0,0,0,-48,48,48,-48,-48,48,0,0,0,0,0,24,-24,-24,
24,24,-24,0,0,0,0,0,-18,18,18,-18,-18,18,18,-18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-8,8,0,0,4,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,0,0,-6,6,6,-6,-6,6,6,-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,-2,2,0
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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],[1728,-1728,1728,-1728,0,0,-64,64,
0,0,-192,192,-192,192,0,0,0,0,-16,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
1728,-1728,1728,-1728,0,0,-64,64,0,0,192,-192,192,-192,0,0,0,0,16,-16,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,-18,18,-18,0,0,0,2,-2,-6,6,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,6,-6,6,-6,0,0,2,-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
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2160,-2160,2160,-2160,0,0,-80,80,0,0,96,-96,
96,-96,0,0,0,0,8,-8,0,-24,24,-24,24,0,0,0,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,-18,18,-18,18,0,0,0,-2,2,6,-6,0,0,0,0,0,0,0,0,4,-4,4,-4,0,0,0,0,-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,-6,6,-6,6,0,0,-2,2,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2160,
-2160,2160,-2160,0,0,-80,80,0,0,-96,96,-96,96,0,0,0,0,-8,8,0,-24,24,-24,24,0,0
,0,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-18,18,-18,18,0,0,0,-2,2,6,-6,0,0,0,
0,0,0,0,0,-4,4,-4,4,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,6,-6,6,-6,0,0,2,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2592,-2592,2592,-2592,0,0,-96,96,0,0,0,0,0,0,0,0
,0,0,0,0,0,48,-48,48,-48,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(180,181),
( 35, 38)( 36, 37)( 87, 90)( 88, 89)( 92, 97)( 93, 96)(117,122)(118,121)
(123,124)(125,126)
,
(131,132)(133,134)(138,139)(140,141)(147,148)(149,150)(152,153)(154,155)
(158,159)(160,161)(162,163)(164,165)(169,170)(171,172)(176,177)(178,179)
(182,183)(184,185)(186,187)(188,189)
,
(  5,  6)( 11, 12)( 13, 14)( 19, 20)( 26, 27)( 35, 36)( 37, 38)( 46, 47)
( 52, 53)( 60, 63)( 61, 64)( 67, 68)( 69, 70)( 75, 76)( 81, 82)( 83, 84)
( 85, 86)( 94, 95)( 98, 99)(100,101)(102,103)(106,107)(113,114)(117,118)
(121,122)(127,130)(128,129)(133,134)(138,139)(149,150)(154,155)(160,161)
(164,165)(171,172)(176,179)(177,178)(184,185)(186,187)
]);
ALF("2.(2x2^(1+8)):U4(2):2","(2x2^(1+8)):U4(2):2",[1,1,2,2,3,3,4,4,5,6,
7,7,8,8,9,9,10,11,12,12,13,14,14,15,15,16,16,17,18,19,20,20,21,21,22,22,
23,23,24,24,25,26,26,27,27,28,28,29,29,30,30,31,31,32,33,33,34,34,35,36,
36,37,38,38,39,40,41,41,42,42,43,43,44,45,46,46,47,47,48,48,49,49,50,50,
51,51,52,52,53,53,54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,
64,64,65,65,66,66,67,67,68,68,69,69,70,70,71,72,73,74,75,75,76,76,77,77,
78,78,79,80,81,82,82,83,83,84,85,86,87,88,89,89,90,90,91,92,92,93,93,94,
95,96,96,97,97,98,98,99,99,100,101,102,103,103,104,104,105,106,107,108,
108,109,109,110,111,112,112,113,113,114,114,115,115]);
ALF("2.(2x2^(1+8)):U4(2):2","2.Fi22",[1,2,6,5,4,3,5,6,7,16,4,3,7,7,6,5,
7,19,17,18,22,6,5,7,7,7,7,16,19,22,21,20,10,11,28,27,27,28,30,29,67,13,12,
40,41,33,34,8,9,32,31,25,26,35,31,32,68,69,70,21,20,19,21,20,16,50,22,22,
17,18,22,22,49,48,51,52,24,23,61,62,60,59,28,27,36,37,30,29,29,30,79,41,
40,33,34,40,41,43,42,35,35,25,26,32,31,72,71,80,41,40,38,39,42,43,53,54,
96,95,102,101,97,98,79,79,67,67,73,74,76,75,5,6,17,18,16,22,7,17,18,16,16,
22,22,19,49,48,21,20,18,17,49,21,20,22,22,48,50,40,41,81,82,31,32,71,72,
70,80,35,69,68,72,71,80,112,111,52,51,52,51,93,94,61,62,103,104,81,82,77,
78]);

MOT("3x(2x2^(1+8)):U4(2):2",
[
"7th maximal subgroup of 3.Fi22"
],
0,
0,
0,
[( 64, 67)( 65, 68)( 66, 69)(154,157)(155,158)(156,159)(163,169)(164,170)
(165,171)(202,208)(203,209)(204,210)(211,214)(212,215)(213,216)(217,220)
(218,221)(219,222),(328,331)(329,332)(330,333),
(106,112)(107,113)(108,114)(223,226)(224,227)(225,228)(322,325)(323,326)
(324,327),(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)
( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)
( 71, 72)( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 86, 87)( 89, 90)( 92, 93)
( 95, 96)( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114)(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)(161,162)(164,165)
(167,168)(170,171)(173,174)(176,177)(179,180)(182,183)(185,186)(188,189)
(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(212,213)
(215,216)(218,219)(221,222)(224,225)(227,228)(230,231)(233,234)(236,237)
(239,240)(242,243)(245,246)(248,249)(251,252)(254,255)(257,258)(260,261)
(263,264)(266,267)(269,270)(272,273)(275,276)(278,279)(281,282)(284,285)
(287,288)(290,291)(293,294)(296,297)(299,300)(302,303)(305,306)(308,309)
(311,312)(314,315)(317,318)(320,321)(323,324)(326,327)(329,330)(332,333)
(335,336)(338,339)(341,342)(344,345)],
["ConstructDirectProduct",[["(2x2^(1+8)):U4(2):2"],["Cyclic",3]]]);
ALF("3x(2x2^(1+8)):U4(2):2","3.Fi22",[1,2,3,7,8,9,4,5,6,7,8,9,10,11,12,19,
20,21,4,5,6,10,11,12,7,8,9,10,11,12,25,26,27,22,23,24,31,32,33,7,8,9,10,
11,12,10,11,12,19,20,21,25,26,27,31,32,33,28,29,30,16,16,16,41,42,40,42,
40,41,43,44,45,92,93,94,17,17,17,55,56,57,49,49,49,13,14,15,46,47,48,37,
38,39,50,51,52,46,47,48,95,96,97,98,99,100,28,29,30,25,26,27,28,29,30,19,
20,21,69,70,71,31,32,33,22,23,24,31,32,33,66,67,68,63,64,65,72,73,74,34,
35,36,83,84,85,80,81,82,40,41,42,53,53,53,44,45,43,45,43,44,107,108,109,
56,57,55,49,49,49,57,55,56,58,58,58,50,51,52,37,38,39,46,47,48,101,102,
103,110,111,112,55,56,57,54,54,54,58,58,58,75,76,77,135,136,137,142,143,
144,138,139,140,108,109,107,109,107,108,94,92,93,93,94,92,104,104,104,105,
105,105,7,8,9,22,23,24,19,20,21,31,32,33,10,11,12,22,23,24,19,20,21,31,32,
33,31,32,33,25,26,27,66,67,68,63,64,65,28,29,30,22,23,24,66,67,68,28,29,
30,31,32,33,63,64,65,69,70,71,55,56,57,113,114,115,46,47,48,101,102,103,
98,99,100,110,111,112,50,51,52,95,96,97,101,102,103,110,111,112,160,161,
162,157,158,159,72,73,74,72,73,74,129,130,131,132,133,134,83,84,85,145,
146,147,113,114,115,106,106,106],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3x(2x2^(1+8)):U4(2):2","3.(2x2^(1+8)):(U4(2):2x2)",[1,2,2,3,4,4,5,6,
6,7,8,8,9,10,10,11,12,12,13,14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,
24,24,25,26,26,27,28,28,29,30,30,31,32,32,33,34,34,35,36,36,37,38,38,39,
40,40,41,42,42,43,44,45,43,45,44,46,47,47,48,49,49,50,51,51,52,53,53,54,
55,55,56,57,57,58,59,59,60,61,61,62,63,63,64,65,65,66,67,67,68,69,69,70,
71,72,73,74,74,70,72,71,75,76,76,77,78,78,79,80,80,81,82,82,83,84,84,85,
86,86,87,88,88,89,90,90,91,92,92,93,94,94,95,96,96,97,98,98,99,100,100,101,
102,103,101,103,102,104,105,105,106,107,108,109,110,110,106,108,107,111,
112,112,113,114,114,115,116,116,117,118,118,119,120,120,121,122,122,123,
124,124,125,126,126,127,128,128,129,130,130,131,132,133,134,135,135,131,
133,132,136,137,138,136,138,137,139,140,141,139,141,140,142,143,144,142,
144,143,145,146,146,147,148,148,149,150,150,151,152,152,153,154,154,155,
156,156,157,158,158,159,160,160,161,162,162,163,164,164,165,166,166,167,
168,168,169,170,170,171,172,172,173,174,174,175,176,176,177,178,178,179,
180,180,181,182,182,183,184,184,185,186,186,187,188,188,189,190,190,191,
192,192,193,194,194,195,196,196,197,198,198,199,200,200,201,202,202,203,
204,204,205,206,206,207,208,209,207,209,208,210,211,212,210,212,211,213,
214,214,215,216,216,217,218,218,219,220,220]);

MOT("3xA10.2",
[
"12th maximal subgroup of 3.Fi22"
],
0,
0,
0,
[
(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)
( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)( 71, 72)
( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 86, 87)( 89, 90)( 92, 93)( 95, 96)
( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114)(116,117)(119,120)
(122,123)(125,126)
],
["ConstructDirectProduct",[["A10.2"],["Cyclic",3]]]);
ALF("3xA10.2","3.Fi22",[1,2,3,7,8,9,10,11,12,13,14,15,17,17,17,18,18,18,
22,23,24,31,32,33,28,29,30,34,35,36,34,35,36,46,47,48,55,56,57,58,58,58,
60,61,62,72,73,74,79,79,79,83,84,85,110,111,112,113,114,115,126,127,128,
148,149,150,4,5,6,7,8,9,10,11,12,22,23,24,31,32,33,28,29,30,37,38,39,54,
54,54,50,51,52,49,49,49,55,56,57,59,59,59,72,73,74,80,81,82,83,84,85,101,
102,103,113,114,115,123,124,125,145,146,147,163,164,165]);

MOT("3xM12",
[
"14th maximal subgroup of 3.Fi22"
],
0,
0,
0,
[(40,43)(41,44)(42,45),
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)
(35,36)(38,39)(41,42)(44,45)
,(16,19)(17,20)(18,21)(31,34)(32,35)(33,36)],
["ConstructDirectProduct",[["M12"],["Cyclic",3]]]);
ALF("3xM12","3.Fi22",[1,2,3,7,8,9,10,11,12,18,18,18,17,17,17,28,29,30,28,
29,30,34,35,36,55,56,57,59,59,59,72,73,74,72,73,74,83,84,85,86,87,88,89,
90,91]);

MOT("3.(2x2^(1+8)):(U4(2):2x2)",
[
"maximal subgroup of 3.Fi22.2"
],
[318504960,159252480,318504960,159252480,159252480,79626240,1179648,589824,
1179648,589824,663552,331776,1769472,884736,1769472,884736,884736,442368,49152
,24576,73728,36864,18432,9216,18432,9216,73728,36864,73728,36864,36864,18432,
12288,6144,12288,6144,3072,1536,3072,1536,62208,31104,31104,31104,31104,62208,
31104,5184,2592,5184,2592,5184,2592,2592,1296,41472,20736,41472,20736,20736,
10368,2304,1152,2304,1152,3456,1728,3456,1728,4608,4608,4608,9216,4608,9216,
4608,768,384,1536,768,1536,768,768,384,768,384,768,384,192,96,240,120,240,120,
120,60,6912,3456,6912,3456,3456,3456,3456,576,288,432,432,432,864,432,864,432,
3456,1728,3456,1728,1728,864,576,288,576,288,576,288,576,288,288,144,216,108,
108,108,108,216,108,288,288,288,288,288,288,144,144,144,276480,138240,276480,
138240,18432,9216,18432,9216,18432,9216,18432,9216,18432,9216,18432,9216,3072,
1536,3072,1536,2304,1152,2304,1152,4608,2304,4608,2304,768,384,1536,768,1536,
768,768,384,384,192,432,216,432,216,1728,864,1728,864,576,288,576,288,576,288,
576,288,576,288,576,288,288,144,288,144,96,96,96,96,96,96,120,60,120,60,144,72
,144,72,1327104,245760,1327104,245760,18432,24576,24576,18432,4096,12288,12288
,4096,4096,1024,1024,2592,2592,864,864,6912,1152,768,6912,1152,768,256,768,256
,256,256,256,64,40,40,288,288,144,144,576,576,192,192,96,96,36,36,48,48,184320
,184320,92160,6144,6144,6144,6144,12288,12288,6144,1024,1024,768,768,3072,3072
,1536,256,1024,1024,512,256,128,288,288,144,1152,1152,576,192,192,192,192,384,
384,192,96,96,64,64,32,80,80,40,96,96,48],
[,[1,2,1,2,1,2,1,2,1,2,3,4,1,2,1,2,1,2,1,2,3,4,7,8,7,8,1,2,1,2,1,2,7,8,7,8,7,8
,9,10,41,42,41,42,42,41,42,46,47,50,51,50,51,50,51,56,57,56,57,56,57,56,57,56,
57,58,59,58,59,15,16,16,17,18,17,18,21,22,27,28,27,28,27,28,33,34,33,34,39,40,
91,92,91,92,91,92,41,42,41,42,41,42,42,46,47,50,51,51,50,51,50,51,56,57,56,57,
56,57,64,65,64,65,50,51,50,51,50,51,129,130,129,130,130,129,130,101,102,103,
101,103,102,99,100,100,1,2,3,4,7,8,7,8,1,2,7,8,7,8,3,4,7,8,7,8,11,12,11,12,29,
30,27,28,33,34,29,30,27,28,33,34,35,36,50,51,52,53,56,57,58,59,64,65,64,65,56,
57,64,65,64,65,58,59,66,67,66,67,70,72,71,77,78,78,91,92,93,94,123,124,125,126
,1,1,3,3,1,7,7,3,7,1,3,7,7,9,7,41,46,50,52,56,56,56,58,58,58,19,21,29,27,33,33
,39,91,93,41,46,50,52,56,58,64,64,50,52,129,134,104,104,1,1,1,7,7,1,1,7,7,7,7,
7,11,11,27,27,27,33,27,27,27,33,35,50,50,50,56,56,56,64,64,56,56,64,64,64,66,
66,75,75,77,91,91,91,123,123,123],[1,1,3,3,5,5,7,7,9,9,11,11,13,13,15,15,17,17
,19,19,21,21,23,23,25,25,27,27,29,29,31,31,33,33,35,35,37,37,39,39,1,1,5,5,5,3
,3,11,11,1,1,3,3,5,5,1,1,3,3,5,5,9,9,7,7,11,11,11,11,70,70,70,73,73,75,75,77,
77,79,79,81,81,83,83,85,85,87,87,89,89,91,91,93,93,95,95,13,13,15,15,17,17,17,
21,21,17,17,17,13,13,15,15,15,15,13,13,17,17,23,23,25,25,27,27,29,29,31,31,41,
41,43,43,43,46,46,73,73,73,75,75,75,70,70,70,145,145,147,147,149,149,151,151,
153,153,155,155,157,157,159,159,161,161,163,163,165,165,167,167,169,169,171,
171,173,173,175,175,177,177,179,179,181,181,145,145,147,147,145,145,147,147,
149,149,151,151,153,153,157,157,155,155,159,159,167,167,165,165,207,207,207,
210,210,210,213,213,215,215,171,171,169,169,221,222,223,224,225,226,227,228,
229,230,231,232,233,234,235,221,223,221,223,221,221,222,223,223,224,246,247,
248,249,250,251,252,253,254,225,228,225,228,225,228,226,227,230,231,236,237,
247,247,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,
286,287,288,289,290,291,270,269,271,269,270,271,272,273,274,275,276,277,278,
281,282,307,308,309,310,311,312,283,284,285],,[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,
66,67,68,69,70,72,71,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,1,2
,3,4,5,6,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,
134,135,136,137,138,139,140,141,142,144,143,145,146,147,148,149,150,151,152,
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,
191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,208,
210,211,212,145,146,147,148,217,218,219,220,221,222,223,224,225,226,227,228,
229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,
248,249,250,251,252,222,224,255,256,257,258,259,260,261,262,263,264,265,266,
268,267,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,
286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,
305,306,307,308,309,270,269,271,313,314,315]],
0,
[( 44, 45)(102,103)(107,108)(132,133)(137,138)(140,141),(211,212),(267,268),
(269,270)(276,277)(283,284)(287,288)(292,293)(295,296)(302,303)(307,308)
(310,311)(313,314),( 71, 72)(143,144)(208,209)],
["ConstructMGA","3x(2x2^(1+8)):U4(2):2","(2x2^(1+8)):(U4(2):2x2)",
  [ [ 2, 3 ], [ 5, 6 ], [ 8, 9 ], [ 11, 12 ], [ 14, 15 ], [ 17, 18 ],
    [ 20, 21 ], [ 23, 24 ], [ 26, 27 ], [ 29, 30 ], [ 32, 33 ], [ 35, 36 ],
    [ 38, 39 ], [ 41, 42 ], [ 44, 45 ], [ 47, 48 ], [ 50, 51 ], [ 53, 54 ],
    [ 56, 57 ], [ 59, 60 ], [ 62, 63 ], [ 65, 66 ], [ 68, 69 ], [ 71, 72 ],
    [ 74, 75 ], [ 77, 81 ], [ 78, 80 ], [ 83, 87 ], [ 84, 86 ], [ 89, 90 ],
    [ 92, 93 ], [ 95, 96 ], [ 98, 99 ], [ 101, 102 ], [ 104, 108 ],
    [ 105, 107 ], [ 110, 111 ], [ 113, 114 ], [ 116, 117 ], [ 119, 120 ],
    [ 122, 123 ], [ 125, 126 ], [ 128, 129 ], [ 131, 132 ], [ 134, 135 ],
    [ 137, 138 ], [ 140, 144 ], [ 141, 143 ], [ 146, 150 ], [ 147, 149 ],
    [ 152, 153 ], [ 155, 156 ], [ 158, 159 ], [ 161, 162 ], [ 164, 165 ],
    [ 167, 168 ], [ 170, 171 ], [ 173, 174 ], [ 176, 177 ], [ 179, 180 ],
    [ 182, 183 ], [ 185, 186 ], [ 188, 189 ], [ 191, 192 ], [ 194, 195 ],
    [ 197, 198 ], [ 200, 201 ], [ 203, 204 ], [ 206, 207 ], [ 209, 210 ],
    [ 212, 213 ], [ 215, 216 ], [ 218, 219 ], [ 221, 222 ], [ 224, 225 ],
    [ 227, 228 ], [ 230, 231 ], [ 233, 234 ], [ 236, 237 ], [ 239, 240 ],
    [ 242, 243 ], [ 245, 246 ], [ 248, 249 ], [ 251, 252 ], [ 254, 255 ],
    [ 257, 258 ], [ 260, 261 ], [ 263, 264 ], [ 266, 267 ], [ 269, 270 ],
    [ 272, 273 ], [ 275, 276 ], [ 278, 279 ], [ 281, 282 ], [ 284, 285 ],
    [ 287, 288 ], [ 290, 294 ], [ 291, 293 ], [ 296, 297 ], [ 299, 303 ],
    [ 300, 302 ], [ 305, 306 ], [ 308, 309 ], [ 311, 312 ], [ 314, 315 ],
    [ 317, 318 ], [ 320, 324 ], [ 321, 323 ], [ 326, 330 ], [ 327, 329 ],
    [ 332, 336 ], [ 333, 335 ], [ 338, 339 ], [ 341, 342 ], [ 344, 345 ] ],
  ()]);
ALF("3.(2x2^(1+8)):(U4(2):2x2)","(2x2^(1+8)):(U4(2):2x2)",[1,1,2,2,3,3,4,
4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,
18,19,19,20,20,21,21,22,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,
30,30,31,31,32,32,33,33,34,34,35,35,35,36,36,37,37,38,38,39,39,40,40,41,
41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50,50,50,51,51,52,52,
52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,63,64,
64,64,65,65,66,66,66,67,67,67,68,68,68,69,69,70,70,71,71,72,72,73,73,74,
74,75,75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,83,83,84,84,85,85,86,
86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,96,96,97,97,98,
98,99,99,100,100,100,101,101,101,102,102,103,103,104,104,105,105,106,107,
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]);
ALF("3.(2x2^(1+8)):(U4(2):2x2)","S3",[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,2,1,2,1,2,1,2,1,2,1,2,
1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
1,2,1,2,1,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,
2,1,2,2,1,2,1,2,2,1,2,2,1,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,
2,1,2,1,2,2,1,2,2,1,2,1,2,1,2,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3]);
ALF("3.(2x2^(1+8)):(U4(2):2x2)","3.Fi22.2",[1,2,5,6,3,4,5,6,7,8,14,15,3,4,
7,8,5,6,7,8,18,19,16,17,22,23,5,6,7,8,7,8,14,15,18,19,22,23,20,21,11,11,
29,28,29,30,31,64,65,12,12,39,40,34,34,9,10,32,33,26,27,35,36,32,33,66,67,
68,69,20,21,21,18,19,14,15,49,50,22,23,16,17,22,23,47,48,45,46,51,52,24,
25,59,60,57,58,28,29,37,37,31,30,31,74,75,40,39,40,34,34,41,41,35,36,26,
27,32,33,70,71,76,77,39,40,38,38,41,41,53,54,91,93,92,95,96,75,74,75,65,
65,64,72,72,72,5,6,16,17,14,15,22,23,7,8,16,17,14,15,22,23,22,23,18,19,47,
48,45,46,20,21,16,17,47,48,20,21,22,23,45,46,49,50,39,40,78,79,32,33,70,
71,68,69,76,77,35,36,66,67,70,71,76,77,106,107,104,105,51,52,52,88,89,90,
59,60,97,98,78,79,73,73,110,111,113,114,112,113,114,115,116,111,116,116,
114,117,115,120,137,122,139,118,119,123,136,138,140,117,131,117,116,130,
129,132,135,153,124,142,128,143,121,141,138,140,127,144,149,161,156,157,
110,111,112,114,115,111,112,113,114,115,116,115,130,129,113,116,115,130,
116,114,115,129,131,127,122,128,118,123,121,140,141,123,121,136,140,141,
155,154,130,129,148,135,133,134,139,144,143],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3x2F4(2)'",
[
"9th maximal subgroup of 3.Fi22"
],
0,
0,
0,
[(55,61)(56,62)(57,63)(58,64)(59,65)(60,66),(43,46)(44,47)(45,48),
(34,37)(35,38)(36,39),
(28,31)(29,32)(30,33)(55,58)(56,59)(57,60)(61,64)(62,65)(63,66),
(49,52)(50,53)(51,54),
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)
(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)
],
["ConstructDirectProduct",[["2F4(2)'"],["Cyclic",3]]]);
ALF("3x2F4(2)'","3.Fi22",[1,2,3,7,8,9,10,11,12,18,18,18,28,29,30,25,26,27,
28,29,30,34,35,36,59,59,59,69,70,71,69,70,71,72,73,74,72,73,74,83,84,85,
116,116,116,116,116,116,117,118,119,120,121,122,129,130,131,132,133,134,
132,133,134,129,130,131]);

MOT("Fi22.2M4",
[
"4th maximal subgroup of Fi22.2, normalizer of a 2^10 subgroup,\n",
"sorted w.r.t. normal series 2^10 < 2^10:M22 < 2^10:M22:2,\n",
"origin: Dixon's Algorithm"
],
[908328960,41287680,3932160,1179648,49152,16384,8192,8192,6144,3072,2048,1152,
1152,288,288,192,1024,1024,512,256,256,256,256,256,128,64,40,40,20,96,96,48,28
,28,28,28,64,64,32,11,344064,49152,43008,49152,16384,12288,6144,20480,20480,
2048,1024,768,256,192,1024,1024,512,256,256,256,96,96,48,96,96,48,64,64,32,20,
20,24,24,28,28,28,28],
[,[1,1,1,1,1,1,3,3,3,4,3,12,12,12,12,12,5,5,5,8,7,7,6,5,8,10,27,27,27,12,13,16
,33,33,35,35,17,18,20,40,1,1,1,3,3,3,3,1,3,3,4,5,6,10,5,5,5,7,8,7,12,12,12,16,
16,16,18,17,20,27,28,30,31,33,33,35,35],[1,2,3,4,5,6,7,8,9,10,11,1,4,2,4,3,17,
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[(33,35)(34,36)(74,77)(75,76)]);
ALF("Fi22.2M4","M22.2",[1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,5,5,5,
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ALF("Fi22.2M4","Fi22.2",[1,2,3,4,3,4,9,11,10,12,13,7,22,19,24,23,9,11,13,29,
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"fusion map is unique"
]);

MOT("2.(3^(1+6):2^(3+4):3^2:2)",
[
"origin: Dixon's Algorithm"
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324,162,162,162,162,162,162,54,54,72,72,72,72,72,72,72,72,72,72,72,72,216,216,
216,216,108,108,72,72,432,48,216,216,216,216,216,108,108,108,108,96,96,96,96,
32,32,32,32,32,32,32,32,24,48,48,48,48],
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324,0,0,0,0,0,0,0,0,-72,72,-24,24,24,-24,36,-36,12,-12,0,0,-12,12,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,27,-27,-27,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-3,3,-3,3,6,-6,-3,3,6,-6,0,0,-3,3,-3,3,0,0,3,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[648,-648,-324,324,0,0,0,0,
0,0,0,0,-72,72,-24,24,24,-24,36,-36,12,-12,0,0,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-27,27,0,0,27,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,-6,
-3,3,-3,3,6,-6,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[648,-648,-324,324,0,0,0,0,0,0,0,0,-72
,72,-24,24,24,-24,36,-36,12,-12,0,0,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,27,-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,-3,3,6,-6,-3,3,-3
,3,-3,3,3,-3,0,0,6,-6,0,0,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0],[768,-768,768,-768,-96,96,-42,42,12,-12,12,-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,-6,6,-6,6,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,-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]]
,
[(151,152)(153,154)(155,157)(156,158)(159,162)(160,161)(164,165)(166,167),
(155,158)(156,157)(159,161)(160,162),(143,144)(145,146)(147,148)(149,150),
(132,134)(133,135),
( 46, 50, 48)( 47, 51, 49)( 52, 58, 56)( 53, 59, 57)( 64, 68, 66)( 65, 69, 67)
( 72, 76, 74)( 73, 77, 75)( 78, 80, 86)( 79, 81, 87)( 82, 84, 90)( 83, 85, 91)
( 88,100, 98)( 89,101, 99)(102,104,106)(103,105,107)(124,130,126)(125,131,127)
,
( 52, 58, 56)( 53, 59, 57)( 54, 60, 62)( 55, 61, 63)( 64, 66, 68)( 65, 67, 69)
( 88,100, 98)( 89,101, 99)( 92, 96, 94)( 93, 97, 95)(102,106,104)(103,107,105)
(120,122,128)(121,123,129)(124,130,126)(125,131,127)
,
( 13, 14)( 17, 18)( 19, 20)( 23, 24)( 25, 26)( 27, 28)( 32, 34)( 33, 35)
( 40, 42)( 41, 43)( 52, 62)( 53, 63)( 54, 56)( 55, 57)( 58, 60)( 59, 61)
( 64, 68)( 65, 69)( 72, 73)( 74, 75)( 76, 77)( 78, 79)( 80, 81)( 86, 87)
( 88, 95)( 89, 94)( 92, 99)( 93, 98)( 96,101)( 97,100)(102,105)(103,104)
(106,107)(114,116)(115,117)(120,130)(121,131)(122,124)(123,125)(126,128)
(127,129)(132,135)(133,134)(136,137)(145,146)(147,148)(153,154)(155,161)
(156,162)(157,160)(158,159)(164,165)
]);
ALF("2.(3^(1+6):2^(3+4):3^2:2)","3^(1+6):2^(3+4):3^2:2",[1,1,2,2,3,3,4,4,
5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,
20,21,21,22,22,23,23,24,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,
33,34,34,35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,
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,
69,70,70,71,71,72,72,73,74,75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,
83,83,84,84,85,85,86,87,87,88,88]);
ALF("2.(3^(1+6):2^(3+4):3^2:2)","2.Fi22",[1,2,10,11,8,9,10,11,12,13,14,15,
3,4,5,6,7,7,27,28,29,30,25,26,36,37,33,34,31,32,16,20,21,20,21,19,67,68,
69,74,73,76,75,70,79,8,9,10,11,12,13,10,11,12,13,12,13,14,15,14,15,10,11,
14,15,12,13,14,15,14,15,27,28,33,34,25,26,36,37,35,35,31,32,40,41,42,43,
37,36,29,30,39,38,37,36,44,45,38,39,45,44,44,45,45,44,43,42,53,54,55,56,
55,56,55,56,55,56,57,58,83,84,74,73,76,75,77,78,77,78,83,84,95,96,97,98,
99,100,101,102,7,22,35,42,43,38,39,45,44,36,37,49,49,48,48,52,51,52,51,51,
52,52,51,80,112,112,111,111],[
"determined using the groups"
]);

MOT("2^12.3_1.U4(3).2_2'",
[
"occurs as factor group of F3+M9"
],
[80263249920,212336640,47185920,39813120,9797760,1769472,196608,294912,49152,
18432,16384,3456,34992,1119744,41472,31104,1492992,27648,18432,124416,13824,
11664,3888,31104,3456,5184,2592,288,864,864,9216,1024,1536,288,1536,512,256,
256,48,480,160,160,160,80,15,432,3456,1152,288,3456,576,384,432,144,3456,384,
576,432,144,21,21,21,192,64,24,324,108,81,1296,144,432,432,54,54,72,144,48,
3317760,122880,92160,73728,73728,6144,4096,2304,3072,1024,256,1536,1536,768,
256,256,1296,1296,3456,576,384,432,144,1152,1152,192,288,288,72,72,72,72,64,64
,32,40,40,40,40,24,48,48,48,48,18,18],
[,[1,1,1,1,5,1,1,1,3,2,3,5,13,14,14,14,17,17,17,17,17,22,22,24,24,24,27,27,27,
27,6,7,8,12,6,7,11,9,12,40,40,40,40,40,45,13,14,14,15,17,18,19,22,22,24,24,24,
24,25,60,62,61,31,32,34,66,66,68,69,69,69,69,74,73,46,47,48,1,3,2,1,3,2,3,4,6,
7,11,7,6,8,11,9,13,13,17,18,19,24,25,17,19,18,20,21,27,28,29,30,32,31,33,40,41
,42,43,46,56,55,57,57,74,73],[1,2,3,4,1,6,7,8,9,10,11,6,1,1,2,4,1,2,3,4,4,1,4,
1,2,4,1,3,4,4,31,32,33,31,35,36,37,38,35,40,42,41,43,44,40,6,6,8,10,6,10,9,6,8
,6,7,8,6,10,60,60,60,63,64,63,14,16,14,14,15,16,16,13,13,31,31,33,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,93,78,78,78,80,79,78,80,81,82,83,85,85,81,82,
85,85,110,111,112,113,115,114,116,86,89,90,91,91,94,95],,[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
,37,38,39,1,3,3,2,4,5,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64
,65,66,67,68,69,70,71,72,74,73,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90
,91,92,93,95,94,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,78,79,79,80,117,118,119,121,120,123,122],,[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,
40,42,41,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,1,5,5,63,64,65,66,
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,
115,114,116,117,118,119,121,120,122,123]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[
21,21,21,21,21,5,5,5,5,5,5,5,-6,-6,-6,-6,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1
,1,1,1,1,1,1,1,1,1,1,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,-1,-1,-1,0,0,
0,0,0,0,0,0,0,-2,-2,-2,9,9,9,1,1,1,1,1,-3,-3,-3,1,1,1,1,1,0,0,-3,-3,-3,3,3,1,1
,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,0,1,1,1,1,0,0],
[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,
-1,-1,-1,-1,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,0,0
,0,-1,-1,-1,2,2,2,2,2,2,2,-1,-1,0,0,0,-5,-5,-5,-5,-5,-5,-5,-5,3,3,3,-1,-1,-1,
-1,-1,4,4,-2,-2,-2,1,1,-2,-2,-2,-2,-2,1,1,1,1,-1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,1
,1],
[TENSOR,[5,2]],[35,35,35,35,35,3,3,3,3,3,3,3,8,8,8,8,-1,-1,-1,-1,-1,-1,-1,8,8
,8,-1,-1,-1,-1,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,0,0,0,0,0,
0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,0,0,0,15,15,15,-1,-1,-1,-1,-1,-1,-1,-1
,3,3,3,3,3,6,6,3,3,3,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,2,0,0,0,0
,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
,9,0,0,0,0,-2,-2,-2,-2,2,2,2,2,2,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1
,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,30,30,30,6,6,6,6,6,2,2,2,2,2,2,2,2,3,3,3,3,3
,3,3,3,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,0,0],
[TENSOR,[9,2]],[140,140,140,140,140,12,12,12,12,12,12,12,5,5,5,5,-4,-4,-4,-4,
-4,-4,-4,-4,-4,-4,5,5,5,5,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,-3,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,20,20,20,4,4,4,4,4,4,4,
4,0,0,0,0,0,-7,-7,2,2,2,2,2,-2,-2,-2,-2,-2,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,-1,
-1],
[TENSOR,[11,2]],[189,189,189,189,189,-3,-3,-3,-3,-3,-3,-3,27,27,27,27,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,5,5,5,5,1,1,1,1,1,-1,-1,-1,-1,-1,-1,3,3,3,3,0,0,0,0,0,0,0
,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,-1,-1,-1,9,9,9,9,9,9,9,9,1,1,1,-3,-3,-3,
-3,-3,9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,-1,1,0,0,0,0,0,0],
[TENSOR,[13,2]],[210,210,210,210,210,2,2,2,2,2,2,2,21,21,21,21,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,5,5,5,5,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,30,30,30,-10,-10,-10,-10,-10,
2,2,2,-2,-2,-2,-2,-2,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,-1
,1,1,1,1,0,0],
[TENSOR,[15,2]],[560,560,560,560,560,-16,-16,-16,-16,-16,-16,-16,20,20,20,20,
20,20,20,20,20,20,20,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,
-4,-4,-4,-4,-4,2,2,2,2,2,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,2,2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[280,280,280,280,280,-8,-8,-8,-8,-8,-8,-8,10,10,10,10,1,1,1,1,1,1,1,10,10
,10,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1,1,1,-2,-2,-2,-2,-2
,0,0,0,0,0,0,1,1,1,1,1,1,1,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,0,0,0,40,40,40,-8,-8,
-8,-8,-8,0,0,0,0,0,0,0,0,2*E(3)-10*E(3)^2,-10*E(3)+2*E(3)^2,1,1,1,-2,-2,1,1,1,
1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,E(3)^2,E(3)],
[TENSOR,[18,2]],
[GALOIS,[18,2]],
[TENSOR,[20,2]],[315,315,315,315,315,11,11,11,11,11,11,11,-9,-9,-9,-9,18,18,
18,18,18,18,18,-9,-9,-9,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,-1,-1,
-1,-1,2,2,2,2,2,-1,-1,-1,-1,-1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,-1,-1,-1,15,15,15
,-9,-9,-9,-9,-9,-5,-5,-5,-1,-1,-1,-1,-1,-3,-3,0,0,0,3,3,0,0,0,0,0,0,0,0,0,1,1,
1,0,0,0,0,1,-1,-1,-1,-1,0,0],
[TENSOR,[22,2]],[315,315,315,315,315,11,11,11,11,11,11,11,-9,-9,-9,-9,-9,-9,
-9,-9,-9,-9,-9,18,18,18,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,-1,-1,
-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,-1,-1,-1,75,75,75
,3,3,3,3,3,-1,-1,-1,3,3,3,3,3,3,3,-3,-3,-3,0,0,-3,-3,-3,-3,-3,0,0,0,0,1,1,1,0,
0,0,0,-1,0,0,0,0,0,0],
[TENSOR,[24,2]],[420,420,420,420,420,4,4,4,4,4,4,4,-39,-39,-39,-39,6,6,6,6,6,
6,6,6,6,6,-3,-3,-3,-3,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-2,-2,-2,-2,-2,-2,
-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,60,60,60,-4,-4,-4,-4,-4,4,4,4,
0,0,0,0,0,-3,-3,-6,-6,-6,0,0,2,2,2,2,2,-1,-1,-1,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0
],
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0,0,0,0,0,0,0,0,0],[161280,0,0,0,-1260,128,0,0,0,0,0,-4,-18,-72,0,0,0,0,0,0,0,
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ALF("2^12.3_1.U4(3).2_2'","3_1.U4(3).2_2'",[1,1,1,1,2,3,3,3,3,3,3,4,5,6,6,6,
7,7,7,7,7,8,8,9,9,9,10,10,10,10,11,11,11,12,13,13,13,13,14,15,15,15,15,15,
16,17,18,18,18,19,19,19,20,20,21,21,21,22,22,23,24,25,26,26,27,28,28,29,
30,30,30,30,31,32,33,34,34,35,35,35,36,36,36,36,36,37,37,37,38,38,38,38,
38,39,40,41,41,41,42,42,43,43,43,43,43,44,44,44,44,45,45,45,46,46,46,46,
47,48,48,48,48,49,50]);

MOT("2^(1+12).3_1.U4(3).2_2'",
[
"9th maximal subgroup of F3+,\n",
"constructed in September 2000 by Thomas Breuer, using a permutation\n",
"representation and the table of F3+, sorted according to the chain\n",
"2 < 2^(1+12) < 2^(1+12).3 < 2^(1+12).3.U4(3) < 2^(1+12).3.U4(3).2,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[160526499840,160526499840,212336640,47185920,39813120,19595520,19595520,
3538944,3538944,196608,294912,49152,18432,16384,6912,6912,69984,69984,2239488,
2239488,41472,31104,2985984,2985984,27648,18432,124416,13824,23328,23328,3888,
62208,62208,3456,5184,5184,5184,288,864,864,18432,18432,1024,1536,576,576,1536
,512,256,256,48,960,960,160,160,160,80,30,30,864,864,6912,6912,1152,288,6912,
6912,576,384,864,864,144,6912,6912,384,576,864,864,144,42,42,42,42,42,42,192,
64,48,48,648,648,108,162,162,2592,2592,144,432,432,108,108,108,108,144,144,288
,288,48,6635520,6635520,122880,92160,73728,73728,6144,4096,2304,3072,1024,256,
3072,3072,1536,768,256,256,2592,2592,2592,2592,6912,6912,576,384,864,864,144,
1152,2304,2304,192,288,288,72,144,144,72,72,64,64,32,80,80,40,40,40,48,48,96,
96,48,48,48,36,36,36,36],
[,[1,1,1,1,2,6,6,1,1,1,2,4,3,4,6,6,17,17,19,19,19,20,23,23,23,23,24,24,29,29,
30,32,32,32,33,36,36,36,37,37,9,9,10,11,16,16,8,10,14,12,15,52,52,52,52,52,53,
58,58,17,17,19,19,20,21,23,23,25,26,29,29,30,32,32,32,33,32,32,34,80,80,84,84,
82,82,42,43,46,46,90,90,91,93,93,95,95,95,96,96,102,102,100,100,61,61,62,62,64
,1,1,4,3,1,4,3,4,5,9,10,14,10,10,8,11,14,12,17,17,17,17,23,23,25,26,32,32,34,
23,26,26,25,27,28,36,38,38,39,40,43,41,44,52,52,54,55,56,61,61,75,75,73,76,76,
102,102,100,100],[1,2,3,4,5,1,2,8,9,10,11,12,13,14,8,9,1,2,1,2,3,5,1,2,3,4,5,5
,1,2,5,1,2,3,5,1,2,4,5,5,41,42,43,44,41,42,47,48,49,50,47,52,53,55,54,56,57,52
,53,8,9,9,8,11,13,8,9,13,12,9,8,11,8,9,10,11,8,9,13,80,81,80,81,80,81,86,87,86
,86,19,20,22,19,20,19,20,21,22,22,17,18,17,18,41,42,41,42,44,109,110,111,112,
113,114,115,116,117,118,119,120,121,122,123,124,125,126,110,109,110,109,109,
110,112,111,110,109,112,113,114,114,115,117,117,113,114,114,117,117,149,150,
151,152,153,155,154,156,118,118,122,121,123,124,124,127,128,129,130],,[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,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,1,2,4,4,3,5,6,7,60
,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
,87,89,88,90,91,92,93,94,95,96,97,98,99,102,103,100,101,104,105,106,107,108,
109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,129,
130,127,128,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,
147,148,149,150,151,110,109,111,111,112,158,157,159,160,161,163,162,166,167,
164,165],,[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,
52,53,55,54,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
78,79,1,2,6,7,6,7,86,87,89,88,90,91,92,93,94,95,96,97,98,99,100,101,102,103,
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,
142,143,144,145,146,147,148,149,150,151,152,153,155,154,156,157,158,159,160,
161,163,162,164,165,166,167]],
0,
[( 39, 40)( 98, 99)(147,148),( 54, 55)(154,155),(82,84)(83,85),(88,89),
(145,146),(162,163),
(109,110)(121,122)(127,128)(129,130)(131,132)(135,136)(139,140)(152,153)
(157,158)(159,160)(164,165)(166,167)
,(100,102)(101,103)(127,129)(128,130)(157,158)(164,166)(165,167)],
["ConstructProj",[["2^12.3_1.U4(3).2_2'",[]],["2^(1+12).3_1.U4(3).2_2'",
[]]]]);
ALF("2^(1+12).3_1.U4(3).2_2'","2^12.3_1.U4(3).2_2'",[1,1,2,3,4,5,5,6,6,7,8,
9,10,11,12,12,13,13,14,14,15,16,17,17,18,19,20,21,22,22,23,24,24,25,26,
27,27,28,29,30,31,31,32,33,34,34,35,36,37,38,39,40,40,41,42,43,44,45,45,
46,46,47,47,48,49,50,50,51,52,53,53,54,55,55,56,57,58,58,59,60,60,61,61,
62,62,63,64,65,65,66,66,67,68,68,69,69,70,71,72,73,73,74,74,75,75,76,76,
77,78,78,79,80,81,82,83,84,85,86,87,88,89,89,90,91,92,93,94,94,95,95,96,
96,97,98,99,99,100,101,102,102,103,104,105,106,107,107,108,109,110,111,
112,113,113,114,115,116,117,117,118,118,119,120,121,122,122,123,123]);
ALF("2^(1+12).3_1.U4(3).2_2'","F3+",[1,3,2,3,9,6,14,2,3,3,11,9,10,11,18,21,
7,20,5,17,15,39,4,16,13,16,38,40,7,22,43,6,21,18,42,8,23,23,46,47,9,11,11,
27,42,48,10,11,28,26,49,12,36,36,36,35,68,56,91,19,22,17,15,45,44,13,16,
41,40,20,19,50,18,14,21,48,18,21,49,25,53,71,104,72,105,28,28,81,82,29,61,
97,33,63,31,59,60,95,96,34,65,34,66,43,50,39,45,80,2,3,9,10,3,9,10,11,26,
11,11,28,9,11,10,28,27,26,20,19,20,19,13,16,41,40,21,18,49,16,40,38,41,76,
77,23,46,47,78,79,28,26,57,36,35,68,68,67,50,50,48,42,49,81,82,66,64,65,
64],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(1+12).3_1.U4(3).2_2'","3_1.U4(3).2_2'",[1,1,1,1,1,2,2,3,3,3,3,3,3,
3,4,4,5,5,6,6,6,6,7,7,7,7,7,7,8,8,8,9,9,9,9,10,10,10,10,10,11,11,11,11,12,
12,13,13,13,13,14,15,15,15,15,15,15,16,16,17,17,18,18,18,18,19,19,19,19,
20,20,20,21,21,21,21,22,22,22,23,23,24,24,25,25,26,26,27,27,28,28,28,29,
29,30,30,30,30,30,31,31,32,32,33,33,34,34,34,35,35,35,35,36,36,36,36,36,
37,37,37,38,38,38,38,38,38,39,39,40,40,41,41,41,41,42,42,42,43,43,43,43,
43,43,44,44,44,44,44,45,45,45,46,46,46,46,46,47,47,48,48,48,48,48,49,49,
50,50]);
ALN("2^(1+12).3_1.U4(3).2_2'",["F3+C2B","F3+N2B"]);

MOT("2^12.3^2.U4(3).2_2'",
[
"factor group of the 3B normalizer in 3.F3+,\n",
"constructed in January 2004 by Thomas Breuer, using a permutation\n",
"representation on 1512 points, sorted according to the chain\n",
"3 < 3x2^12 < (3x2^12).3.U4(3) < (3x2^12).3.U4(3).2,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[240789749760,240789749760,240789749760,637009920,637009920,637009920,
141557760,141557760,141557760,119439360,119439360,119439360,29393280,29393280,
29393280,5308416,5308416,5308416,589824,589824,589824,884736,884736,884736,
147456,147456,147456,55296,55296,55296,49152,49152,49152,10368,10368,10368,
104976,104976,104976,3359232,3359232,3359232,124416,124416,124416,93312,93312,
93312,1492992,82944,82944,82944,18432,124416,13824,11664,3888,93312,93312,
93312,10368,10368,10368,15552,15552,15552,2592,288,864,864,27648,27648,27648,
3072,3072,3072,4608,4608,4608,864,864,864,4608,4608,4608,1536,1536,1536,768,
768,768,768,768,768,144,144,144,1440,1440,1440,480,480,480,480,480,480,480,480
,480,240,240,240,45,45,45,1296,1296,1296,10368,10368,10368,3456,3456,3456,864,
864,864,10368,10368,10368,1728,1728,1728,1152,1152,1152,1296,1296,1296,432,432
,432,10368,10368,10368,1152,1152,1152,1728,1728,1728,1296,1296,1296,432,432,
432,63,63,63,63,63,63,63,63,63,576,576,576,192,192,192,72,72,72,324,108,81,
1296,432,432,432,432,432,162,162,162,162,162,162,216,216,216,432,432,432,144,
144,144,9953280,9953280,9953280,368640,368640,368640,276480,276480,276480,
221184,221184,221184,221184,221184,221184,18432,18432,18432,12288,12288,12288,
6912,6912,6912,9216,9216,9216,3072,3072,3072,768,768,768,4608,4608,4608,4608,
4608,4608,2304,2304,2304,768,768,768,768,768,768,3888,3888,3888,3888,3888,3888
,10368,10368,10368,1728,1728,1728,1152,1152,1152,1296,1296,1296,432,432,432,
1152,1152,576,576,576,288,288,72,72,72,72,192,192,192,192,192,192,96,96,96,120
,120,120,120,120,120,120,120,120,120,120,120,72,72,72,144,144,144,144,144,144,
144,144,144,144,144,144,54,54,54,54,54,54],
[,[1,3,2,1,3,2,1,3,2,1,3,2,13,15,14,1,3,2,1,3,2,1,3,2,7,9,8,4,6,5,7,9,8,13,15,
14,37,39,38,40,42,41,40,42,41,40,42,41,49,49,49,49,49,49,49,56,56,58,60,59,58,
60,59,58,60,59,67,67,67,67,16,18,17,19,21,20,22,24,23,34,36,35,16,18,17,19,21,
20,31,33,32,25,27,26,34,36,35,98,100,99,98,100,99,98,100,99,98,100,99,98,100,
99,113,115,114,37,39,38,40,42,41,40,42,41,43,45,44,49,49,49,50,52,51,53,53,53,
56,56,56,56,56,56,58,60,59,58,60,59,58,60,59,58,60,59,61,63,62,158,160,159,164
,166,165,161,163,162,71,73,72,74,76,75,80,82,81,176,176,178,179,179,179,179,
179,179,188,190,189,185,187,186,116,118,117,119,121,120,122,124,123,1,3,2,7,9,
8,4,6,5,1,3,2,7,9,8,4,6,5,7,9,8,10,12,11,16,18,17,19,21,20,31,33,32,19,21,20,
16,18,17,22,24,23,31,33,32,25,27,26,39,38,37,37,39,38,49,49,49,50,52,51,53,53,
53,58,60,59,61,63,62,49,53,50,52,51,54,55,67,68,69,70,74,76,75,71,73,72,77,79,
78,98,100,99,101,103,102,104,106,105,107,109,108,116,118,117,146,148,147,143,
145,144,149,151,150,149,151,150,188,190,189,185,187,186],[1,1,1,4,4,4,7,7,7,10
,10,10,1,1,1,16,16,16,19,19,19,22,22,22,25,25,25,28,28,28,31,31,31,16,16,16,1,
1,1,1,1,1,4,4,4,10,10,10,1,4,4,4,7,10,10,1,10,1,1,1,4,4,4,10,10,10,1,7,10,10,
71,71,71,74,74,74,77,77,77,71,71,71,83,83,83,86,86,86,89,89,89,92,92,92,83,83,
83,98,98,98,104,104,104,101,101,101,107,107,107,110,110,110,98,98,98,16,16,16,
16,16,16,22,22,22,28,28,28,16,16,16,28,28,28,25,25,25,16,16,16,22,22,22,16,16,
16,19,19,19,22,22,22,16,16,16,28,28,28,158,158,158,158,158,158,158,158,158,167
,167,167,170,170,170,167,167,167,40,46,40,40,43,43,43,46,46,38,38,38,39,39,39,
71,71,71,71,71,71,77,77,77,200,200,200,203,203,203,206,206,206,209,209,209,212
,212,212,215,215,215,218,218,218,221,221,221,224,224,224,227,227,227,230,230,
230,233,233,233,236,236,236,239,239,239,242,242,242,245,245,245,200,200,200,
200,200,200,200,200,200,206,206,206,203,203,203,200,200,200,206,206,206,209,
212,215,215,215,221,221,209,212,221,221,280,280,280,283,283,283,286,286,286,
289,289,289,295,295,295,292,292,292,298,298,298,224,224,224,233,233,233,236,
236,236,239,239,239,239,239,239,248,248,248,253,253,253],,[1,3,2,4,6,5,7,9,8,
10,12,11,13,15,14,16,18,17,19,21,20,22,24,23,25,27,26,28,30,29,31,33,32,34,36,
35,37,39,38,40,42,41,43,45,44,46,48,47,49,50,52,51,53,54,55,56,57,58,60,59,61,
63,62,64,66,65,67,68,69,70,71,73,72,74,76,75,77,79,78,80,82,81,83,85,84,86,88,
87,89,91,90,92,94,93,95,97,96,1,3,2,7,9,8,7,9,8,4,6,5,10,12,11,13,15,14,116,
118,117,119,121,120,122,124,123,125,127,126,128,130,129,131,133,132,134,136,
135,137,139,138,140,142,141,143,145,144,146,148,147,149,151,150,152,154,153,
155,157,156,158,160,159,161,163,162,164,166,165,167,169,168,170,172,171,173,
175,174,176,177,178,179,180,182,181,183,184,188,190,189,185,187,186,191,193,
192,194,196,195,197,199,198,200,202,201,203,205,204,206,208,207,209,211,210,
212,214,213,215,217,216,218,220,219,221,223,222,224,226,225,227,229,228,230,
232,231,233,235,234,236,238,237,239,241,240,242,244,243,245,247,246,253,252,
251,250,249,248,254,256,255,257,259,258,260,262,261,263,265,264,266,268,267,
269,270,271,273,272,274,275,276,277,278,279,280,282,281,283,285,284,286,288,
287,200,202,201,203,205,204,203,205,204,206,208,207,301,303,302,304,306,305,
307,309,308,313,315,314,310,312,311,319,321,320,316,318,317],,[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,
87,88,89,90,91,92,93,94,95,96,97,98,99,100,104,105,106,101,102,103,107,108,109
,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,
148,149,150,151,152,153,154,155,156,157,1,2,3,13,14,15,13,14,15,167,168,169,
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,
284,285,286,287,288,289,290,291,295,296,297,292,293,294,298,299,300,301,302,
303,304,305,306,307,308,309,313,314,315,310,311,312,316,317,318,319,320,321]],
0,
[(310,313)(311,314)(312,315),(101,104)(102,105)(103,106)(292,295)(293,296)
(294,297),(69,70)(183,184)(278,279),(161,164)(162,165)(163,166),(2,3)(5,6)(8,
9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,
42)(44,45)(47,48)(51,52)(59,60)(62,63)(65,66)(72,73)(75,76)(78,79)(81,82)(84,
85)(87,88)(90,91)(93,94)(96,97)(99,100)(102,103)(105,106)(108,109)(111,112)
(114,115)(117,118)(120,121)(123,124)(126,127)(129,130)(132,133)(135,136)(138,
139)(141,142)(144,145)(147,148)(150,151)(153,154)(156,157)(159,160)(162,163)
(165,166)(168,169)(171,172)(174,175)(181,182)(185,188)(186,190)(187,189)(192,
193)(195,196)(198,199)(201,202)(204,205)(207,208)(210,211)(213,214)(216,217)
(219,220)(222,223)(225,226)(228,229)(231,232)(234,235)(237,238)(240,241)(243,
244)(246,247)(248,253)(249,252)(250,251)(255,256)(258,259)(261,262)(264,265)
(267,268)(272,273)(281,282)(284,285)(287,288)(290,291)(293,294)(296,297)(299,
300)(302,303)(305,306)(308,309)(311,312)(314,315)(316,319)(317,321)(318,320)],
["ConstructProj",[["2^12.3_1.U4(3).2_2'",[]],,["2^12.3^2.U4(3).2_2'",[2,2,2,8,
8,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,11,11,2,2,2,2,2,2,2,2,5,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]]]]);
ALF("2^12.3^2.U4(3).2_2'","2^12.3_1.U4(3).2_2'",[1,1,1,2,2,2,
3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,
13,13,14,14,14,15,15,15,16,16,16,17,18,18,18,19,20,21,22,23,24,24,24,25,
25,25,26,26,26,27,28,29,30,31,31,31,32,32,32,33,33,33,34,34,34,35,35,35,
36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,43,43,43,
44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,49,49,50,50,50,51,51,51,
52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57,57,58,58,58,59,59,59,
60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65,66,67,68,69,70,70,
70,71,72,73,73,73,74,74,74,75,75,75,76,76,76,77,77,77,78,78,78,79,79,79,
80,80,80,81,81,81,82,82,82,83,83,83,84,84,84,85,85,85,86,86,86,87,87,87,
88,88,88,89,89,89,90,90,90,91,91,91,92,92,92,93,93,93,94,94,94,95,95,95,
96,96,96,97,97,97,98,98,98,99,99,99,100,100,100,101,102,103,103,103,104,
105,106,107,108,109,110,110,110,111,111,111,112,112,112,113,113,113,114,
114,114,115,115,115,116,116,116,117,117,117,118,118,118,119,119,119,120,
120,120,121,121,121,122,122,122,123,123,123]);

MOT("3.2^(1+12).3U4(3).2",
[
"9th maximal subgroup of 3.F3+,\n",
"constructed in January 2004 by Thomas Breuer from the tables of the\n",
"factor groups modulo the central subgroups of orders 2 and 3,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[481579499520,481579499520,481579499520,481579499520,481579499520,481579499520
,637009920,637009920,637009920,141557760,141557760,141557760,119439360,
119439360,119439360,58786560,58786560,58786560,58786560,58786560,58786560,
10616832,10616832,10616832,10616832,10616832,10616832,589824,589824,589824,
884736,884736,884736,147456,147456,147456,55296,55296,55296,49152,49152,49152,
20736,20736,20736,20736,20736,20736,209952,209952,209952,209952,209952,209952,
6718464,6718464,6718464,6718464,6718464,6718464,124416,124416,124416,93312,
93312,93312,2985984,2985984,82944,82944,82944,18432,124416,13824,23328,23328,
3888,186624,186624,186624,186624,186624,186624,10368,10368,10368,15552,15552,
15552,5184,5184,288,864,864,55296,55296,55296,55296,55296,55296,3072,3072,3072
,4608,4608,4608,1728,1728,1728,1728,1728,1728,4608,4608,4608,1536,1536,1536,
768,768,768,768,768,768,144,144,144,2880,2880,2880,2880,2880,2880,480,480,480,
480,480,480,480,480,480,240,240,240,90,90,90,90,90,90,2592,2592,2592,2592,2592
,2592,20736,20736,20736,20736,20736,20736,3456,3456,3456,864,864,864,20736,
20736,20736,20736,20736,20736,1728,1728,1728,1152,1152,1152,2592,2592,2592,
2592,2592,2592,432,432,432,20736,20736,20736,20736,20736,20736,1152,1152,1152,
1728,1728,1728,2592,2592,2592,2592,2592,2592,432,432,432,126,126,126,126,126,
126,126,126,126,126,126,126,126,126,126,126,126,126,576,576,576,192,192,192,
144,144,144,144,144,144,648,648,108,162,162,2592,2592,432,432,432,432,432,324,
324,324,324,324,324,324,324,324,324,324,324,432,432,432,432,432,432,864,864,
864,864,864,864,144,144,144,19906560,19906560,19906560,19906560,19906560,
19906560,368640,368640,368640,276480,276480,276480,221184,221184,221184,221184
,221184,221184,18432,18432,18432,12288,12288,12288,6912,6912,6912,9216,9216,
9216,3072,3072,3072,768,768,768,9216,9216,9216,9216,9216,9216,4608,4608,4608,
2304,2304,2304,768,768,768,768,768,768,7776,7776,7776,7776,7776,7776,7776,7776
,7776,7776,7776,7776,20736,20736,20736,20736,20736,20736,1728,1728,1728,1152,
1152,1152,2592,2592,2592,2592,2592,2592,432,432,432,1152,2304,2304,576,576,576
,288,288,72,144,144,72,72,192,192,192,192,192,192,96,96,96,240,240,240,240,240
,240,120,120,120,120,120,120,120,120,120,144,144,144,144,144,144,288,288,288,
288,288,288,144,144,144,144,144,144,144,144,144,108,108,108,108,108,108,108,
108,108,108,108,108],
[,[1,3,5,1,3,5,1,3,5,1,3,5,4,6,2,16,18,20,16,18,20,1,3,5,1,3,5,1,3,5,4,6,2,10,
12,11,7,9,8,10,12,11,16,18,20,16,18,20,49,51,53,49,51,53,55,57,59,55,57,59,55,
57,59,58,60,56,67,67,67,67,67,67,68,68,75,75,76,78,80,82,78,80,82,78,80,82,81,
83,79,90,90,90,91,91,25,27,23,25,27,23,28,30,29,31,33,32,46,48,44,46,48,44,22,
24,26,28,30,29,40,42,41,34,36,35,43,45,47,128,130,132,128,130,132,128,130,132,
128,130,132,128,130,132,131,133,129,146,148,150,146,148,150,49,51,53,49,51,53,
55,57,59,55,57,59,58,60,56,61,63,62,67,67,67,67,67,67,69,71,70,72,72,72,75,75,
75,75,75,75,76,76,76,78,80,82,78,80,82,78,80,82,81,83,79,78,80,82,78,80,82,84,
86,85,212,214,216,212,214,216,224,226,228,224,226,228,218,220,222,218,220,222,
98,100,96,101,103,102,110,112,108,110,112,108,242,242,243,245,245,247,247,247,
247,247,248,248,260,262,264,260,262,264,254,256,258,254,256,258,155,157,153,
155,157,153,158,160,162,158,160,162,164,166,165,1,3,5,1,3,5,10,12,11,7,9,8,1,3
,5,10,12,11,7,9,8,10,12,11,13,15,14,25,27,23,28,30,29,40,42,41,28,30,29,28,30,
29,22,24,26,31,33,32,40,42,41,34,36,35,51,53,49,51,53,49,49,51,53,49,51,53,67,
67,67,67,67,67,69,71,70,72,72,72,78,80,82,78,80,82,84,86,85,67,72,72,69,71,70,
73,74,90,92,92,93,94,101,103,102,95,97,99,104,106,105,128,130,132,128,130,132,
134,136,135,137,139,138,140,142,141,155,157,153,155,157,153,197,199,198,197,
199,198,191,193,195,200,202,201,200,202,201,260,262,264,260,262,264,254,256,
258,254,256,258],[1,4,1,4,1,4,7,7,7,10,10,10,13,13,13,1,4,1,4,1,4,22,25,22,25,
22,25,28,28,28,31,31,31,34,34,34,37,37,37,40,40,40,22,25,22,25,22,25,1,4,1,4,1
,4,1,4,1,4,1,4,7,7,7,13,13,13,1,4,7,7,7,10,13,13,1,4,13,1,4,1,4,1,4,7,7,7,13,
13,13,1,4,10,13,13,95,98,95,98,95,98,101,101,101,104,104,104,95,98,95,98,95,98
,113,113,113,116,116,116,119,119,119,122,122,122,113,113,113,128,131,128,131,
128,131,137,137,137,134,134,134,140,140,140,143,143,143,128,131,128,131,128,
131,22,25,22,25,22,25,25,22,25,22,25,22,31,31,31,37,37,37,22,25,22,25,22,25,37
,37,37,34,34,34,25,22,25,22,25,22,31,31,31,22,25,22,25,22,25,28,28,28,31,31,31
,22,25,22,25,22,25,37,37,37,212,215,212,215,212,215,212,215,212,215,212,215,
212,215,212,215,212,215,230,230,230,233,233,233,230,230,230,230,230,230,55,58,
64,55,58,55,58,61,61,61,64,64,53,50,53,50,53,50,51,54,51,54,51,54,95,98,95,98,
95,98,95,98,95,98,95,98,104,104,104,281,284,281,284,281,284,287,287,287,290,
290,290,293,293,293,296,296,296,299,299,299,302,302,302,305,305,305,308,308,
308,311,311,311,314,314,314,317,320,317,320,317,320,323,323,323,326,326,326,
329,329,329,332,332,332,284,281,284,281,284,281,284,281,284,281,284,281,281,
284,281,284,281,284,290,290,290,287,287,287,284,281,284,281,284,281,290,290,
290,293,296,296,299,299,299,305,305,293,296,296,305,305,381,381,381,384,384,
384,387,387,387,390,393,390,393,390,393,399,399,399,396,396,396,402,402,402,
308,308,308,308,308,308,320,317,320,317,320,317,323,323,323,326,326,326,326,
326,326,335,338,335,338,335,338,343,346,343,346,343,346],,[1,6,5,4,3,2,7,9,8,
10,12,11,13,15,14,16,21,20,19,18,17,22,27,26,25,24,23,28,30,29,31,33,32,34,36,
35,37,39,38,40,42,41,43,48,47,46,45,44,49,54,53,52,51,50,55,60,59,58,57,56,61,
63,62,64,66,65,67,68,69,71,70,72,73,74,75,76,77,78,83,82,81,80,79,84,86,85,87,
89,88,90,91,92,93,94,95,100,99,98,97,96,101,103,102,104,106,105,107,112,111,
110,109,108,113,115,114,116,118,117,119,121,120,122,124,123,125,127,126,1,6,5,
4,3,2,10,12,11,10,12,11,7,9,8,13,15,14,16,21,20,19,18,17,152,157,156,155,154,
153,158,163,162,161,160,159,164,166,165,167,169,168,170,175,174,173,172,171,
176,178,177,179,181,180,182,187,186,185,184,183,188,190,189,191,196,195,194,
193,192,197,199,198,200,202,201,203,208,207,206,205,204,209,211,210,212,217,
216,215,214,213,218,223,222,221,220,219,224,229,228,227,226,225,230,232,231,
233,235,234,239,238,237,236,241,240,242,243,244,245,246,247,248,249,251,250,
252,253,260,265,264,263,262,261,254,259,258,257,256,255,266,271,270,269,268,
267,272,277,276,275,274,273,278,280,279,281,286,285,284,283,282,287,289,288,
290,292,291,293,295,294,296,298,297,299,301,300,302,304,303,305,307,306,308,
310,309,311,313,312,314,316,315,317,322,321,320,319,318,323,325,324,326,328,
327,329,331,330,332,334,333,343,342,341,346,345,344,337,336,335,340,339,338,
347,352,351,350,349,348,353,355,354,356,358,357,359,364,363,362,361,360,365,
367,366,368,369,370,371,373,372,374,375,376,377,378,379,380,381,383,382,384,
386,385,387,389,388,284,283,282,281,286,285,287,289,288,287,289,288,290,292,
291,408,407,406,405,410,409,411,416,415,414,413,412,417,419,418,423,425,424,
420,422,421,432,437,436,435,434,433,426,431,430,429,428,427],,[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,
129,130,131,132,133,137,138,139,134,135,136,140,141,142,143,144,145,146,147,
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,
205,206,207,208,209,210,211,1,2,3,4,5,6,16,17,18,19,20,21,16,17,18,19,20,21,
230,231,232,233,234,235,239,240,241,236,237,238,242,243,244,245,246,247,248,
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,
382,383,384,385,386,387,388,389,390,391,392,393,394,395,399,400,401,396,397,
398,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,
423,424,425,420,421,422,426,427,428,429,430,431,432,433,434,435,436,437]],
0,
[(420,423)(421,424)(422,425),(377,378),(281,284)(282,285)(283,286)(317,320)
(318,321)(319,322)(335,338)(336,339)(337,340)(341,344)(342,345)(343,346)(347,
350)(348,351)(349,352)(359,362)(360,363)(361,364)(369,370)(390,393)(391,394)
(392,395)(405,408)(406,409)(407,410)(411,414)(412,415)(413,416)(426,429)(427,
430)(428,431)(432,435)(433,436)(434,437),(236,239)(237,240)(238,241),(134,137)
(135,138)(136,139)(396,399)(397,400)(398,401),(93,94)(252,253)(379,380),(218,
224)(219,225)(220,226)(221,227)(222,228)(223,229),(2,6)(3,5)(8,9)(11,12)(14,
15)(17,21)(18,20)(23,27)(24,26)(29,30)(32,33)(35,36)(38,39)(41,42)(44,48)(45,
47)(50,54)(51,53)(56,60)(57,59)(62,63)(65,66)(70,71)(79,83)(80,82)(85,86)(88,
89)(96,100)(97,99)(102,103)(105,106)(108,112)(109,111)(114,115)(117,118)(120,
121)(123,124)(126,127)(129,133)(130,132)(135,136)(138,139)(141,142)(144,145)
(147,151)(148,150)(153,157)(154,156)(159,163)(160,162)(165,166)(168,169)(171,
175)(172,174)(177,178)(180,181)(183,187)(184,186)(189,190)(192,196)(193,195)
(198,199)(201,202)(204,208)(205,207)(210,211)(213,217)(214,216)(219,223)(220,
222)(225,229)(226,228)(231,232)(234,235)(237,241)(238,240)(250,251)(254,260)
(255,265)(256,264)(257,263)(258,262)(259,261)(267,271)(268,270)(273,277)(274,
276)(279,280)(282,286)(283,285)(288,289)(291,292)(294,295)(297,298)(300,301)
(303,304)(306,307)(309,310)(312,313)(315,316)(318,322)(319,321)(324,325)(327,
328)(330,331)(333,334)(335,343)(336,342)(337,341)(338,346)(339,345)(340,344)
(348,352)(349,351)(354,355)(357,358)(360,364)(361,363)(366,367)(372,373)(382,
383)(385,386)(388,389)(391,395)(392,394)(397,398)(400,401)(403,404)(405,408)
(406,407)(409,410)(412,416)(413,415)(418,419)(421,422)(424,425)(426,432)(427,
437)(428,436)(429,435)(430,434)(431,433)],
["ConstructProj",[["2^12.3_1.U4(3).2_2'",[]],["2^(1+12).3_1.U4(3).2_2'",[]],
["2^12.3^2.U4(3).2_2'",[2,2,2,8,8,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,11,11,2,2,2,2,2,2,2,2,5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]],,,
["3.2^(1+12).3U4(3).2",[5,5,5,5,5,5,5,5,5,5,5,5,5,29,29,5,5,5,5,5,5,5,5,5,5
]]]]);
ALF("3.2^(1+12).3U4(3).2","2^(1+12).3_1.U4(3).2_2'",[1,2,1,2,1,2,3,3,3,4,
4,4,5,5,5,6,7,6,7,6,7,8,9,8,9,8,9,10,10,10,11,11,11,12,12,12,13,13,13,14,
14,14,15,16,15,16,15,16,17,18,17,18,17,18,19,20,19,20,19,20,21,21,21,22,
22,22,23,24,25,25,25,26,27,28,29,30,31,32,33,32,33,32,33,34,34,34,35,35,
35,36,37,38,39,40,41,42,41,42,41,42,43,43,43,44,44,44,45,46,45,46,45,46,
47,47,47,48,48,48,49,49,49,50,50,50,51,51,51,52,53,52,53,52,53,54,54,54,
55,55,55,56,56,56,57,57,57,58,59,58,59,58,59,60,61,60,61,60,61,62,63,62,
63,62,63,64,64,64,65,65,65,66,67,66,67,66,67,68,68,68,69,69,69,70,71,70,
71,70,71,72,72,72,73,74,73,74,73,74,75,75,75,76,76,76,77,78,77,78,77,78,
79,79,79,80,81,80,81,80,81,82,83,82,83,82,83,84,85,84,85,84,85,86,86,86,
87,87,87,88,89,88,89,88,89,90,91,92,93,94,95,96,97,97,97,98,99,100,101,
100,101,100,101,102,103,102,103,102,103,104,105,104,105,104,105,106,107,
106,107,106,107,108,108,108,109,110,109,110,109,110,111,111,111,112,112,
112,113,113,113,114,114,114,115,115,115,116,116,116,117,117,117,118,118,
118,119,119,119,120,120,120,121,122,121,122,121,122,123,123,123,124,124,
124,125,125,125,126,126,126,127,128,127,128,127,128,129,130,129,130,129,
130,131,132,131,132,131,132,133,133,133,134,134,134,135,136,135,136,135,
136,137,137,137,138,139,140,141,141,141,142,143,144,145,146,147,148,149,
149,149,150,150,150,151,151,151,152,153,152,153,152,153,154,154,154,155,
155,155,156,156,156,157,158,157,158,157,158,159,160,159,160,159,160,161,
161,161,162,162,162,163,163,163,164,165,164,165,164,165,166,167,166,167,
166,167]);
ALF("3.2^(1+12).3U4(3).2","2^12.3^2.U4(3).2_2'",[1,2,3,1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,13,14,15,16,17,18,16,17,18,19,20,21,22,23,24,25,26,27,
28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,40,41,42,40,41,42,
43,44,45,46,47,48,49,49,50,51,52,53,54,55,56,56,57,58,59,60,58,59,60,61,
62,63,64,65,66,67,67,68,69,70,71,72,73,71,72,73,74,75,76,77,78,79,80,81,
82,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,113,114,
115,116,117,118,116,117,118,119,120,121,119,120,121,122,123,124,125,126,
127,128,129,130,128,129,130,131,132,133,134,135,136,137,138,139,137,138,
139,140,141,142,143,144,145,143,144,145,146,147,148,149,150,151,152,153,
154,152,153,154,155,156,157,158,159,160,158,159,160,161,162,163,161,162,
163,164,165,166,164,165,166,167,168,169,170,171,172,173,174,175,173,174,
175,176,176,177,178,178,179,179,180,181,182,183,184,185,186,187,185,186,
187,188,189,190,188,189,190,191,192,193,191,192,193,194,195,196,194,195,
196,197,198,199,200,201,202,200,201,202,203,204,205,206,207,208,209,210,
211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,
229,230,231,232,233,234,235,233,234,235,236,237,238,239,240,241,242,243,
244,245,246,247,248,249,250,248,249,250,251,252,253,251,252,253,254,255,
256,254,255,256,257,258,259,260,261,262,263,264,265,263,264,265,266,267,
268,269,270,270,271,272,273,274,275,276,277,277,278,279,280,281,282,283,
284,285,286,287,288,289,290,291,289,290,291,292,293,294,295,296,297,298,
299,300,301,302,303,301,302,303,304,305,306,304,305,306,307,308,309,310,
311,312,313,314,315,316,317,318,316,317,318,319,320,321,319,320,321]);
ALF("3.2^(1+12).3U4(3).2","2^12.3_1.U4(3).2_2'",[1,1,1,1,1,1,2,2,2,3,3,3,
4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,
12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,16,16,16,17,17,
18,18,18,19,20,21,22,22,23,24,24,24,24,24,24,25,25,25,26,26,26,27,27,28,
29,30,31,31,31,31,31,31,32,32,32,33,33,33,34,34,34,34,34,34,35,35,35,36,
36,36,37,37,37,38,38,38,39,39,39,40,40,40,40,40,40,41,41,41,42,42,42,43,
43,43,44,44,44,45,45,45,45,45,45,46,46,46,46,46,46,47,47,47,47,47,47,48,
48,48,49,49,49,50,50,50,50,50,50,51,51,51,52,52,52,53,53,53,53,53,53,54,
54,54,55,55,55,55,55,55,56,56,56,57,57,57,58,58,58,58,58,58,59,59,59,60,
60,60,60,60,60,61,61,61,61,61,61,62,62,62,62,62,62,63,63,63,64,64,64,65,
65,65,65,65,65,66,66,67,68,68,69,69,70,70,70,71,72,73,73,73,73,73,73,74,
74,74,74,74,74,75,75,75,75,75,75,76,76,76,76,76,76,77,77,77,78,78,78,78,
78,78,79,79,79,80,80,80,81,81,81,82,82,82,83,83,83,84,84,84,85,85,85,86,
86,86,87,87,87,88,88,88,89,89,89,89,89,89,90,90,90,91,91,91,92,92,92,93,
93,93,94,94,94,94,94,94,95,95,95,95,95,95,96,96,96,96,96,96,97,97,97,98,
98,98,99,99,99,99,99,99,100,100,100,101,102,102,103,103,103,104,105,106,
107,107,108,109,110,110,110,111,111,111,112,112,112,113,113,113,113,113,
113,114,114,114,115,115,115,116,116,116,117,117,117,117,117,117,118,118,
118,118,118,118,119,119,119,120,120,120,121,121,121,122,122,122,122,122,
122,123,123,123,123,123,123]);
ALF("3.2^(1+12).3U4(3).2","3.F3+",[1,8,3,7,2,9,4,5,6,7,8,9,19,20,21,14,35,
16,34,15,36,4,8,6,7,5,9,7,8,9,25,26,27,19,20,21,22,23,24,25,26,27,44,54,
46,53,45,55,17,51,17,50,17,52,11,42,13,41,12,43,37,38,39,93,94,95,10,40,
31,32,33,40,92,96,17,56,103,14,54,16,53,15,55,44,45,46,100,101,102,18,57,
57,110,111,19,26,21,25,20,27,25,26,27,67,68,69,100,113,102,112,101,114,22,
23,24,25,26,27,70,71,72,64,65,66,115,116,117,28,87,30,86,29,88,86,87,88,
86,87,88,83,84,85,166,167,168,136,218,138,217,137,219,47,56,49,56,48,56,
41,38,43,37,42,39,107,108,109,104,105,106,31,40,33,40,32,40,97,98,99,96,
96,96,50,48,52,47,51,49,118,119,120,44,35,46,34,45,36,53,54,55,112,113,
114,44,54,46,53,45,55,115,116,117,61,128,63,127,62,129,171,243,173,242,
172,244,174,246,176,245,175,247,70,71,72,70,71,72,193,197,195,196,194,198,
73,149,231,79,153,77,145,146,147,148,229,230,80,158,82,157,81,159,80,161,
82,160,81,162,103,119,103,118,103,120,93,108,95,107,94,109,190,191,192,4,
8,6,7,5,9,19,20,21,22,23,24,7,8,9,19,20,21,22,23,24,25,26,27,64,65,66,25,
26,27,25,26,27,70,71,72,19,26,21,25,20,27,22,23,24,70,71,72,67,68,69,64,
65,66,52,48,51,47,50,49,52,49,51,48,50,47,31,40,33,40,32,40,97,98,99,96,
96,96,53,45,55,44,54,46,115,116,117,40,96,92,97,98,99,186,187,57,110,111,
188,189,70,71,72,64,65,66,139,140,141,86,84,88,83,87,85,166,167,168,166,
167,168,163,164,165,119,118,118,120,120,119,112,101,114,100,113,102,115,
116,117,193,194,195,196,197,198,160,155,162,154,161,156,157,155,159,154,
158,156],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("3.2^(1+12).3U4(3).2",["3.F3+N2B"]);

MOT("3^3.[3^10].GL3(3)",
[
"origin: computed by Thomas Breuer in December 2000,\n",
"using a combination of Dixon's Algorithm and other techniques"
],
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354294,11664,23328,118098,162,13122,38263752,76527504,972,972,972,236196,
236196,236196,972,972,972,69984,34992,1458,354294,162,13122,162,13122,162,
39366,324,324,324,1944,1944,1944,12754584,12754584,12754584,1944,3888,162,
13122,2916,2916,2916,972,972,972,708588,708588,708588,6561,6561,52488,108,648,
472392,648,3888,331619184,648,52488,39366,19683,19683,39366,162,177147,1062882
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3888,3888,3888,72,72,72,144,72,78,78,78,78,26,26,26,26,39,39,39,39,24,24,48,48
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ALF("3^3.[3^10].GL3(3)","F3+",[1,5,62,30,7,5,6,18,15,19,15,2,6,7,5,4,21,
17,22,7,6,7,5,17,3,7,63,33,7,4,21,20,22,7,7,6,21,22,20,3,17,22,7,59,31,63,
33,61,29,42,39,38,17,21,16,5,4,6,39,9,62,30,19,19,18,17,21,22,6,5,7,31,32,
31,97,61,29,38,16,4,59,31,29,32,32,29,61,7,7,4,7,32,33,61,63,6,7,6,7,59,
31,6,22,23,8,78,78,46,23,8,26,26,21,6,7,18,19,15,21,17,16,18,13,15,19,20,
17,14,21,43,42,39,17,21,22,45,50,48,11,45,51,51,51,51,83,83,83,83,99,100,
99,100,76,76,26,26,30,33,33,21,21,8,23,8,30,33,8,23,16,7,4,33,32,31,32,33,
31,23,84,32,85,65,66,34,34,59,61,63,31,33,29,32,33,31,33,32,63,33,20,14,
17,31,33,7,32,31,30,95,96,59,42,79,79,47,76,76,43,38,22,16,40,77,77,22,7,
23,22,16,33,60,62,19,31,7,30,21,17,16,16,22,22,16,86,21,22,20,7,6,7,33,29,
31,34,34,64],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^12.M24",
[
"8th maximal subgroup of Fi24,\n",
"sorted w.r.t. the normal series 2^11.2.M24,\n",
"computed by T. Breuer in July 2005 using Dixon's algorithm and\n",
"character theoretic methods"
],
[1002795171840,3633315840,566231040,41783132160,495452160,5505024,786432,
688128,688128,196608,196608,98304,98304,86016,491520,491520,40960,24576,16384,
69120,69120,11520,11520,4608,4608,3456,8064,1152,1008,6144,6144,2048,2048,1536
,1536,4096,4096,2048,2048,2048,1024,1024,1024,1024,512,768,768,256,256,960,960
,240,240,160,384,384,192,384,384,192,192,192,96,96,96,48,336,336,112,112,336,
336,112,112,128,128,128,128,64,64,80,80,40,44,44,44,44,48,48,48,48,24,24,56,56
,56,56,56,56,56,56,60,60,60,60,60,60,60,60,42,42,42,42,46,46,46,46],
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,10,11,7,7,6,7,6,10,10,11,11,10,15,16,19,19,50,50,50,50,50,20,20,20,25,25,24,
25,24,24,27,28,28,67,67,67,67,71,71,71,71,36,37,37,36,44,44,50,51,54,84,84,84,
84,56,55,58,59,64,65,67,67,69,69,71,71,73,73,102,102,102,102,106,106,106,106,
110,110,112,112,114,114,116,116],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18
,19,1,3,5,4,2,3,5,1,3,5,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,6,7,8,10,11,13,12,9,14,15,16,18,71,72,73,74,67,68,69,70,
75,76,77,78,79,80,81,82,83,84,85,86,87,31,30,34,35,46,47,98,99,100,101,94,95,
96,97,50,51,52,53,50,51,52,53,71,72,67,68,114,115,116,117],,[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
,36,37,38,39,40,41,42,43,44,45,46,47,48,49,1,3,5,4,2,55,56,57,58,59,60,61,62,
63,64,65,66,71,72,73,74,67,68,69,70,75,76,77,78,79,80,15,16,17,84,85,86,87,88,
89,90,91,92,93,98,99,100,101,94,95,96,97,20,21,22,23,20,21,22,23,112,113,110,
111,116,117,114,115],,[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,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,1,5,2,4,1,5,2,4,75,76
,77,78,79,80,81,82,83,84,85,87,86,88,89,90,91,92,93,8,6,9,14,8,6,9,14,106,107,
108,109,102,103,104,105,27,29,27,29,116,117,114,115],,,,[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,
63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,1,2,4,4,88,89,
90,91,92,93,94,95,96,97,98,99,100,101,106,107,108,109,102,103,104,105,110,111,
112,113,116,117,114,115],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
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,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
,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,1,4,1,4]]
,
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[GALOIS,[5,7]],[252,252,252,252,252,28,28,28,28,28,28,28,28,28,12,12,12,12,12
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E(23)+E(23)^2+E(23)^3+E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13
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,
E(23)+E(23)^2+E(23)^3+E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13
 +E(23)^16+E(23)^18
,
E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20
 +E(23)^21+E(23)^22
,
E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20
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],
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0,0,0],[141680,-6160,880,0,0,784,-112,0,0,-112,112,0,0,0,160,-160,0,0,0,20,-20
,0,0,-4,4,0,14,-2,0,0,0,0,0,0,0,-8,-8,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0
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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],[141680,-6160,880,0,0,-112,16,0
,0,16,-16,0,0,0,160,-160,0,0,0,20,-20,0,0,-4,4,0,14,-2,0,0,0,0,0,0,0,8,8,-16,
16,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,4,0,4,-4,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,4
,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[105,27]],[159390,11550,-1890,53130,-630,462,78,154,154,14,-82,-6,-38
,14,-90,-90,-30,18,6,-45,-45,-15,-15,3,3,9,0,0,0,-10,-14,2,6,2,-2,-6,-6,-2,-2,
-6,-2,-2,6,2,2,-6,6,-2,2,0,0,0,0,0,3,3,1,-1,-1,1,-3,1,-1,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0],
[TENSOR,[107,27]],[170016,-7392,1056,0,0,224,-32,0,0,-32,32,0,0,0,-192,192,0,
0,0,60,-60,0,0,-12,12,0,0,0,0,0,0,0,0,0,0,-16,-16,0,0,16,0,0,0,0,0,0,0,0,0,6,6
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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],[239085,17325,
-2835,79695,-945,-147,-339,-273,63,45,-3,63,-33,21,45,45,15,-9,-3,0,0,0,0,0,0,
0,0,0,0,-3,-9,-1,5,3,-3,-3,13,7,7,5,3,-5,-5,-7,1,3,-3,1,-1,0,0,0,0,0,0,0,0,0,0
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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],
[TENSOR,[110,27]],[239085,17325,-2835,79695,-945,-483,93,63,-273,-99,45,15,15
,21,-75,-75,-25,15,5,0,0,0,0,0,0,0,0,0,0,21,15,-9,-3,3,-3,9,-7,-5,-5,1,-1,7,-1
,5,-3,3,-3,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,-1
,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[112,27]],[255024,-11088,1584,0,0,336,-48,0,0,-48,48,0,0,0,32,-32,0,0
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,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,2,-2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[309120,-13440,1920,0,0,
-896,128,0,0,128,-128,0,0,0,0,0,0,0,0,60,-60,0,0,-12,12,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,-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,-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],[370944,-16128,2304,0,0,0,0,0,0,0,0,0,0,0,-128,128,0,0,0,0,0,0,0,0,0
,0,-42,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,-6,0,0,2,0,0,0,0,0,0,0,0
,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[453376,-19712,2816,0,0,0,0,0,0,0,0,0,0,0
,128,-128,0,0,0,-80,80,0,0,16,-16,0,-14,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,6,6,0,0,-2,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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]],
[(114,116)(115,117),(102,106)(103,107)(104,108)(105,109),(86,87),
( 67, 71)( 68, 72)( 69, 73)( 70, 74)( 94, 98)( 95, 99)( 96,100)( 97,101)
(110,112)(111,113)
]);
ALF("2^12.M24","F3+.2",[1,2,3,98,99,2,3,99,100,9,11,102,101,10,3,9,101,
103,11,6,14,111,107,18,21,112,8,23,114,10,102,103,11,116,28,9,11,101,102,
10,116,115,117,27,26,103,26,28,117,12,36,119,118,35,18,21,112,42,47,130,
131,124,48,23,46,134,24,136,51,135,24,136,51,135,116,117,27,26,137,56,36,
66,149,37,70,151,151,131,48,154,77,134,75,136,51,158,81,136,51,158,81,55,
84,164,163,55,84,164,163,68,173,68,173,71,174,72,175],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^12.M24","M24",[1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,
5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,9,9,9,9,9,10,10,10,10,10,10,
10,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,14,15,15,15,16,
16,16,16,17,17,17,17,18,18,19,19,19,19,20,20,20,20,21,21,21,21,22,22,22,
22,23,23,24,24,25,25,26,26]);

MOT("3xFi23",
[
"1st maximal subgroup of 3.F3+"
],
0,
0,
0,
[(238,241)(239,242)(240,243),(232,235)(233,236)(234,237),
(187,190)(188,191)(189,192),
(169,172)(170,173)(171,174)(253,256)(254,257)(255,258)(283,286)(284,287)
(285,288)
,
(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)
( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)( 71, 72)
( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 86, 87)( 89, 90)( 92, 93)( 95, 96)
( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114)(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)(161,162)(164,165)(167,168)
(170,171)(173,174)(176,177)(179,180)(182,183)(185,186)(188,189)(191,192)
(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(212,213)(215,216)
(218,219)(221,222)(224,225)(227,228)(230,231)(233,234)(236,237)(239,240)
(242,243)(245,246)(248,249)(251,252)(254,255)(257,258)(260,261)(263,264)
(266,267)(269,270)(272,273)(275,276)(278,279)(281,282)(284,285)(287,288)
(290,291)(293,294)
],
["ConstructDirectProduct",[["Fi23"],["Cyclic",3]]]);
ALF("3xFi23","3.F3+",[1,2,3,4,5,6,4,5,6,7,8,9,10,10,10,11,12,13,14,15,16,
17,17,17,22,23,24,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,37,38,39,
31,32,33,37,38,39,44,45,46,41,42,43,34,35,36,41,42,43,40,40,40,47,48,49,
44,45,46,53,54,55,53,54,55,50,51,52,56,56,56,58,59,60,64,65,66,64,65,66,
67,68,69,73,73,73,74,75,76,77,77,77,79,79,79,80,81,82,83,84,85,83,84,85,
86,87,88,89,90,91,97,98,99,93,94,95,92,92,92,104,105,106,93,94,95,107,108,
109,96,96,96,100,101,102,97,98,99,115,116,117,107,108,109,112,113,114,103,
103,103,115,116,117,118,119,120,121,122,123,121,122,123,124,125,126,124,
125,126,130,131,132,136,137,138,139,140,141,139,140,141,142,143,144,146,
147,148,150,151,152,145,145,145,149,149,149,150,151,152,146,147,148,153,
153,153,154,155,156,163,164,165,163,164,165,169,169,169,177,178,179,177,
178,179,177,178,179,180,181,182,183,184,185,186,186,186,190,191,192,187,
187,187,199,200,201,199,200,201,202,202,202,205,206,207,214,215,216,214,
215,216,217,218,219,226,227,228,231,231,231,232,233,234,236,236,236,235,
235,235,239,240,241,254,255,256],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("3xFi23",["3.F3+M1"]);

MOT("2^(5+8):(S3xS6)",
[
"9th maximal subgroup of Fi22.2,\n",
"origin: Dixon's Algorithm"
],
[35389440,2359296,5898240,3538944,98304,32768,24576,24576,9216,12288,12288,
12288,12288,6144,6144,2048,2048,1024,512,512,256,3456,3456,192,288,864,864,288
,288,768,768,768,768,128,128,60,60,147456,147456,8192,49152,49152,8192,4096,
3072,1536,512,73728,24576,18432,73728,24576,18432,2048,2048,1024,768,768,768,
768,768,128,128,288,288,48,144,144,144,144,69120,11520,6912,4608,384,384,384,
384,192,192,432,432,72,6912,6912,2304,2304,192,192,144,96,96,96,96,30,30,1152,
1152,384,384,2304,768,576,2304,768,576,96,96,96,96,144,144,24,288,288,288,288,
48,48,737280,122880,73728,49152,6144,2048,2048,2048,2048,2048,2048,2048,1024,
1024,1024,512,256,256,64,288,288,48,288,288,96,96,256,256,256,256,128,128,32,
20,20,6144,12288,12288,4096,4096,2048,512,512,192,6144,6144,6144,6144,4096,
4096,2048,1024,256,256,256,256,256,256,128,128,32,48,96,96,24,48,48,48,48],
[,[1,1,1,1,1,1,2,2,4,1,1,2,2,2,2,5,5,5,6,5,8,22,22,22,23,26,26,26,26,10,10,13,
13,16,17,36,36,1,1,1,2,2,2,2,4,5,6,1,1,1,2,2,2,5,5,5,8,10,10,13,13,16,17,22,22
,24,26,26,29,29,71,71,71,71,71,71,74,74,74,74,81,81,82,84,84,84,84,86,86,85,76
,76,77,77,95,95,71,71,74,74,71,71,71,74,74,74,76,76,77,77,81,81,82,84,84,86,86
,88,88,1,1,1,1,5,5,1,2,5,5,5,5,5,5,2,6,7,7,9,22,22,24,26,26,26,26,10,10,13,13,
17,16,21,36,36,1,5,5,5,5,2,5,6,9,1,1,2,2,5,5,5,5,7,7,10,10,13,13,17,16,21,22,
24,24,25,26,26,29,29],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1
,4,5,9,1,4,3,2,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,38,39,46,48,50,51,53,1,3,4,2,11,10,13,
12,15,14,1,4,9,1,4,2,3,8,7,9,30,31,32,33,36,37,38,39,41,42,48,49,50,51,52,53,
59,58,61,60,38,39,45,48,50,53,51,57,57,120,121,122,123,124,125,126,127,128,129
,130,131,132,133,134,135,136,137,138,122,120,124,122,120,121,123,146,147,148,
149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,
168,169,170,171,172,173,174,175,176,177,178,179,180,155,156,157,163,165,164,
166,167],,[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,
26,27,28,29,30,31,32,33,34,35,1,3,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52
,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
,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,71,72,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,119,118,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143,144,145,146,147,148,149,150,151,152,120,121,155,156,157,158,159,
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]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[5,5,5,5,5
,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,3,3
,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,0,0,0,-1,-1,-1,-1,5
,5,5,5,1,1,1,1,1,1,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,3,3,3,3,-1,-1,-1
,-1,-1,-1,1,1,1,1,0,0,0,-1,-1,-1,-1,-1,-1,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,
1,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,2,2,2,2
,-1,-1,-1,-1,-1,-1,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,3,3,3,3,3,3,1,1,1
,1,1,1,-1,-1,-1,0,0,0,0,5,5,5,5,1,1,1,1,1,1,-1,-1,-1,2,2,2,2,2,2,2,-1,-1,-1,-1
,0,0,-1,-1,-1,-1,3,3,3,3,3,3,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,5,5,5,5,5,5,1,1,1,1,
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[(118,119)]);
ALF("2^(5+8):(S3xS6)","S3xS6",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,
9,9,9,9,9,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,13,13,14,14,14,15,
15,15,15,15,15,15,16,16,16,16,17,17,18,18,18,18,19,19,19,19,19,19,20,20,
20,20,21,21,21,22,22,22,22,22,22,23,23,23,23,23,23,24,24,24,24,24,24,24,
24,24,24,24,24,24,25,25,25,26,26,26,26,27,27,27,27,27,27,27,28,28,29,29,
29,29,29,29,29,29,29,30,30,30,30,30,30,30,30,30,30,31,31,31,31,31,31,31,
32,32,32,32,33,33,33,33]);
ALF("2^(5+8):(S3xS6)","Fi22.2",[1,3,2,4,3,4,9,11,12,3,4,9,9,13,10,9,11,13,
12,13,29,7,22,23,42,7,24,19,23,13,9,27,28,27,29,14,34,61,60,61,64,63,64,
66,67,65,67,60,61,62,63,64,65,64,66,65,81,65,64,79,80,79,81,77,72,93,72,
78,89,93,5,15,20,18,20,18,38,39,40,44,8,25,46,6,21,17,16,43,37,41,44,39,
58,57,49,59,73,69,90,88,68,73,71,86,90,91,90,91,105,104,76,75,95,70,74,92,
87,106,107,2,3,4,4,10,13,4,11,13,11,9,10,13,10,13,12,28,27,30,24,19,45,22,
19,23,24,13,11,28,27,29,28,50,34,35,62,66,63,66,64,65,66,67,82,61,62,65,
66,63,64,66,65,79,80,66,65,79,80,81,80,98,78,94,89,108,78,77,93,94],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^5:(2xU4(2).2)",
[
"10th maximal subgroup of Fi22.2,\n",
"origin: Dixon's Algorithm"
],
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[]);
ALF("3^5:(2xU4(2).2)","Fi22.2",[1,5,6,7,61,4,22,60,68,72,70,3,23,17,18,61,
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85,25,21,75,75,20,25,69,75,99,22,24,72,70,100,18,53,73,77,76,33,32,102,46,
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45,71,78,15,19,51,78,74,19,19,52,78,101,24,21,22,25,82,108,30,84,110,34,
88,111,44],[
"fusion map is unique"
]);
ALF("3^5:(2xU4(2).2)","O7(3).2",[1,6,5,7,54,4,20,53,62,63,61,3,21,19,23,
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15,48,77,22,27,61,70,24,29,62,70,88,25,28,63,70,89,23,51,64,71,72,34,35,
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11,41,40,67,71,17,26,49,68,72,18,26,50,69,90,20,29,28,27,73,92,31,75,97,
37,81,98,44],[
"fusion map is unique"
]);

LIBTABLE.LOADSTATUS.ctomaxi4:="userloaded";

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