#############################################################################
##
#W  ctomaxi5.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 $S_6(2)$ and $S_6(3)$, and the table of $F_4(2)M1$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctomaxi5.tbl,v $
#H  Revision 4.24  2012/06/20 14:45:32  gap
#H  added tables and fusions, as documented in ctbldiff.dat
#H      TB
#H
#H  Revision 4.23  2012/04/23 16:16:13  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 4.22  2012/01/30 08:31:56  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.21  2011/09/28 14:32:21  gap
#H  removed revision entry and SET_TABLEFILENAME call
#H      TB
#H
#H  Revision 4.20  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 4.19  2009/04/22 12:39:05  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.18  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 4.17  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 4.16  2003/06/20 15:03:02  gap
#H  added several fusions
#H      TB
#H
#H  Revision 4.15  2003/05/15 17:38:12  gap
#H  next step towards the closer connection to the library of tables of marks:
#H  added fusions tbl -> tom, adjusted fusions between character tables
#H  in order to make the diagrams commute, adjusted orderings of maxes
#H      TB
#H
#H  Revision 4.14  2003/03/07 15:53:37  gap
#H  added tables of `Isoclinic(2.A5.2)' and `L2(125)',
#H  and many `tomidentifier' components (still several are missing)
#H      TB
#H
#H  Revision 4.13  2003/01/24 15:57:31  gap
#H  replaced several fusions by ones that are compatible with Brauer tables
#H      TB
#H
#H  Revision 4.12  2002/10/22 12:44:09  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 4.11  2002/07/17 15:25:32  gap
#H  added missing table automorphisms
#H      TB
#H
#H  Revision 4.10  2002/07/12 06:45:55  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.9  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 4.8  2001/05/04 16:48:26  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/ctomaxi5.tbl,v
#H  Working file: ctomaxi5.tbl
#H  head: 4.7
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H  	GAP4R2: 4.6.0.6
#H  	GAP4R2PRE2: 4.6.0.4
#H  	GAP4R2PRE1: 4.6.0.2
#H  	GAP4R1: 4.4.0.2
#H  keyword substitution: kv
#H  total revisions: 9;	selected revisions: 9
#H  description:
#H  ----------------------------
#H  revision 4.7
#H  date: 2000/12/04 15:43:21;  author: gap;  state: Exp;  lines: +767 -3
#H  added missing maxes of S6(3)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/10/21 14:15:47;  author: gap;  state: Exp;  lines: +3 -3
#H  added many `tomidentifer' and `tomfusion' values, which yields a better
#H  interface between `tom' and `tbl';
#H  
#H  added maxes of McL.2,
#H  
#H  unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/10/04 15:57:15;  author: gap;  state: Exp;  lines: +4 -4
#H  added and corrected several fusions from character tables
#H  to their tables of marks,
#H  unified two instances of the table of (A6xA6):2^2,
#H  corrected the name of the table of marks of 2F4(2).
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 1999/07/14 11:39:40;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1998/03/11 08:05:43;  author: gap;  state: Exp;  lines: +15 -2
#H  mainly new fusions to tables of marks added
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/11/25 15:45:14;  author: gap;  state: Exp;  lines: +6 -2
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:43:10;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.2
#H  date: 1996/10/23 15:35:18;  author: sam;  state: Exp;  lines: +1249 -3
#H  added table of F4(2)M1 and its factor group modulo the centre
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:00:13;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("2.[2^6]:(S3xS3)",
[
"origin: Dixon's Algorithm,\n",
"6th maximal subgroup of S6(2),\n",
"table is sorted w.r.t. normal series 2.2^2.2^4.3.2.3.2,\n",
"module for S3xS3 is 2^2 x 2^{1+4}_+"
],
[4608,4608,1536,1536,256,256,128,128,384,36,36,192,192,32,32,192,192,144,144,
48,48,12,72,72,24,24,24,24,384,384,64,128,128,32,64,12,12,64,64,32,16,32,64,
64,16],
[,[1,1,1,1,1,1,2,1,2,10,10,1,1,5,6,4,4,18,18,18,18,23,24,24,18,18,20,20,1,1,6,
1,1,6,6,10,10,5,5,4,9,1,6,6,7],[1,2,3,4,5,6,7,8,9,1,2,12,13,14,15,16,17,1,2,4,
3,9,2,1,13,12,16,17,29,30,31,32,33,34,35,29,30,38,39,40,41,42,43,44,45]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-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,-1,-1,0,0,
0,0,0,0,2,2,2,2,-1,-1,-1,0,0,0,0,2,2,2,2,2,2,2,-1,-1,0,0,0,0,0,0,0,0],[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],
[TENSOR,[2,4]],
[TENSOR,[3,4]],[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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[7,2]],[4,4,4,4,4,4,4,4,4,-2,-2,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,-2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,
0,0,-1,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,0,2,-2,-2,0],
[TENSOR,[10,2]],[9,9,9,9,1,1,-3,1,-3,0,0,-3,-3,1,1,-3,-3,0,0,0,0,0,0,0,0,0,0,
0,3,3,-1,3,3,-1,-1,0,0,-1,-1,-1,1,-1,-1,-1,1],
[TENSOR,[12,2]],
[TENSOR,[12,4]],
[TENSOR,[12,5]],[12,12,12,12,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,-3,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,-1,-1,-1,3,-1,-1,3,0,0,-1,-1,1,-1,
1,1,3,3,-1,-1,0,0,0,-1,-1,1,1,-3,-3,1,1,1,1,-3,0,0,-1,-1,-1,1,1,1,1,-1],
[TENSOR,[17,2]],
[TENSOR,[17,4]],
[TENSOR,[17,5]],[6,6,-2,-2,-2,6,-2,-2,6,0,0,2,2,-2,2,-2,-2,-3,-3,1,1,0,0,0,-1,
-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[21,2]],[9,9,-3,-3,5,1,1,-3,-3,0,0,-3,-3,-1,1,3,3,0,0,0,0,0,0,0,0,0,0,
0,3,3,3,-1,-1,-1,-1,0,0,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[23,2]],
[TENSOR,[23,4]],
[TENSOR,[23,5]],[18,18,-6,-6,-6,2,2,2,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-6,-6,2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,4]],[18,18,-6,-6,2,-6,-2,2,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,2,2,-2,0,2,-2,-2,0],
[TENSOR,[29,2]],[4,-4,-4,4,0,0,0,0,0,1,-1,2,-2,0,0,-2,2,1,-1,1,-1,0,2,-2,1,-1,
1,-1,-2,2,0,2,-2,0,0,1,-1,2,-2,0,0,0,2,-2,0],
[TENSOR,[31,2]],
[TENSOR,[31,4]],
[TENSOR,[31,5]],[8,-8,-8,8,0,0,0,0,0,-1,1,0,0,0,0,0,0,2,-2,2,-2,0,-2,2,0,0,0,
0,4,-4,0,-4,4,0,0,1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[35,4]],[8,-8,-8,8,0,0,0,0,0,2,-2,4,-4,0,0,-4,4,-1,1,-1,1,0,-2,2,-1,1,
-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[37,2]],[12,-12,4,-4,0,0,0,0,0,0,0,-2,2,0,0,-2,2,3,-3,-1,1,0,0,0,-1,1,
1,-1,-6,6,0,-2,2,0,0,0,0,2,-2,0,0,0,-2,2,0],
[TENSOR,[39,2]],
[TENSOR,[39,5]],
[TENSOR,[39,4]],[16,-16,-16,16,0,0,0,0,0,-2,2,0,0,0,0,0,0,-2,2,-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],[24,-24,8,-8,0,0,0,0,0,0,0,-4,4,0,0,
-4,4,-3,3,1,-1,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[44,2]]],
[(29,30)(32,33)(36,37)(38,39)(43,44),(12,13)(16,17)(25,26)(27,28)(38,39)
(43,44)]);
ARC("2.[2^6]:(S3xS3)","tomfusion",rec(name:="2.[2^6]:(S3xS3)",map:=[1,2,3,4,8,
7,36,11,21,17,122,9,10,91,88,31,28,15,114,120,121,476,117,16,127,126,464,456,
5,6,71,12,13,83,47,132,130,72,45,103,439,14,58,57,438],text:=[
"fusion map is unique up to table autom. (very expensive)"
]));
ALF("2.[2^6]:(S3xS3)","S6(2)",[1,3,2,4,3,4,12,5,9,8,20,4,3,12,13,11,10,6,
16,18,15,29,17,7,16,18,28,27,2,5,10,4,5,13,11,19,21,9,12,13,23,5,10,11,24],[
"fusion map is unique up to table automorphisms,\n",
"unique map that is compatible with 2^2.[2^6].(S3xS3) -> 2.S6(2)"
]);
ALN("2.[2^6]:(S3xS3)",["S6(2)C2B","S6(2)N2B"]);

MOT("2^5:S6",
[
"origin: Dixon's Algorithm,\n",
"3rd maximal subgroup of S6(2)"
],
[23040,1536,1536,23040,128,128,32,128,128,36,36,144,48,144,48,16,32,32,10,10,
64,384,384,192,192,768,768,128,16,32,32,12,12,24,24,24,24],
[,[1,1,1,1,2,2,3,1,1,10,10,12,12,12,12,5,9,9,19,19,2,1,1,3,3,1,1,1,6,9,9,10,
10,13,13,12,12],[1,2,3,4,5,6,7,8,9,1,4,1,3,4,2,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,23,22,24,25,26,27],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,1,4,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1],[5,5,5,5,1,1,1,1,1,2,2,-1,-1,-1,-1,-1,-1,-1,0,0,3,3,3,-1,-1,
-1,-1,-1,1,1,1,0,0,-1,-1,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,1,1,1,1,1,-1,-1,2,2,2,2,-1,-1,-1,0,0,-1,-1,-1,3,3,3,3,
3,1,1,1,-1,-1,0,0,0,0],
[TENSOR,[5,2]],[16,16,16,16,0,0,0,0,0,-2,-2,-2,-2,-2,-2,0,0,0,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[9,9,9,9,1,1,1,1,1,0,0,0,0,0,0,1,1,1,-1,-1,3,3,3,3,3,3,
3,3,-1,-1,-1,0,0,0,0,0,0],
[TENSOR,[8,2]],[10,10,10,10,-2,-2,-2,-2,-2,1,1,1,1,1,1,0,0,0,0,0,2,2,2,-2,-2,
-2,-2,-2,0,0,0,-1,-1,1,1,1,1],
[TENSOR,[10,2]],[6,-2,2,-6,-2,2,0,-2,2,0,0,3,-1,-3,1,0,0,0,1,-1,0,0,0,-2,2,-4,
4,0,0,-2,2,0,0,1,-1,-1,1],
[TENSOR,[12,2]],[10,2,-2,-10,2,-2,0,-2,2,1,-1,1,1,-1,-1,0,-2,2,0,0,0,4,-4,-2,
2,4,-4,0,0,0,0,-1,1,1,-1,1,-1],[10,2,-2,-10,2,-2,0,-2,2,1,-1,1,1,-1,-1,0,2,-2,
0,0,0,-4,4,-2,2,4,-4,0,0,0,0,1,-1,1,-1,1,-1],
[TENSOR,[15,2]],
[TENSOR,[14,2]],[15,-1,-1,15,-1,-1,-1,3,3,0,0,3,-1,3,-1,-1,1,1,0,0,1,-3,-3,1,
1,-7,-7,1,1,-1,-1,0,0,1,1,-1,-1],
[TENSOR,[18,2]],[15,-1,-1,15,3,3,-1,-1,-1,0,0,3,-1,3,-1,1,-1,-1,0,0,-1,3,3,-1,
-1,-5,-5,3,1,-1,-1,0,0,-1,-1,1,1],
[TENSOR,[20,2]],[20,4,-4,-20,-4,4,0,4,-4,2,-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],[24,-8,8,-24,0,0,0,0,0,0,0,3,-1,-3,1,0,0,0,-1,1,0,0,0,
4,-4,8,-8,0,0,0,0,0,0,1,-1,-1,1],
[TENSOR,[23,2]],[30,-10,10,-30,-2,2,0,-2,2,0,0,-3,1,3,-1,0,0,0,0,0,0,0,0,-2,2,
-4,4,0,0,2,-2,0,0,1,-1,-1,1],
[TENSOR,[25,2]],[30,-2,-2,30,2,2,-2,2,2,0,0,-3,1,-3,1,0,0,0,0,0,2,-6,-6,2,2,
-2,-2,-2,0,0,0,0,0,-1,-1,1,1],
[TENSOR,[27,2]],[36,-12,12,-36,4,-4,0,4,-4,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[40,8,-8,-40,0,0,0,0,0,-2,2,1,1,-1,-1,0,0,0,0,0,0,0,0,
4,-4,-8,8,0,0,0,0,0,0,1,-1,1,-1],
[TENSOR,[30,2]],[40,8,-8,-40,0,0,0,0,0,1,-1,-2,-2,2,2,0,0,0,0,0,0,-8,8,0,0,0,
0,0,0,0,0,-1,1,0,0,0,0],
[TENSOR,[32,2]],[45,-3,-3,45,1,1,1,-3,-3,0,0,0,0,0,0,-1,1,1,0,0,1,-3,-3,-3,-3,
-3,-3,5,-1,1,1,0,0,0,0,0,0],
[TENSOR,[34,2]],[45,-3,-3,45,-3,-3,1,1,1,0,0,0,0,0,0,1,-1,-1,0,0,1,-3,-3,-3,
-3,9,9,1,1,-1,-1,0,0,0,0,0,0],
[TENSOR,[36,2]]],
[(22,23)(24,25)(26,27)(30,31)(32,33)(34,35)(36,37),(17,18)(24,25)(26,27)
(30,31)(34,35)(36,37)]);
ARC("2^5:S6","tomfusion",rec(name:="2^5:S6",map:=[1,3,4,2,31,30,72,11,9,13,94,
12,92,89,91,294,65,70,86,373,54,7,8,27,22,6,5,10,345,82,74,102,103,389,396,98,
97],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^5:S6","S6(2)",[1,3,4,2,12,9,13,5,4,8,19,6,18,15,16,24,10,13,14,26,
12,3,5,10,11,4,2,5,23,13,11,21,20,27,28,18,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^5:S6","A6.2_1",[1,1,1,1,2,2,2,2,2,3,3,4,4,4,4,5,5,5,6,6,7,7,7,8,8,
8,8,8,9,9,9,10,10,11,11,11,11]);
ALF("2^5:S6","A12",[1,4,2,3,12,10,11,3,4,7,20,6,17,18,19,24,12,12,14,29,
12,3,3,9,11,2,3,4,23,10,12,20,20,33,35,17,18],[
"fusion map is unique up to table autom."
]);
ALF("2^5:S6","2.M22.2",[1,3,4,2,7,8,9,4,3,5,6,5,13,6,12,18,7,8,10,11,26,
21,22,25,24,22,21,23,29,26,26,28,27,33,32,28,27],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^5:S6","O7(3)",[1,4,3,2,14,13,15,4,3,10,27,6,24,18,25,35,15,15,16,
41,14,4,4,12,15,2,3,4,34,12,15,30,31,45,49,18,24],[
"fusion map is unique up to table aut."
]);
ALN("2^5:S6",["A12C2B","A12N2B","S6(2)C2A","S6(2)N2A"]);

MOT("2^6:L3(2)",
[
"origin: Dixon's Algorithm,\n",
"5th maximal subgroup of S6(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["P11/G2/L1/V1/ext2"],(2,3)(4,5)(6,13,7,10,11,14)(8,12)
(16,17,18)(19,22,20,21)(23,24),(2,3)(7,8)(15,16)(17,20)(18,19)(22,23)]);
ARC("2^6:L3(2)","tomfusion",rec(name:="2^6:L3(2)",map:=[1,3,4,2,5,19,20,40,29,
42,48,7,6,8,9,62,65,63,225,222,59,60,68,68],text:=[
"fusion map is unique up to table autom."
]));
ALF("2^6:L3(2)","S6(2)",[1,3,4,2,5,12,9,12,10,11,13,3,4,5,8,20,19,21,24,
23,12,13,22,22],[
"fusion map is unique up to table automorphisms,\n",
"unique map that is compatible with 2.2^6.L3(2) -> 2.S6(2)"
]);
ALF("2^6:L3(2)","L3(2)",[1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,5,6]);

MOT("S3xS6",
[
"7th maximal subgroup of S6(2)"
],
0,
0,
0,
[( 3, 4)( 7, 8)(10,11)(14,15)(18,19)(21,22)(25,26)(29,30)(32,33)],
["ConstructDirectProduct",[["Dihedral",6],["A6.2_1"]]]);
ARC("S3xS6","tomfusion",rec(name:="S6xS3",map:=[1,5,10,11,22,35,4,3,21,45,51,
9,44,12,13,127,147,39,37,120,55,53,2,8,48,46,27,105,6,7,29,60,58],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("S3xS6","A9.2",[1,2,4,6,7,9,17,18,19,21,24,4,10,6,5,15,16,21,22,28,23,
25,17,18,21,23,20,27,2,3,7,10,11],[
"fusion map is unique up to table autom."
]);
ALF("S3xS6","S6(2)",[1,4,6,8,10,14,2,3,11,15,20,6,18,8,7,27,30,15,16,28,
19,17,2,5,15,19,13,26,4,5,13,18,21],[
"fusion map is unique up to table automorphisms"
]);
ALF("S3xS6","S6x2",[1,3,5,7,9,11,13,15,17,19,21,1,3,5,7,9,11,13,15,17,19,
21,2,4,6,8,10,12,14,16,18,20,22]);

MOT("(2^6x2^8):S6(2)",
[
"factor group of F4(2)M1 by central involution"
],
[23781703680,377487360,3145728,25165824,176160768,7077888,5505024,65536,
196608,49152,786432,737280,11796480,98304,98304,16384,49152,16384,65536,
196608,262144,262144,65536,131072,393216,1572864,4718592,8192,8192,8192,8192,
16384,131072,65536,32768,131072,98304,393216,131072,49152,8192,4096,4096,8192,
8192,8192,1536,1536,16384,49152,16384,49152,16384,16384,49152,49152,2304,
34560,864,2592,384,1152,2304,6912,768,768,384,4096,12288,24576,8192,1024,1024,
24576,8192,1024,1024,512,2048,6144,1536,512,1024,1024,2048,1536,6144,4096,
8192,8192,1024,2048,2048,512,512,4096,4096,4096,4096,4096,8192,8192,128,128,
512,512,512,512,512,512,512,512,40,120,384,288,1152,192,576,288,96,96,192,192,
96,96,288,288,96,192,192,192,576,96,96,48,48,96,96,28,28,28,28,64,64,128,128,
128,128,64,64,128,128,128,128,9,20,20,48,48,48,48,48,48,48,48,15],
[,[1,1,1,1,1,1,1,5,5,4,1,2,1,4,4,4,4,4,2,1,2,2,2,1,2,1,1,4,3,3,4,4,5,5,4,5,2,
1,1,2,4,3,3,4,4,5,7,6,4,5,4,4,2,2,2,1,58,58,60,60,64,64,64,64,64,64,64,26,27,
27,26,19,19,27,26,35,35,36,38,38,37,33,35,35,38,37,38,26,27,26,19,19,19,21,22,
27,26,26,26,26,26,27,29,30,35,35,33,36,38,39,37,37,114,114,58,57,58,57,58,60,
60,57,57,58,65,66,64,63,66,66,66,64,64,66,65,62,61,63,64,143,143,143,143,73,
73,74,75,71,70,93,92,90,89,101,102,156,113,114,123,124,123,124,120,120,120,
120,167],[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,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,54,55,56,2,1,6,1,7,6,2,1,5,4,3,68,69,70,71,72,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,
105,106,107,108,109,110,111,112,113,114,11,12,13,25,27,27,20,40,37,38,9,10,13,
12,17,15,14,26,27,52,50,48,47,55,56,140,142,141,143,145,144,146,147,148,149,
150,151,152,153,154,155,60,157,158,81,80,86,87,74,69,70,69,114],,[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,
109,110,111,112,2,1,115,116,117,118,119,120,121,122,123,124,125,126,127,128,
129,130,131,132,133,134,135,136,137,138,139,140,142,141,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,12,13,159,160,161,162,163,166,165,164,
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,
104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,7,5,5,1,
145,144,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,
163,164,165,166,167]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1],[7,7,7,7,7,7,7,-5,-5,-5,-5,-5,-5,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,4,4,-2,-2,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,1,1,1,1,1,1,-3,
-3,-3,-3,-3,-3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,
1,2,2,-2,-2,-2,2,2,2,2,0,0,0,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,
-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,0,0,-2,-2,0,0,0,0,0,0,-1],[15,15,15,15,15,15,
15,-5,-5,-5,-5,-5,-5,7,7,7,7,7,7,7,7,7,7,7,7,7,7,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,-3,-3,3,3,3,3,3,3,3,-1,-1,-1,
-1,-1,-1,-1,-1,-3,-3,-3,-3,-3,-3,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,
1,1,1,1,1,1,1,1,1,0,0,-2,-2,-2,-2,-2,1,1,0,0,0,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,-2,-2,-1,-1,-1,-1,0],[
21,21,21,21,21,21,21,9,9,9,9,9,9,-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,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,6,6,3,
3,0,0,0,0,0,0,0,5,5,5,5,5,5,5,5,-1,-1,-1,-1,-1,-1,3,3,3,3,3,3,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,0,0,0,0,0,3,3,-2,-2,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,0,-1,-1,2,2,0,0,
-1,-1,-1,-1,1],[21,21,21,21,21,21,21,-11,-11,-11,-11,-11,-11,5,5,5,5,5,5,5,5,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,
-3,-3,-3,6,6,3,3,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,
-3,-3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,2,2,-1,
-1,2,2,2,-2,-2,-2,-2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,0,-1,-1,0,0,0,0,1,1,1,1,1],[27,27,27,27,27,27,27,15,15,15,15,15,15,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,7,7,7,7,7,7,7,7,7,7,7,7,7,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,9,9,0,0,0,0,0,0,0,0,0,3,3,3,3,3,3,3,3,1,1,1,1,1,1,5,5,5,5,5,5,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,2,2,3,3,3,3,3,0,0,1,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,
0,1,1,-1,-1,0,0,0,0,-1],[35,35,35,35,35,35,35,-5,-5,-5,-5,-5,-5,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,-5,-5,-5,-5,-5,-5,-5,-5,-5,-5,-5,-5,-5,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,5,5,-1,-1,2,2,2,2,2,2,2,7,7,7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,0,0,1,1,1,-3,-3,3,3,1,1,1,-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,-1,0,0,-1,-1,-1,-1,1,1,1,1,0],[35,35,35,35,35,35,35,15,15,
15,15,15,15,11,11,11,11,11,11,11,11,11,11,11,11,11,11,7,7,7,7,7,7,7,7,7,7,7,7,
7,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,-1,-1,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,
-1,-1,5,5,5,5,5,5,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,
1,0,0,3,3,3,-1,-1,-1,-1,1,1,1,0,0,0,0,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,
-1,-1,-1,1,1,1,1,1,1,-1,0,0,-1,-1,1,1,-1,-1,-1,-1,0],[56,56,56,56,56,56,56,
-24,-24,-24,-24,-24,-24,-8,-8,-8,-8,-8,-8,-8,-8,-8,-8,-8,-8,-8,-8,8,8,8,8,8,8,
8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,11,11,2,2,2,2,2,2,2,2,2,0,0,0,0,
0,0,0,0,4,4,4,4,4,4,-4,-4,-4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,1,-3,-3,-3,1,1,-2,-2,-1,-1,-1,0,0,0,0,-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,-1,1,1,1,1,-1,-1,0,0,0,0,1],[70,70,70,70,70,
70,70,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,
-10,-10,6,6,6,6,6,6,6,6,6,6,6,6,6,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-5,-5,7,7,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,-1,-1,-1,-1,-1,-1,-1,
3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,-1,-1,-1,-1,-1,-1,-1,-1,0],[84,84,84,84,84,84,84,4,4,4,4,4,4,20,20,20,
20,20,20,20,20,20,20,20,20,20,20,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,-6,-6,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,-1,-1,-2,-2,-2,2,2,-1,-1,-2,
-2,-2,1,1,1,1,-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,-1,
-1,0,0,0,0,1,1,1,1,-1],[105,105,105,105,105,105,105,-35,-35,-35,-35,-35,-35,1,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0],[26880,-3840,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-384,384,0,0,0,0,0,0,0,0,0,64,
128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,-60,0,-6,0,0,0,0,0,0,0,0,0,64,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,6,0,0,-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,-2,0,0],[26880,-3840,0,0,0,0,0,0,0,0,0,160,640,
0,0,0,0,0,0,0,0,0,0,0,0,128,-128,0,0,0,0,0,0,0,0,0,64,128,0,0,0,0,0,0,0,0,0,0,
0,32,0,-32,0,0,0,0,6,-30,0,12,0,0,12,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,-8,0,0,
0,0,8,0,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-4,0,4,
-4,0,0,2,-2,0,0,-2,-2,0,0,0,2,-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,-2,0,0,0,0,0,0,0],[28672,-4096,0,0,0,0,0,0,0,0,0,-256,-1024,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-8,40,0,-16,0,0,8,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,3,0,-4,-8,0,0,0,0,0,0,0,0,0,-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,-1,-1,-1,0,0,0,0,0,0,0,
0,0],[28672,-4096,0,0,0,0,0,0,0,0,0,256,1024,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,40,0,-16,0,0,8,-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,
0,0,0,0,0,0,0,0,-1,3,0,4,8,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0],[32256,3584,0,0,0,0,0,0,0,
0,0,-64,256,0,0,0,0,0,0,0,0,0,0,0,0,-256,-768,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,64,0,64,0,0,0,0,-8,-24,0,0,0,0,-4,-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,-1,-1,0,
-4,8,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,2,6,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,-1,0,0,0,0,0,0,0,0,1],[32256,3584,0,0,0,0,0,0,0,0,0,64,-256,0,0,0,0,
0,0,0,0,0,0,0,0,-256,-768,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-64,0,
-64,0,0,0,0,-8,-24,0,0,0,0,-4,-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,-1,-1,0,4,-8,0,0,0,0,0,0,
0,0,0,2,-2,0,0,0,2,6,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,
0,0,0,0,0,0,1],[35840,-5120,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,512,
-512,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,-40,0,-20,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,-4,0,0,0,0,0,0,0,0,0,0,0,-4,4,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],[36288,-5184,0,
0,0,0,0,0,0,0,0,-144,-576,0,0,0,0,0,0,0,0,0,0,0,0,-288,288,0,0,0,0,0,0,0,0,0,
-48,-96,0,0,0,0,0,0,0,0,0,0,0,48,0,-48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-48,
0,0,0,0,0,0,0,0,12,-12,0,0,0,0,-4,0,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-4,4,0,0,1,-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,
0,0,4,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0],[36288,-5184,0,0,0,0,0,0,0,0,0,
144,576,0,0,0,0,0,0,0,0,0,0,0,0,-288,288,0,0,0,0,0,0,0,0,0,-48,-96,0,0,0,0,0,
0,0,0,0,0,0,-48,0,48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-48,0,0,0,0,0,0,0,0,
-12,12,0,0,0,0,4,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,4,0,0,1,-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,-4,0,0,0,0,0,
0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0],[36864,4096,0,0,0,0,0,0,0,0,0,-256,1024,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,8,24,0,0,0,0,-8,-24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,-4,8,0,0,0,0,0,0,0,0,0,4,-4,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,
-1],[36864,4096,0,0,0,0,0,0,0,0,0,256,-1024,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,24,0,0,0,0,-8,-24,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,1,0,4,-8,0,0,0,0,0,0,0,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,-1],[40320,-5760,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,192,-192,0,0,0,0,0,0,0,0,0,-96,-192,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,-8,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,2,0,0],[40320,4480,0,0,0,0,0,0,0,0,0,-160,640,0,0,0,0,0,0,0,0,0,0,
0,0,64,192,0,0,0,0,0,0,0,0,0,-32,64,0,0,0,0,0,0,0,0,0,0,0,-32,0,-32,0,0,0,0,
-10,-30,0,0,0,0,4,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,0,-16,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-4,0,0,0,0,0,2,2,0,0,-2,2,
0,0,0,-2,-6,2,-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,-2,0,0,0,
0,0],[40320,4480,0,0,0,0,0,0,0,0,0,160,-640,0,0,0,0,0,0,0,0,0,0,0,0,64,192,0,
0,0,0,0,0,0,0,0,-32,64,0,0,0,0,0,0,0,0,0,0,0,32,0,32,0,0,0,0,-10,-30,0,0,0,0,
4,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-16,0,16,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,4,0,0,0,0,0,2,2,0,0,2,-2,0,0,0,-2,-6,-2,
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0],[51840,
5760,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,192,576,0,0,0,0,0,0,0,0,0,
96,-192,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,-8,-8,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("(2^6x2^8):S6(2)","S6(2)",[1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,
7,7,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,12,
12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,
14,14,15,15,15,16,16,17,17,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,
21,21,21,22,22,22,22,23,23,23,23,23,23,24,24,24,24,24,24,25,26,26,27,27,
28,28,29,29,29,29,30]);

MOT("(2^(1+8)x2^6):S6(2)",
[
"1st and 2nd maximal subgroup of F4(2),\n",
"constructed by T. Breuer using the representation on 69615 points\n",
"of F4(2), and the character tables of F4(2) and S6(2),\n",
"table is sorted w.r.t. (unique) normal series 2.2^6.2^8.S6(2)"
],
[47563407360,47563407360,754974720,754974720,3145728,25165824,176160768,
7077888,5505024,65536,196608,49152,786432,1474560,1474560,23592960,23592960,
98304,98304,16384,49152,16384,65536,196608,262144,262144,65536,131072,393216,
3145728,3145728,9437184,9437184,8192,8192,8192,8192,16384,131072,65536,32768,
131072,196608,196608,786432,786432,131072,49152,8192,4096,4096,8192,8192,8192,
1536,1536,16384,98304,98304,16384,98304,98304,16384,16384,49152,49152,4608,
4608,69120,69120,864,5184,5184,384,1152,4608,4608,13824,13824,768,768,384,
4096,12288,49152,49152,8192,1024,1024,24576,8192,1024,1024,512,4096,4096,
12288,12288,1536,512,1024,1024,4096,4096,1536,12288,12288,4096,8192,8192,1024,
2048,2048,512,512,4096,4096,4096,4096,4096,8192,16384,16384,128,128,512,512,
512,512,1024,1024,1024,1024,512,512,80,80,240,240,384,576,576,2304,2304,192,
1152,1152,576,576,96,96,384,384,384,384,96,96,576,576,576,576,96,192,192,384,
384,1152,1152,192,192,192,192,48,48,96,96,28,28,28,56,56,64,64,128,256,256,
128,128,64,64,256,256,128,128,128,18,18,40,40,40,40,48,96,96,48,96,96,48,48,
96,96,48,30,30],
[,[1,1,1,1,1,1,1,2,2,7,7,6,1,4,4,1,1,6,6,6,6,6,4,2,3,3,3,1,3,1,1,1,1,6,5,5,6,
6,7,7,6,7,3,3,1,1,1,4,6,5,5,6,6,7,9,8,6,7,7,6,6,6,3,4,4,1,69,69,69,69,72,73,
73,79,79,78,78,78,78,78,78,78,31,32,33,33,30,23,23,32,31,41,41,42,45,45,45,45,
44,39,41,41,45,45,43,45,45,30,32,31,23,23,23,25,26,33,30,31,31,31,30,33,33,35,
36,41,41,39,42,45,45,47,47,43,44,139,139,139,139,69,67,67,69,69,68,69,69,73,
73,72,67,68,68,69,69,80,81,78,78,77,77,81,81,81,78,78,78,78,81,81,80,80,75,74,
77,78,180,181,181,181,181,89,89,90,91,91,87,85,113,112,110,110,109,121,122,
197,197,137,137,139,139,152,155,155,153,155,155,149,149,148,148,149,213,213],[
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,
56,57,58,59,60,61,62,63,64,65,66,4,3,1,2,8,2,1,9,8,3,4,1,2,7,6,5,83,84,85,86,
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,
128,129,130,131,132,133,134,135,136,137,138,139,13,14,15,17,16,29,32,33,33,32,
24,48,44,43,46,45,11,12,16,17,14,15,21,19,18,30,31,32,33,62,61,58,59,56,55,65,
66,177,179,178,180,181,183,182,184,185,186,187,188,189,190,191,192,193,194,
195,72,73,198,199,200,201,99,97,98,105,107,106,90,84,85,86,84,139,138],,[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,
125,126,127,128,129,130,131,132,133,134,135,3,4,2,1,140,141,142,143,144,145,
146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,
165,166,167,168,169,170,171,172,173,174,175,176,177,179,178,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,14,15,17,16,202,203,
204,205,206,207,208,212,210,211,209,69,70],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,
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["ConstructProj",[["(2^6x2^8):S6(2)",[]],["(2^(1+8)x2^6):S6(2)",[]]]]);
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,2,-6,18,18,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,12,-12,0,0,0,0,0,0,2,2,-2,2,2,-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,-2,2,0,0,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[45360,-45360,-720,720,0,0,0,0,0,0,0,0,252,180,180,900,900,0,0,0,0,0,0,0,0,
0,0,0,24,-24,24,360,-360,0,0,0,0,0,0,0,0,0,60,60,-36,36,-100,12,0,0,0,0,0,0,0,
0,-12,-12,-12,4,-36,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-
36,-12,0,0,0,2,2,18,18,-6,0,0,0,10,10,-6,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,-12,-20
,-4,4,0,0,0,0,0,0,2,2,-2,2,-6,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,2,2,2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("(2^(1+8)x2^6):S6(2)","F4(2)",[1,2,3,4,5,4,2,9,11,15,11,19,5,13,14,4,
2,13,14,18,19,21,17,15,12,10,16,5,12,5,4,5,3,21,23,20,19,21,9,15,17,11,10,
12,4,5,5,18,17,23,22,21,19,15,40,42,17,9,11,18,14,13,16,21,19,5,31,27,6,
25,56,29,8,63,55,26,32,7,28,28,32,34,21,22,10,16,23,45,46,20,17,38,45,40,
19,21,13,18,41,42,39,45,19,21,43,14,18,22,23,17,44,38,39,41,43,16,23,18,
21,18,20,12,16,48,47,44,46,42,40,21,18,23,20,43,41,52,53,51,24,33,58,60,
25,31,62,33,27,30,35,66,64,62,54,33,31,63,65,32,28,59,61,65,61,59,34,32,
34,26,59,61,55,63,91,89,65,34,92,72,72,72,36,78,79,47,39,44,48,43,77,76,
38,44,48,47,41,82,49,84,85,51,53,88,58,64,90,64,60,68,69,57,67,70,74,94]);
ALF("(2^(1+8)x2^6):S6(2)","(2^6x2^8):S6(2)",[1,1,2,2,3,4,5,6,7,8,9,10,11,
12,12,13,13,14,15,16,17,18,19,20,21,22,23,24,25,26,26,27,27,28,29,30,31,
32,33,34,35,36,37,37,38,38,39,40,41,42,43,44,45,46,47,48,49,50,50,51,52,
52,53,54,55,56,57,57,58,58,59,60,60,61,62,63,63,64,64,65,66,67,68,69,70,
70,71,72,73,74,75,76,77,78,79,79,80,80,81,82,83,84,85,85,86,87,87,88,89,
90,91,92,93,94,95,96,97,98,99,100,101,102,102,103,104,105,106,107,108,109,
109,110,110,111,112,113,113,114,114,115,116,116,117,117,118,119,119,120,
120,121,122,123,123,124,124,125,126,127,127,128,128,129,130,131,132,132,
133,133,134,134,135,135,136,137,138,139,140,141,142,143,143,144,145,146,
147,147,148,149,150,151,152,152,153,154,155,156,156,157,157,158,158,159,
160,160,161,162,162,163,164,165,165,166,167,167]);
ALF("(2^(1+8)x2^6):S6(2)","S6(2)",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,
5,5,5,5,5,5,5,5,5,5,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,10,
10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,
12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,15,
15,15,15,15,16,16,16,17,17,17,18,18,18,18,18,19,19,19,19,19,19,20,20,20,
20,20,20,20,21,21,21,21,21,21,21,21,22,22,22,22,22,23,23,23,23,23,23,23,
24,24,24,24,24,24,24,25,25,26,26,26,26,27,27,27,28,28,28,29,29,29,29,29,
30,30]);
ALN("(2^(1+8)x2^6):S6(2)",["F4(2)C2A","F4(2)N2A"]);

MOT("2.F4(2)M1",
[
"computed using Magma V2.23-4     Thu Oct 19 2017 17:46:11 on schedir\n",
"[Seed = 1959126426]\n",
"Total time: 2871.289 seconds, Total memory usage: 2133.88MB"
],
[95126814720,95126814720,95126814720,95126814720,1509949440,1509949440,
1509949440,1509949440,6291456,6291456,50331648,50331648,352321536,352321536,
7077888,11010048,11010048,65536,393216,393216,98304,98304,1572864,1572864,
2949120,2949120,2949120,2949120,47185920,47185920,47185920,47185920,196608,
196608,196608,196608,32768,32768,98304,98304,16384,131072,131072,196608,524288
,524288,262144,65536,262144,262144,786432,786432,6291456,6291456,6291456,
6291456,18874368,18874368,18874368,18874368,8192,8192,16384,16384,16384,16384,
16384,131072,65536,65536,65536,262144,262144,393216,393216,393216,393216,
1572864,1572864,1572864,1572864,262144,262144,98304,98304,16384,16384,4096,
4096,8192,16384,16384,8192,3072,3072,3072,3072,32768,32768,196608,196608,
196608,196608,32768,32768,196608,196608,196608,196608,16384,16384,98304,98304,
98304,98304,9216,9216,9216,9216,138240,138240,138240,138240,864,10368,10368,
10368,10368,768,768,2304,2304,9216,9216,9216,9216,27648,27648,27648,27648,1536
,1536,1536,1536,768,768,4096,12288,49152,49152,8192,1024,1024,49152,49152,
16384,16384,2048,2048,1024,1024,1024,8192,8192,8192,8192,24576,24576,24576,
24576,3072,3072,1024,1024,1024,1024,8192,8192,8192,8192,3072,3072,24576,24576,
24576,24576,4096,8192,16384,16384,1024,4096,4096,2048,1024,1024,1024,1024,4096
,4096,8192,8192,4096,8192,8192,16384,16384,32768,32768,32768,32768,256,256,128
,512,512,1024,1024,1024,1024,2048,2048,2048,2048,2048,2048,2048,2048,1024,1024
,1024,1024,160,160,160,160,480,480,480,480,768,768,1152,1152,1152,1152,4608,
4608,4608,4608,384,384,2304,2304,2304,2304,1152,1152,1152,1152,96,192,192,768,
768,768,768,768,768,768,768,192,192,192,192,1152,1152,1152,1152,1152,1152,1152
,1152,192,192,384,384,384,384,768,768,768,768,2304,2304,2304,2304,384,384,384,
384,384,384,384,384,96,96,96,96,192,192,192,192,56,56,56,56,56,56,112,112,112,
112,64,64,128,256,256,256,256,256,256,128,128,128,128,512,512,512,512,256,256,
128,256,256,36,36,36,36,80,80,80,80,80,80,80,80,96,96,192,192,192,192,96,96,
192,192,192,192,96,96,48,96,96,48,60,60,60,60],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,13,13,13,11,11,1,1,8,8,8,8,1,1,1,1,11,11,
11,11,11,11,11,11,11,7,7,3,5,5,5,5,1,1,5,5,1,1,1,1,1,1,1,1,11,9,9,9,11,11,11,
13,13,12,12,13,13,5,5,5,5,1,1,1,1,1,1,8,8,12,12,9,10,11,11,11,13,17,17,15,15,
12,12,13,13,13,13,11,11,11,11,11,11,5,8,8,8,1,1,120,120,120,120,120,120,120,
120,125,127,127,127,127,139,139,139,139,137,137,137,137,137,137,137,137,137,
137,137,137,137,137,55,58,59,59,54,42,43,57,57,56,56,70,70,70,72,72,78,78,78,
78,78,78,78,78,76,76,68,68,70,70,78,78,78,78,74,74,78,78,78,78,53,57,56,56,42,
42,42,42,45,45,47,47,59,54,55,55,55,55,55,54,54,59,59,59,59,62,62,63,70,71,68,
68,72,72,78,78,78,78,82,82,82,82,74,74,76,76,239,239,239,239,239,239,239,239,
120,120,117,117,117,117,120,120,120,120,118,118,120,120,120,120,127,127,127,
127,125,117,117,118,118,118,118,120,120,120,120,142,142,143,143,137,137,137,
137,136,136,136,136,143,143,143,143,143,143,137,137,137,137,137,137,137,137,
143,143,143,143,142,142,142,142,131,131,130,130,136,136,137,137,321,321,322,
322,322,322,322,322,322,322,153,153,154,157,157,151,151,149,149,194,194,192,
192,189,189,189,189,188,188,206,208,208,348,348,348,348,235,235,235,235,239,
239,239,239,265,265,270,270,270,270,266,266,270,270,270,270,260,260,259,257,
257,259,376,376,376,376],[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,
99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,7,8,5,6,1,2
,4,3,15,3,4,1,2,16,17,15,15,5,6,7,8,1,2,3,4,14,13,11,12,9,10,147,148,149,150,
151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,
170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,
189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,
208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,
227,228,229,230,231,232,233,234,235,236,237,238,239,240,23,24,26,25,28,27,32,
31,30,29,52,51,57,58,59,60,59,60,58,57,44,85,84,77,76,74,75,81,80,78,79,19,20,
21,22,30,29,32,31,25,26,27,28,40,39,35,36,34,33,53,54,55,56,57,58,60,59,108,
109,106,107,101,100,102,103,96,97,94,95,113,112,114,115,314,315,318,319,316,
317,320,321,322,323,325,324,326,327,328,329,330,331,332,333,334,336,335,337,
338,339,340,341,342,343,344,345,126,125,127,128,350,351,352,353,354,355,356,
357,171,172,167,168,169,170,181,182,186,185,183,184,155,154,148,149,150,148,
239,240,237,238],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23
,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49
,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75
,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,
101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,
120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,
139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,
158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,
177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,
196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,
215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,5,6,8,
7,3,4,1,2,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,
258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,
277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,
296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,
315,318,319,316,317,320,321,322,323,324,325,326,327,328,329,330,331,332,333,
334,336,335,337,338,339,340,341,342,343,344,345,346,347,348,349,25,26,28,27,32
,31,30,29,358,359,360,361,362,363,364,365,366,367,368,369,370,371,375,373,374,
372,120,121,123,122],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,
157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,
176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,
195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,
214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,
233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,
252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,
271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,
290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,
309,310,311,312,313,17,16,14,13,14,13,4,3,1,2,325,324,326,327,328,329,330,331,
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]],
0,
[(372,375),(335,336),(324,325),(316,318)(317,319),(19,20)(21,22)(25,27)(26,28)
(29,31)(30,32)(86,87)(91,92)(94,95)(96,97)(100,102)(101,103)(106,109)(107,108)
(112,113)(114,115)(158,159)(161,162)(163,165)(164,166)(167,169)(168,170)(173,
174)(177,179)(178,180)(183,185)(184,186)(243,245)(244,246)(247,249)(248,250)(
272,273)(274,275)(276,278)(277,279)(280,282)(281,283)(298,301)(299,300)(302,
305)(303,304)(306,307)(308,309)(310,311)(312,313)(327,328)(333,334)(337,339)(
338,340)(344,345)(350,353)(351,352)(354,356)(355,357)(360,362)(361,363)(366,
369)(367,368)],
["ConstructProj",[["(2^(1+8)x2^6):S6(2)",[]],["2.F4(2)M1",[]]]]);
ALF("2.F4(2)M1","S6(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,
12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,
13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,
14,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,17,17,17,17,17,18,18,
18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,
20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,
21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,24,24,24,
24,24,24,24,24,24,24,24,24,24,25,25,25,25,26,26,26,26,26,26,26,26,27,27,
27,27,27,27,28,28,28,28,28,28,29,29,29,29,29,29,30,30,30,30]);
ALF("2.F4(2)M1","(2^(1+8)x2^6):S6(2)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,
10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,
23,23,24,25,25,26,27,28,28,29,29,30,30,31,31,32,32,33,33,34,35,36,36,37,
37,38,39,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50,51,
52,53,53,54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,64,65,65,
66,66,67,67,68,68,69,69,70,70,71,72,72,73,73,74,74,75,75,76,76,77,77,78,
78,79,79,80,80,81,81,82,82,83,84,85,86,87,88,89,90,90,91,91,92,92,93,94,
94,95,95,96,96,97,97,98,98,99,99,100,100,101,102,103,103,104,104,105,105,
106,106,107,107,108,109,110,110,111,112,112,113,114,114,115,115,116,117,
118,118,119,120,120,121,121,122,122,123,123,124,124,125,126,127,128,128,
129,129,130,130,131,131,132,132,133,133,134,134,135,135,136,136,137,137,
138,138,139,139,140,140,141,141,142,142,143,143,144,144,145,145,146,146,
147,147,148,148,149,149,150,151,151,152,152,153,153,154,154,155,155,156,
156,157,157,158,158,159,159,160,160,161,161,162,162,163,163,164,164,165,
165,166,166,167,167,168,168,169,169,170,170,171,171,172,172,173,173,174,
174,175,175,176,176,177,177,178,178,179,179,180,180,181,181,182,183,184,
185,186,187,187,188,188,189,189,190,190,191,191,192,192,193,193,194,195,
195,196,196,197,197,198,198,199,199,200,200,201,201,202,202,203,203,204,
204,205,205,206,206,207,207,208,208,209,210,211,212,213,213,214,214]);
ALF("2.F4(2)M1","2.F4(2)",[1,2,3,4,5,6,8,7,9,10,7,8,3,4,17,20,19,27,20,19,
33,34,9,10,24,23,25,26,7,8,4,3,24,23,26,25,32,31,33,34,37,29,30,27,21,22,
18,28,10,9,21,22,10,9,7,8,9,10,5,6,37,39,35,36,33,34,37,17,27,29,30,19,20,
18,18,21,22,7,8,9,10,9,10,31,32,30,29,39,38,37,33,34,27,71,72,76,75,30,29,
17,17,20,19,32,31,26,25,24,23,28,37,33,34,9,10,55,54,46,47,11,12,43,42,99,
50,51,15,16,112,111,97,98,44,45,57,56,13,14,48,49,49,48,56,57,60,61,37,38,
18,28,39,80,81,35,36,30,29,68,69,80,71,72,33,34,37,37,23,24,32,31,73,74,
76,75,70,80,33,34,37,37,77,78,25,26,31,32,38,39,29,30,79,68,69,70,74,73,
77,78,28,39,31,32,37,32,31,35,36,21,22,28,28,84,83,82,79,81,76,75,72,71,
37,37,31,32,39,39,35,36,77,78,73,74,91,92,93,94,89,90,40,41,58,59,101,102,
106,105,42,43,55,54,110,109,58,59,46,47,52,53,63,62,117,114,113,110,109,
95,96,59,58,54,55,112,111,115,116,57,56,48,49,104,103,107,108,116,115,108,
107,103,104,61,60,56,57,60,61,45,44,104,103,108,107,98,97,112,111,162,161,
157,158,116,115,60,61,163,164,126,125,126,125,126,125,64,65,137,138,82,70,
79,84,83,78,77,136,135,133,134,69,68,79,79,83,84,82,73,74,144,143,85,86,
148,147,150,149,89,90,94,93,155,156,101,102,114,113,159,160,114,113,105,
106,120,119,121,100,118,122,129,130,168,167],[
"fusion map is unique up to table automorphisms,\n",
"map is compatible with F4(2)M1 -> F4(2)"
]);

MOT("F4(2)M2",
[
"2nd maximal subgroup of F4(2),\n",
"differs from F4(2)M1 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(2^(1+8)x2^6):S6(2)"]]);
ALF("F4(2)M2","F4(2)",[1,3,2,4,5,4,3,10,12,16,12,18,5,13,14,4,3,13,14,19,
18,21,17,16,11,9,15,5,11,5,4,5,2,21,23,20,18,21,10,16,17,12,9,11,4,5,5,19,
17,23,22,21,18,16,41,43,17,10,12,19,14,13,15,21,18,5,32,28,7,26,57,30,8,
62,54,25,31,6,27,27,31,33,21,22,9,15,23,44,46,20,17,38,44,41,18,21,13,19,
40,43,39,44,18,21,42,14,19,22,23,17,45,38,39,40,42,15,23,19,21,19,20,11,
15,48,47,45,46,43,41,21,19,23,20,42,40,51,53,52,24,34,59,61,26,32,63,34,
28,29,35,67,65,63,55,34,32,62,64,31,27,58,60,64,60,58,33,31,33,25,58,60,
54,62,90,88,64,33,93,73,73,73,37,78,79,47,39,45,48,42,77,76,38,45,48,47,
40,83,50,84,85,52,53,89,59,65,91,65,61,68,69,56,66,70,75,95],[
"fusion (2^(1+8)x2^6):S6(2) -> F4(2) mapped under F4(2).2"
]);

MOT("2.F4(2)M2",
[
"2nd maximal subgroup of 2.F4(2),\n",
"differs from 2.F4(2)M1 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2.F4(2)M1"]]);
ALF("2.F4(2)M2","2.F4(2)",[1,2,5,6,3,4,8,7,9,10,7,8,5,6,18,22,21,28,22,21,
31,32,9,10,24,23,26,25,7,8,6,5,24,23,25,26,34,33,31,32,37,29,30,28,19,20,
17,27,10,9,19,20,10,9,7,8,9,10,3,4,37,39,35,36,31,32,37,18,28,29,30,21,22,
17,17,19,20,7,8,9,10,9,10,33,34,30,29,39,38,37,31,32,28,73,74,78,77,30,29,
18,18,22,21,34,33,25,26,24,23,27,37,31,32,9,10,57,56,48,49,13,14,45,44,
100,52,53,15,16,110,109,95,96,42,43,55,54,11,12,46,47,47,46,54,55,58,59,
37,38,17,27,39,79,81,35,36,30,29,68,69,79,73,74,31,32,37,37,23,24,34,33,
71,72,78,77,70,79,31,32,37,37,75,76,26,25,33,34,38,39,29,30,80,68,69,70,
72,71,75,76,27,39,33,34,37,34,33,35,36,19,20,27,27,84,83,82,80,81,78,77,
74,73,37,37,33,34,39,39,35,36,75,76,71,72,89,90,93,94,91,92,40,41,60,61,
103,104,107,108,44,45,57,56,112,111,60,61,48,49,50,51,63,62,118,116,115,
112,111,97,98,61,60,56,57,110,109,113,114,55,54,46,47,102,101,106,105,114,
113,105,106,101,102,59,58,54,55,58,59,43,42,102,101,105,106,96,95,110,109,
160,159,155,156,114,113,58,59,165,166,128,127,128,127,128,127,66,67,137,
138,82,70,80,84,83,76,75,136,135,133,134,69,68,80,80,83,84,82,71,72,146,
145,87,88,148,147,149,150,91,92,94,93,157,158,103,104,116,115,161,162,116,
115,108,107,120,119,121,99,117,122,131,132,169,170],[
"fusion 2.F4(2)M1 -> 2.F4(2) mapped under 2.F4(2).2"
]);

MOT("3^6:L3(3)",
[
"2nd maximal subgroup of S6(3),\n",
"origin: Dixon's Algorithm"
],
[4094064,314928,314928,52488,26244,17496,17496,3888,3888,3888,972,972,972,972,
972,972,648,648,648,324,324,324,1458,1458,1458,243,486,486,486,486,486,486,81,
81,81,27,27,72,72,72,36,36,36,54,54,54,54,54,54,54,54,54,24,24,24,24,24,24,13,
13,13,13],
[,[1,3,2,4,5,7,6,1,3,2,5,5,4,4,3,2,4,6,7,5,7,6,23,25,24,26,28,27,30,29,32,31,
33,35,34,37,36,8,9,10,17,18,19,23,25,24,29,30,31,32,28,27,38,40,39,38,40,39,61
,62,60,59],[1,1,1,1,1,1,1,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,1,1,1,1,2,3,3,2,2,3,1,
3,2,7,6,38,38,38,38,38,38,8,8,8,15,16,16,15,15,16,53,53,53,56,56,56,59,60,61,
62],,,,,,,,,,[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,
51,52,56,57,58,53,54,55,1,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[12,12,12,12,12,12,12,4,4,4,4
,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1
,1,1,0,0,0,0,0,0,-1,-1,-1,-1],[13,13,13,13,13,13,13,-3,-3,-3,-3,-3,-3,-3,-3,-3
,-3,-3,-3,-3,-3,-3,4,4,4,4,4,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0
,-1,-1,-1,-1,-1,-1,0,0,0,0],[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,-2,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,E(13)+E(13)^3+E(13)^9,E(13)^4+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6,
E(13)^7+E(13)^8+E(13)^11],
[GALOIS,[4,4]],
[GALOIS,[4,7]],
[GALOIS,[4,2]],[26,26,26,26,26,26,26,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0
,0,0,0,0,0,0,0,0],[26,26,26,26,26,26,26,-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,-1,0,0,0,0,0,0,1,1,1,1,1,1,1,
1,1,E(8)+E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3
,0,0,0,0],
[GALOIS,[9,5]],[27,27,27,27,27,27,27,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,1,1,
1,1],[39,39,39,39,39,39,39,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,
3,3,3,3,3,3,3,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1
,1,0,0,0,0],[13,5*E(3)-4*E(3)^2,-4*E(3)+5*E(3)^2,-5,4,-E(3)+2*E(3)^2,
2*E(3)-E(3)^2,-3,5*E(3)+4*E(3)^2,4*E(3)+5*E(3)^2,2*E(3)-2*E(3)^2,
-2*E(3)+2*E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,-3*E(3),-3*E(3)^2,3,-2*E(3)-E(3)^2,
-E(3)-2*E(3)^2,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,4,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,1,
1,1,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,-2,-2,1,1,1,E(3)^2,E(3),1,E(3)^2,E(3),1,E(3),
E(3)^2,0,2*E(3)+E(3)^2,E(3)+2*E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,0,0,
E(3)-E(3)^2,-E(3)+E(3)^2,-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),0,0,0,0],
[GALOIS,[13,2]],[13,5*E(3)-4*E(3)^2,-4*E(3)+5*E(3)^2,-5,4,-E(3)+2*E(3)^2,
2*E(3)-E(3)^2,5,-3*E(3)-4*E(3)^2,-4*E(3)-3*E(3)^2,2*E(3)^2,2*E(3),
-E(3)+3*E(3)^2,3*E(3)-E(3)^2,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-1,2*E(3)+3*E(3)^2,
3*E(3)+2*E(3)^2,2,-E(3),-E(3)^2,4,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,1,1,1,
2*E(3)-E(3)^2,-E(3)+2*E(3)^2,-2,-2,1,1,1,E(3)^2,E(3),1,E(3)^2,E(3),1,E(3),
E(3)^2,2,-E(3)^2,-E(3),-E(3),-E(3)^2,2*E(3),2*E(3)^2,-1,-1,1,E(3)^2,E(3),1,
E(3)^2,E(3),0,0,0,0],
[GALOIS,[15,2]],[26,10*E(3)-8*E(3)^2,-8*E(3)+10*E(3)^2,-10,8,-2*E(3)+4*E(3)^2
,4*E(3)-2*E(3)^2,2,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2*E(3)^2,2*E(3),2,2,2,
2*E(3)^2,2*E(3),2,2*E(3)^2,2*E(3),-1,-5*E(3)-2*E(3)^2,-2*E(3)-5*E(3)^2,2,
E(3)+4*E(3)^2,4*E(3)+E(3)^2,-1,-1,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,-1,-1,-1,
-E(3)^2,-E(3),2,2*E(3)^2,2*E(3),2,2*E(3),2*E(3)^2,-1,-E(3),-E(3)^2,-1,-1,-E(3)
,-E(3)^2,-E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[17,2]],[26,10*E(3)-8*E(3)^2,-8*E(3)+10*E(3)^2,-10,8,-2*E(3)+4*E(3)^2
,4*E(3)-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2*E(3),-2*E(3)^2,-2*E(3)^2,-2*E(3),-2,
-2,-2,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),-1,-5*E(3)-2*E(3)^2,
-2*E(3)-5*E(3)^2,2,E(3)+4*E(3)^2,4*E(3)+E(3)^2,-1,-1,-2*E(3)+E(3)^2,
E(3)-2*E(3)^2,-1,-1,-1,-E(3)^2,-E(3),0,0,0,0,0,0,1,E(3),E(3)^2,1,1,E(3),E(3)^2
,E(3),E(3)^2,-E(8)-E(8)^3,-E(24)-E(24)^19,-E(24)^11-E(24)^17,E(8)+E(8)^3,
E(24)+E(24)^19,E(24)^11+E(24)^17,0,0,0,0],
[GALOIS,[19,7]],
[GALOIS,[19,11]],
[GALOIS,[19,5]],[39,15*E(3)-12*E(3)^2,-12*E(3)+15*E(3)^2,-15,12,
-3*E(3)+6*E(3)^2,6*E(3)-3*E(3)^2,-1,7*E(3)+4*E(3)^2,4*E(3)+7*E(3)^2,
4*E(3)-2*E(3)^2,-2*E(3)+4*E(3)^2,-1,-1,-5*E(3)-2*E(3)^2,-2*E(3)-5*E(3)^2,5,
-2*E(3)+E(3)^2,E(3)-2*E(3)^2,2,E(3)+4*E(3)^2,4*E(3)+E(3)^2,3,3,3,3,3*E(3)^2,
3*E(3),3*E(3),3*E(3)^2,3*E(3)^2,3*E(3),0,0,0,0,0,-1,-E(3)^2,-E(3),-1,-E(3),
-E(3)^2,-1,-1,-1,-E(3)^2,-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3),1,E(3)^2,E(3),1,
E(3)^2,E(3),0,0,0,0],
[GALOIS,[23,2]],[39,15*E(3)-12*E(3)^2,-12*E(3)+15*E(3)^2,-15,12,
-3*E(3)+6*E(3)^2,6*E(3)-3*E(3)^2,7,-E(3)-4*E(3)^2,-4*E(3)-E(3)^2,-2,-2,
-E(3)+5*E(3)^2,5*E(3)-E(3)^2,-E(3)-4*E(3)^2,-4*E(3)-E(3)^2,1,2*E(3)+5*E(3)^2,
5*E(3)+2*E(3)^2,4,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,3,3,3,3,3*E(3)^2,3*E(3),3*E(3),
3*E(3)^2,3*E(3)^2,3*E(3),0,0,0,0,0,-1,-E(3)^2,-E(3),-1,-E(3),-E(3)^2,1,1,1,
E(3)^2,E(3),E(3),E(3)^2,E(3)^2,E(3),-1,-E(3)^2,-E(3),-1,-E(3)^2,-E(3),0,0,0,0]
,
[GALOIS,[25,2]],[52,20*E(3)-16*E(3)^2,-16*E(3)+20*E(3)^2,-20,16,
-4*E(3)+8*E(3)^2,8*E(3)-4*E(3)^2,-4,-4*E(3),-4*E(3)^2,-4*E(3),-4*E(3)^2,
-4*E(3)^2,-4*E(3),-4,-4,-4,-4*E(3)^2,-4*E(3),-4,-4*E(3)^2,-4*E(3),7,
-E(3)-4*E(3)^2,-4*E(3)-E(3)^2,4,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,5*E(3)-E(3)^2,
-E(3)+5*E(3)^2,2*E(3)+5*E(3)^2,5*E(3)+2*E(3)^2,1,1,1,E(3)^2,E(3),0,0,0,0,0,0,
-1,-E(3),-E(3)^2,-1,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[27,2]],[78,-30,-30,15,6,-3,-3,-2,10,10,-8,-8,1,1,-2,-2,7,1,1,-2,1,1,
6,-3,-3,0,0,0,-3,-3,3,3,0,0,0,0,0,2,2,2,-1,-1,-1,-2,1,1,1,1,1,1,-2,-2,0,0,0,0,
0,0,0,0,0,0],[78,-30,-30,15,6,-3,-3,14,2,2,2,2,-7,-7,-4,-4,-1,5,5,2,-1,-1,6,-3
,-3,0,0,0,-3,-3,3,3,0,0,0,0,0,2,2,2,-1,-1,-1,2,-1,-1,-1,-1,-1,-1,2,2,0,0,0,0,0
,0,0,0,0,0],[78,-30,-30,15,6,-3,-3,6,-10*E(3)-2*E(3)^2,-2*E(3)-10*E(3)^2,
2*E(3)+4*E(3)^2,4*E(3)+2*E(3)^2,E(3)+5*E(3)^2,5*E(3)+E(3)^2,6*E(3)^2,6*E(3),3,
-5*E(3)-E(3)^2,-E(3)-5*E(3)^2,0,E(3)-E(3)^2,-E(3)+E(3)^2,6,-3,-3,0,0,0,-3,-3,3
,3,0,0,0,0,0,-2,-2,-2,1,1,1,0,-E(3)+E(3)^2,E(3)-E(3)^2,E(3)-E(3)^2,
-E(3)+E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[31,2]],[104,40*E(3)-32*E(3)^2,-32*E(3)+40*E(3)^2,-40,32,
-8*E(3)+16*E(3)^2,16*E(3)-8*E(3)^2,-8,-8,-8,2*E(3)-4*E(3)^2,-4*E(3)+2*E(3)^2,
2*E(3)-4*E(3)^2,-4*E(3)+2*E(3)^2,-4*E(3)+2*E(3)^2,2*E(3)-4*E(3)^2,4,4,4,-2,-2,
-2,5,7*E(3)+E(3)^2,E(3)+7*E(3)^2,-1,-2*E(3)-5*E(3)^2,-5*E(3)-2*E(3)^2,
E(3)-2*E(3)^2,-2*E(3)+E(3)^2,4*E(3)+E(3)^2,E(3)+4*E(3)^2,-1,-1,-1,-E(3)^2,
-E(3),0,0,0,0,0,0,1,1,1,E(3)^2,E(3),E(3),E(3)^2,E(3)^2,E(3),0,0,0,0,0,0,0,0,0,
0],
[GALOIS,[33,2]],[104,40*E(3)-32*E(3)^2,-32*E(3)+40*E(3)^2,-40,32,
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-2*E(3)+4*E(3)^2,4*E(3)-2*E(3)^2,4*E(3)-2*E(3)^2,-2*E(3)+4*E(3)^2,-4,-4,-4,2,2
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E(3)-2*E(3)^2,-2*E(3)+E(3)^2,4*E(3)+E(3)^2,E(3)+4*E(3)^2,-1,-1,-1,-E(3)^2,
-E(3),0,0,0,0,0,0,-1,-1,-1,-E(3)^2,-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3),0,0,0,0,0
,0,0,0,0,0],
[GALOIS,[35,2]],[156,48,48,12,3,-6,-6,20,8,8,-1,-1,8,8,2,2,-4,2,2,-1,-4,-4,12
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0,0,0,0,0],[156,48,48,12,3,-6,-6,4,16,16,7,7,-2,-2,4,4,4,-2,-2,-5,-2,-2,12,3,3
,-3,-3,-3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,1,1,1,-2,-2,1,1,0,0,0,0,0,0,0,0,0
,0],[156,-60,-60,30,12,-6,-6,-12,-12,-12,6,6,6,6,6,6,-6,-6,-6,0,0,0,12,-6,-6,0
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156,48,48,12,3,-6,-6,-12,8*E(3)+16*E(3)^2,16*E(3)+8*E(3)^2,5*E(3)+E(3)^2,
E(3)+5*E(3)^2,4*E(3)+2*E(3)^2,2*E(3)+4*E(3)^2,6*E(3),6*E(3)^2,0,
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E(3)-E(3)^2,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[40,2]],[208,80*E(3)-64*E(3)^2,-64*E(3)+80*E(3)^2,-80,64,
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[GALOIS,[42,2]],[234,36*E(3)-18*E(3)^2,-18*E(3)+36*E(3)^2,-9,-9,-9*E(3)^2,
-9*E(3),-6,-12*E(3)+6*E(3)^2,6*E(3)-12*E(3)^2,3,3,3,3,-6,-6,3,3*E(3),3*E(3)^2,
3,3*E(3)^2,3*E(3),0,0,0,0,0,0,0,0,0,0,3,3*E(3),3*E(3)^2,0,0,-2,-2*E(3),
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[GALOIS,[44,2]],[234,36*E(3)-18*E(3)^2,-18*E(3)+36*E(3)^2,-9,-9,-9*E(3)^2,
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[GALOIS,[46,2]],[312,96,96,24,6,-12,-12,-8,-8*E(3),-8*E(3)^2,-2*E(3)-6*E(3)^2
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[GALOIS,[48,2]],[312,96,96,24,6,-12,-12,8,8*E(3)^2,8*E(3),6*E(3)+2*E(3)^2,
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[GALOIS,[50,2]],[312,-120,-120,60,24,-12,-12,-8,-8*E(3),-8*E(3)^2,
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[GALOIS,[54,2]],[468,72*E(3)-36*E(3)^2,-36*E(3)+72*E(3)^2,-18,-18,-18*E(3)^2,
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[GALOIS,[56,2]],[624,192,192,48,12,-24,-24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,
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6,12*E(3)-6*E(3)^2,-6*E(3)+12*E(3)^2,-3,-3,-3,-3,6,6,-3,-3*E(3),-3*E(3)^2,-3,
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[GALOIS,[61,2]]],
[(2,3)(6,7)(9,10)(11,12)(13,14)(15,16)(18,19)(21,22)(24,25)(27,28)(29,30)(31,
32)(34,35)(36,37)(39,40)(42,43)(45,46)(47,48)(49,50)(51,52)(54,55)(57,58),
(53,56)(54,57)(55,58),(59,60)(61,62),(59,61,60,62)]);
ALF("3^6:L3(3)","S6(3)",[1,4,5,6,7,9,8,2,15,16,21,22,19,20,17,18,23,25,26,
24,29,28,7,8,9,10,36,37,35,34,38,39,10,37,36,40,41,13,47,46,51,56,55,24,
28,29,62,63,67,66,64,65,32,70,69,32,70,69,58,58,57,57],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("3^6:L3(3)","L3(3)",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,
3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,9,10,
11,12]);

MOT("3^(3+4):2(S4xA4)",
[
"3rd maximal subgroup of S6(3),\n",
"origin: Dixon's Algorithm"
],
[1259712,314928,314928,209952,104976,4374,4374,4374,972,15552,3888,3888,2592,
1296,2592,648,648,432,216,34992,8748,8748,5832,2916,3888,972,972,648,324,486,
486,486,34992,8748,8748,5832,2916,3888,972,972,648,324,486,486,486,288,144,864
,432,36,72,36,72,36,1944,243,216,1944,1944,243,243,216,216,36,36,36,486,243,54
,486,486,243,243,27,54,54,486,243,54,486,486,243,243,27,54,54,3888,3888,3888,
3888,3888,3888,3888,3888,3888,162,162,162,144,144,144,72,72,72,324,324,324,324
,324,324,324,324,324,54,54,54,324,324,324,324,324,324,324,324,324,54,54,54,96,
96,16,24,24,24,24],
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,44,45,43,20,23,23,21,24,22,22,21,24,31,32,30,46,46,46,53,53,51,51],[1,1,1,1,1
,1,1,1,1,10,10,10,10,10,15,15,15,15,15,1,1,1,1,1,10,10,10,10,10,3,3,3,1,1,1,1,
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,87,87,87,95,95,95,129,130,131,129,130,129,130]],
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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,
E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3),E(3)^2,E(3)^2
,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,
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E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,1,1,1,E(3),E(3),E(3)^2,E(3)^2
],
[TENSOR,[2,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,
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-1],
[TENSOR,[2,5]],
[TENSOR,[2,6]],
[TENSOR,[4,5]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
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0,0,0,0],
[TENSOR,[9,2]],
[TENSOR,[9,3]],[6,6,6,6,6,6,6,6,6,6,6,6,6,6,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,
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ALF("3^(3+4):2(S4xA4)","S6(3)",[1,4,5,6,7,7,8,9,10,2,17,18,23,24,11,43,44,
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19,26,24,21,23,29,66,64,62,32,32,33,69,69,70,70],[
"fusion map is unique up to table automorphisms"
]);

MOT("A4xU4(2)",
0,
0,
0,
0,
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(52,72)(53,73)(54,74)(55,75)(56,76)(57,77)(58,78)(59,79)(60,80),(4,5)(11,12)
(13,14)(17,18)(19,20)(24,25)(31,32)(33,34)(37,38)(39,40)(44,45)(51,52)(53,54)
(57,58)(59,60)(64,65)(71,72)(73,74)(77,78)(79,80)],
["ConstructDirectProduct",[["A4"],["U4(2)"]]]);
ARC("A4xU4(2)","projectives",["2.(A4xU4(2))",[[8,0,0,4*E(3)-2*E(3)^2,
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ALF("A4xU4(2)","3xU4(2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
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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]);

MOT("2.(A4xU4(2))",
[
"4th maximal subgroup of S6(3),\n",
"origin: Dixon's Algorithm"
],
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432,432,108,108,108,108,36,54,54,54,54,72,72,72,72],
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36,36,36,37,38,39,42,42,1,2,3,4,1,2,1,2,1,2,1,2,14,13,15,16,17,3,3,3,3,3,3,3,3
,4,5,6,7,8,13,14,14,13,1,2,3,4,1,2,1,2,1,2,1,2,14,13,15,16,17,3,3,3,3,3,3,3,3,
4,5,6,7,8,14,13,13,14],,[1,2,3,4,7,8,5,6,9,10,11,12,13,14,15,1,2,20,21,18,19,
23,22,25,24,26,29,30,27,28,33,34,31,32,35,36,37,39,38,40,41,42,43,35,46,45,48,
47,49,50,52,51,54,53,89,90,91,92,95,96,93,94,97,98,99,100,101,102,103,89,90,
108,109,106,107,111,110,112,113,114,117,118,115,116,121,122,119,120,55,56,57,
58,61,62,59,60,63,64,65,66,67,68,69,55,56,74,75,72,73,77,76,78,79,80,83,84,81,
82,87,88,85,86]],
0,
[(  5,  7)(  6,  8)( 18, 20)( 19, 21)( 22, 23)( 24, 25)( 27, 29)( 28, 30)
( 31, 33)( 32, 34)( 38, 39)( 45, 46)( 47, 48)( 51, 52)( 53, 54)( 59, 61)
( 60, 62)( 72, 75)( 73, 74)( 76, 77)( 78, 79)( 81, 83)( 82, 84)( 85, 88)
( 86, 87)( 93, 95)( 94, 96)(106,109)(107,108)(110,111)(112,113)(115,117)
(116,118)(119,122)(120,121),
( 55, 89)( 56, 90)( 57, 91)( 58, 92)( 59, 93)( 60, 94)( 61, 95)( 62, 96)
( 63, 97)( 64, 98)( 65, 99)( 66,100)( 67,101)( 68,102)( 69,103)( 70,104)
( 71,105)( 72,107)( 73,106)( 74,109)( 75,108)( 76,110)( 77,111)( 78,113)
( 79,112)( 80,114)( 81,115)( 82,116)( 83,117)( 84,118)( 85,120)( 86,119)
( 87,122)( 88,121)],
["ConstructProj",[["A4xU4(2)",[]],["2.(A4xU4(2))",[]]]]);
ALF("2.(A4xU4(2))","A4xU4(2)",[1,1,2,3,4,4,5,5,6,6,7,7,8,8,9,
10,10,11,11,12,12,13,14,15,15,16,17,17,18,18,19,19,20,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,41,42,43,44,44,45,45,46,
46,47,47,48,48,49,50,50,51,51,52,52,53,54,55,55,56,57,57,58,58,59,59,60,
60,61,61,62,63,64,64,65,65,66,66,67,67,68,68,69,70,70,71,71,72,72,73,74,
75,75,76,77,77,78,78,79,79,80,80]);
ALF("2.(A4xU4(2))","S6(3)",[1,2,2,13,4,17,5,18,6,23,7,24,12,11,32,14,42,
17,15,18,16,19,20,21,22,51,34,62,35,63,48,43,49,44,11,12,3,43,44,45,50,13,
33,68,48,49,52,53,54,27,73,74,46,47,4,15,17,46,6,20,7,21,9,26,8,28,43,48,
69,60,71,23,20,22,24,29,26,25,28,56,36,64,39,67,53,45,50,54,5,16,18,47,7,
22,6,19,8,25,9,29,44,49,70,61,72,21,24,23,19,25,28,26,29,55,38,66,37,65,
50,54,52,45],[
"fusion map is unique up to table automorphisms"
]);
ALF("2.(A4xU4(2))","3xU4(2)",[1,1,2,3,4,4,5,5,6,6,7,7,8,8,9,10,10,11,11,
12,12,13,14,15,15,16,17,17,18,18,19,19,20,20,1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,21,22,23,24,24,25,25,26,26,27,27,28,28,29,30,
30,31,31,32,32,33,34,35,35,36,37,37,38,38,39,39,40,40,41,41,42,43,44,44,
45,45,46,46,47,47,48,48,49,50,50,51,51,52,52,53,54,55,55,56,57,57,58,58,
59,59,60,60]);
ALN("2.(A4xU4(2))",["S6(3)C2A","S6(3)N2A"]);

MOT("2^(2+6):3^3:S3",
[
"5th maximal subgroup of S6(3),\n",
"origin: Dixon's Algorithm"
],
[41472,13824,384,2304,2304,384,648,648,216,216,432,432,432,432,72,72,3456,3456
,864,864,216,216,3456,3456,1728,1728,864,864,432,432,216,216,108,108,288,288,
288,288,144,144,144,144,96,96,36,12,9,9,576,192,576,192,144,144,144,144,48,48,
36,36,36,36,96,32,144,144,144,144,48,48,36,36,36,36,24,24],
[,[1,1,1,2,2,2,8,7,8,7,11,11,11,11,12,12,18,17,20,19,22,21,18,17,18,17,20,19,
20,19,22,21,22,21,26,25,26,25,28,27,28,27,24,23,45,45,48,47,1,1,2,2,19,20,18,
17,19,20,21,22,8,7,6,6,27,28,24,23,27,28,31,32,10,9,44,43],[1,2,3,4,5,6,1,1,2,
2,1,2,2,2,4,5,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,5,5,4,4,5,5,6,6,1,3,7,8,
49,50,51,52,49,49,49,49,50,50,49,49,49,49,63,64,51,51,51,51,52,52,51,51,51,51,
63,63]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-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,-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],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,E(3),E(3)^2,E(3)^2
,E(3),E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3)^2,E(3),E(3)^2,E(3),E(3),E(3)^2,
E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3)^2,E(3),E(3)^2,E(3),E(3),E(3)^2,1,1,
E(3),E(3)^2,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3)^2,E(3),1,1,1,1,
E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3)^2,E(3),1,1,E(3),E(3)^2],
[TENSOR,[4,4]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],
[TENSOR,[3,4]],
[TENSOR,[3,5]],[6,6,6,6,6,6,6,6,6,6,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3*E(3)^2,3*E(3),3*E(3)^2,3*E(3),0,0,0,0,0,0,
-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,
2*E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,
-E(3)+E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,2*E(3)+E(3)^2,
E(3)+2*E(3)^2,2*E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,
-E(3)-2*E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,
-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,0,0,0,-1,-1,-1,-1,-1,-1,-E(3)^2,-E(3),-1,-1,
-E(3)^2,-E(3),-E(3)^2,-E(3),-1,-1,-1,-1,-E(3)^2,-E(3),-1,-1,-E(3)^2,-E(3),
-E(3)^2,-E(3),-E(3)^2,-E(3)],
[GALOIS,[11,2]],
[TENSOR,[11,2]],
[TENSOR,[12,2]],
[TENSOR,[12,5]],
[TENSOR,[11,4]],
[TENSOR,[12,7]],
[TENSOR,[11,6]],
[TENSOR,[11,5]],
[TENSOR,[12,4]],
[TENSOR,[11,7]],
[TENSOR,[12,6]],[9,9,-3,5,5,1,0,0,0,0,3,3,3,3,-1,-1,6,6,3,3,0,0,6,6,6,6,3,3,3
,3,0,0,0,0,2,2,2,2,-1,-1,-1,-1,-2,-2,0,0,0,0,-3,1,-3,1,-3,-3,0,0,1,1,0,0,0,0,
-3,1,-3,-3,0,0,1,1,0,0,0,0,0,0],
[TENSOR,[23,2]],
[TENSOR,[23,5]],
[TENSOR,[23,4]],
[TENSOR,[23,7]],
[TENSOR,[23,6]],[18,18,-6,10,10,2,0,0,0,0,-3,-3,-3,-3,1,1,-6,-6,6,6,0,0,-6,-6
,-6,-6,6,6,6,6,0,0,0,0,-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],
[TENSOR,[29,5]],
[TENSOR,[29,4]],[27,27,3,3,3,-5,0,0,0,0,0,0,0,0,0,0,9,9,0,0,0,0,9,9,9,9,0,0,0
,0,0,0,0,0,-3,-3,-3,-3,0,0,0,0,1,1,0,0,0,0,-3,-3,-3,-3,0,0,-3,-3,0,0,0,0,0,0,1
,1,0,0,-3,-3,0,0,0,0,0,0,1,1],
[TENSOR,[32,2]],[27,27,-1,-9,-9,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,-1,0,0,-9,3,-9,3,0,0,0,0,0,0,0,0,0,0,3,-1,0
,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[34,2]],
[TENSOR,[32,5]],
[TENSOR,[32,4]],
[TENSOR,[32,7]],
[TENSOR,[32,6]],[54,54,-2,-18,-18,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[12,-4,0,4,-4,0,3,3,-1,-1,-3,5,-1,-1,1,-1,0,0,-3,-3,3,3
,8,8,-4,-4,5,5,-1,-1,-1,-1,-1,-1,-2,-2,2,2,1,1,-1,-1,0,0,0,0,0,0,-2,2,2,-2,1,1
,-2,-2,-1,-1,1,1,1,1,0,0,-1,-1,2,2,1,1,-1,-1,-1,-1,0,0],
[TENSOR,[41,2]],
[TENSOR,[41,4]],
[TENSOR,[41,5]],
[TENSOR,[41,6]],
[TENSOR,[41,7]],[12,-4,0,4,-4,0,3*E(3)^2,3*E(3),-E(3)^2,-E(3),3,-1,
-E(3)+3*E(3)^2,3*E(3)-E(3)^2,1,-1,-8*E(3)-4*E(3)^2,-4*E(3)-8*E(3)^2,
-4*E(3)+E(3)^2,E(3)-4*E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,-4*E(3)^2,-4*E(3),
-4,-4,4*E(3)+E(3)^2,E(3)+4*E(3)^2,-E(3)^2,-E(3),2*E(3)+3*E(3)^2,
3*E(3)+2*E(3)^2,-E(3)^2,-E(3),-2*E(3),-2*E(3)^2,2*E(3),2*E(3)^2,E(3)^2,E(3),
-E(3)^2,-E(3),0,0,0,0,0,0,-2,2,2,-2,E(3),E(3)^2,-2,-2,-E(3),-E(3)^2,E(3),
E(3)^2,E(3)^2,E(3),0,0,-E(3),-E(3)^2,2,2,E(3),E(3)^2,-E(3),-E(3)^2,-E(3)^2,
-E(3),0,0],
[GALOIS,[47,2]],
[TENSOR,[47,2]],
[TENSOR,[48,2]],
[TENSOR,[48,5]],
[TENSOR,[47,4]],
[TENSOR,[48,7]],
[TENSOR,[47,6]],
[TENSOR,[47,5]],
[TENSOR,[48,4]],
[TENSOR,[47,7]],
[TENSOR,[48,6]],[24,-8,0,8,-8,0,6,6,-2,-2,3,-5,1,1,-1,1,12,12,6,6,0,0,4,4,-8,
-8,-2,-2,-2,-2,4,4,-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],[24,-8,0,8,-8,0,6*E(3),6*E(3)^2,-2*E(3),
-2*E(3)^2,-3,1,-3*E(3)+E(3)^2,E(3)-3*E(3)^2,-1,1,4*E(3)+8*E(3)^2,
8*E(3)+4*E(3)^2,-4*E(3)-2*E(3)^2,-2*E(3)-4*E(3)^2,-2*E(3)-4*E(3)^2,
-4*E(3)-2*E(3)^2,-4*E(3)+8*E(3)^2,8*E(3)-4*E(3)^2,-8*E(3)^2,-8*E(3),
4*E(3)+6*E(3)^2,6*E(3)+4*E(3)^2,-2*E(3)^2,-2*E(3),-2*E(3),-2*E(3)^2,-2,-2,
2*E(3),2*E(3)^2,-2*E(3),-2*E(3)^2,2*E(3)^2,2*E(3),-2*E(3)^2,-2*E(3),0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[60,2]],
[TENSOR,[60,4]],
[TENSOR,[61,5]],
[TENSOR,[60,5]],
[TENSOR,[61,4]],
[TENSOR,[59,4]],
[TENSOR,[59,5]],[36,-12,0,-4,4,0,0,0,0,0,3,3,-3,-3,-1,1,-12,-12,3,3,0,0,12,12
,0,0,3,3,-3,-3,0,0,0,0,2,2,-2,-2,-1,-1,1,1,0,0,0,0,0,0,-6,-2,6,2,3,3,0,0,1,1,0
,0,0,0,0,0,-3,-3,0,0,-1,-1,0,0,0,0,0,0],
[TENSOR,[68,2]],
[TENSOR,[68,4]],
[TENSOR,[68,5]],
[TENSOR,[68,6]],
[TENSOR,[68,7]],[72,-24,0,-8,8,0,0,0,0,0,-3,-3,3,3,1,-1,12,12,6,6,0,0,-12,-12
,0,0,6,6,-6,-6,0,0,0,0,-2,-2,2,2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[74,5]],
[TENSOR,[74,4]]],
[(7,8)(9,10)(13,14)(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)(47,48)(53,54)(55,56)(57,58)(59,60)
(61,62)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)]);
ALF("2^(2+6):3^3:S3","S6(3)",[1,2,3,11,12,13,8,9,25,26,7,24,21,22,50,54,5,
4,6,6,9,8,16,15,18,17,23,23,19,20,26,25,29,28,44,43,49,48,45,45,52,53,47,
46,10,30,40,41,2,3,13,12,19,20,18,17,27,27,25,26,28,29,32,33,51,51,47,46,
52,53,55,56,55,56,70,69],[
"fusion map is unique up to table automorphisms"
]);

MOT("2xU3(3).2",
[
"7th maximal subgroup of S6(3)"
],
0,
0,
0,
[(15,16)(31,32),(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)],
["ConstructDirectProduct",[["Cyclic",2],["U3(3).2"]]]);
ARC("2xU3(3).2","tomfusion",rec(name:="U3(3):2x2",map:=[1,2,8,7,19,17,25,
37,87,95,3,11,28,79,91,91,6,5,36,30,9,20,35,108,86,89,4,10,32,80,90,90],
text:=[
"fusion map is unique up to table autom."
]));
ALF("2xU3(3).2","G2(4).2",[1,2,4,5,6,6,11,13,14,18,3,7,12,14,19,20,25,25,
28,29,26,26,28,35,32,33,25,26,29,30,33,33],[
"fusion map is unique up to table autom."
]);
ALF("2xU3(3).2","2.S6(2)",[1,4,9,11,13,17,23,29,31,40,6,13,28,32,40,40,2,
4,10,12,14,17,24,30,31,41,6,14,28,33,41,41],[
"fusion map is unique up to table autom."
]);
ALF("2xU3(3).2","S6(3)",[1,2,6,10,13,13,23,31,33,51,3,12,30,33,52,53,3,3,27,
30,11,12,27,59,32,45,3,12,30,33,53,52],[
"fusion map is unique up to table automorphisms"
]);
ALF("2xU3(3).2","U4(3).(2^2)_{133}",[1,2,3,5,6,6,9,11,12,14,27,28,29,31,
34,34,15,15,19,21,17,18,19,26,22,24,36,37,38,40,43,43],[
"fusion map is unique up to table autom."
]);
ALN("2xU3(3).2",["S6(3)C2B","S6(3)N2B"]);

LIBTABLE.LOADSTATUS.ctomaxi5:="userloaded";

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