Quelle  ctomax19.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctomax19.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of some subgroups of
##  groups contained in the library of tables of marks.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctomax19.tbl,v $
#H  Revision 4.9  2012/06/20 14:45:31  gap
#H  added tables and fusions, as documented in ctbldiff.dat
#H      TB
#H
#H  Revision 4.8  2012/04/23 16:16:09  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 4.7  2012/01/30 08:31:54  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.6  2012/01/26 11:18:39  gap
#H  added missing table automorphisms
#H      TB
#H
#H  Revision 4.5  2011/09/28 12:55:44  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - renamed (6x2.U4(2)):2 and (6xU4(2)):2 to 2x(3x2.U4(2)):2 and
#H    2x(3xU4(2)):2, respectively (and changed the constructions accordingly)
#H  - renamed 2.(3^(1+2)+:2S4), 2^2.(7:3xS3), and 2^2.(L2(7)x2)
#H    to 2x3^(1+2)_+:2S4, 7:3xS4, and D8xL3(2), respectively
#H    (and changed the construction accordingly)
#H  - added tables of 2^{3+6}:(L3(2)x3), 2^{1+8}_+:(S3xA5),
#H  - added maxes entry for O8-(2)
#H      TB
#H
#H  Revision 4.4  2011/02/09 16:06:28  gap
#H  replaced tables: 27:2^2 -> D108, 28.2^2 -> D112, D62x2 -> D124;
#H  the old names (used in the library of tables of marks) are still
#H  admissible
#H      TB
#H
#H  Revision 4.3  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 4.2  2010/05/05 13:20:04  gap
#H  - added many class fusions,
#H  - changed several class fusions according to consistency conditions,
#H    after systematic checks of consistency
#H    - with Brauer tables w.r.t. the restriction of characters,
#H    - of subgroup fusions with the corresponding subgroup fusions between
#H      proper factors where the factor fusions are stored,
#H    - of subgroup fusions from maximal subgroups with subgroup fusions of
#H      extensions inside automorphic extensions
#H
#H      TB
#H
#H  Revision 4.1  2010/01/19 17:05:32  gap
#H  added several tables of maximal subgroups of central extensions of
#H  simple groups (many of them were contributed by S. Dany)
#H      TB
#H
##

MOT("3^3:L3(3)",
[
"origin: Dixon's Algorithm"
],
[151632,5832,144,72,486,486,486,81,27,27,27,24,12,18,18,18,8,8,13,13,13,13],
[,[1,2,1,2,5,6,7,8,9,10,11,3,4,5,7,6,12,12,21,22,20,19],[1,1,3,3,1,1,1,1,1,2,2
,12,12,3,3,3,17,18,19,20,21,22],,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,18,17,1,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[12,12,4,4,3,3,3,3,0,0,0,0,0,1,
1,1,0,0,-1,-1,-1,-1],[13,13,-3,-3,4,4,4,4,1,1,1,1,1,0,0,0,-1,-1,0,0,0,0],[16,
16,0,0,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,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]],[26,26,2,2,-1,-1,-1,-1,-1,-1,-1,2,2,-1,-1,-1,0,0,0,0,0,0],[26,
26,-2,-2,-1,-1,-1,-1,-1,-1,-1,0,0,1,1,1,E(8)+E(8)^3,-E(8)-E(8)^3,0,0,0,0],
[GALOIS,[9,5]],[27,27,3,3,0,0,0,0,0,0,0,-1,-1,0,0,0,-1,-1,1,1,1,1],[39,39,-1,
-1,3,3,3,3,0,0,0,-1,-1,-1,-1,-1,1,1,0,0,0,0],[26,-1,2,-1,8,-1,-1,-1,2,-1,-1,2,
-1,2,-1,-1,0,0,0,0,0,0],[26,-1,2,-1,-1,8,-1,-1,-1,2,-1,2,-1,-1,-1,2,0,0,0,0,0,
0],[26,-1,2,-1,-1,-1,8,-1,-1,-1,2,2,-1,-1,2,-1,0,0,0,0,0,0],[52,-2,-4,2,7,-2,7
,-2,1,-2,1,0,0,-1,-1,2,0,0,0,0,0,0],[52,-2,-4,2,7,7,-2,-2,1,1,-2,0,0,-1,2,-1,0
,0,0,0,0,0],[52,-2,-4,2,-2,7,7,-2,-2,1,1,0,0,2,-1,-1,0,0,0,0,0,0],[78,-3,6,-3,
6,6,6,-3,0,0,0,-2,1,0,0,0,0,0,0,0,0,0],[208,-8,0,0,10,-8,-8,1,-2,1,1,0,0,0,0,0
,0,0,0,0,0,0],[208,-8,0,0,-8,10,-8,1,1,-2,1,0,0,0,0,0,0,0,0,0,0,0],[208,-8,0,0
,-8,-8,10,1,1,1,-2,0,0,0,0,0,0,0,0,0,0,0]],
[( 6, 7)(10,11)(15,16),(17,18),(19,21,20,22)]);
ARC("3^3:L3(3)","tomfusion",rec(name:="3^3:L3(3)",map:=[1,3,2,11,4,5,6,7,
8,40,43,9,48,17,19,16,26,26,54,54,54,54],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^3:L3(3)","L3(3)",[1,1,2,2,3,3,3,3,4,4,4,5,5,6,6,6,7,8,9,10,11,12]);
ALF("3^3:L3(3)","L4(3)",[1,4,3,14,4,6,5,7,7,18,19,9,23,14,15,16,17,17,24,
25,26,27],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("L4(3)M4",
[
"4th maximal subgroup of L4(3),\n",
"differs from L4(3)M3 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["U4(2).2"]]);
ALF("L4(3)M4","L4(3)",[1,3,2,4,6,5,9,10,11,14,16,15,13,19,23,2,3,8,10,13,
12,15,17,20,22],[
"fusion U4(2).2 -> L4(3) mapped under L4(3).2_3"
]);

MOT("3^4:2(A4xA4).2",
[
"origin: Dixon's Algorithm"
],
[46656,1944,1458,1944,576,288,72,72,96,96,648,81,72,12,648,81,72,12,162,27,81,
18,162,27,81,18,72,18,36,36,36,144,36,16,8,8],
[,[1,2,3,4,1,1,4,2,5,5,11,12,11,13,15,16,15,17,19,20,21,19,23,24,25,23,1,3,2,4
,7,6,8,6,9,10],[1,1,1,1,5,6,6,6,9,10,1,1,5,9,1,1,5,10,1,3,1,5,1,3,1,5,27,27,27
,27,32,32,32,34,35,36]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1],[2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0
,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,-1,-1,-1,-1,0
,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2
,2,2,2,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2
,2,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,-1,-1,-1,-1,3,3,3,3,-1,0,0,0,0,
0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,1,-1],
[TENSOR,[7,2]],[3,3,3,3,3,-1,-1,-1,3,-1,0,0,0,0,3,3,3,-1,0,0,0,0,0,0,0,0,-1,
-1,-1,-1,1,1,1,1,-1,1],
[TENSOR,[9,2]],[4,4,4,4,-4,0,0,0,0,0,-2,-2,2,0,-2,-2,2,0,1,1,1,-1,1,1,1,-1,0,
0,0,0,-2,-2,-2,2,0,0],
[TENSOR,[11,2]],[6,6,6,6,6,-2,-2,-2,6,-2,0,0,0,0,-3,-3,-3,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,-2,-2,-2,-2,6,-3,-3,-3,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,0,0,0,0,-4,-4,4,0,2,2,-2,0,-1,-1,-1,1,-1,
-1,-1,1,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,0,0,0,0,2,2,-2,0,-4,-4,4,0,-1,-1,-1
,1,-1,-1,-1,1,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,0,0,0,0,2,2,-2,0,2,2,-2,0,-1,
-1,-1,1,2,2,2,-2,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,0,0,0,0,2,2,-2,0,2,2,-2,0,
2,2,2,-2,-1,-1,-1,1,0,0,0,0,0,0,0,0,0,0],[9,9,9,9,9,1,1,1,-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],
[TENSOR,[19,2]],[24,6,-3,-3,0,4,1,-2,0,0,0,0,0,0,0,0,0,0,6,0,-3,0,0,0,0,0,-2,
1,-2,1,-1,-4,2,0,0,0],
[TENSOR,[21,2]],[24,-3,-3,6,0,4,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,-3,0,-2,
1,1,-2,2,-4,-1,0,0,0],
[TENSOR,[23,2]],[32,-4,5,-4,0,0,0,0,0,0,8,-1,0,0,8,-1,0,0,2,-1,2,0,2,-1,2,0,
-4,-1,2,2,0,0,0,0,0,0],
[TENSOR,[25,2]],[48,12,-6,-6,0,8,2,-4,0,0,0,0,0,0,0,0,0,0,-6,0,3,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[48,-6,-6,12,0,8,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,0,3,0,
0,0,0,0,0,0,0,0,0,0],[64,-8,10,-8,0,0,0,0,0,0,-8,1,0,0,16,-2,0,0,-2,1,-2,0,-2,
1,-2,0,0,0,0,0,0,0,0,0,0,0],[64,-8,10,-8,0,0,0,0,0,0,16,-2,0,0,-8,1,0,0,-2,1,
-2,0,-2,1,-2,0,0,0,0,0,0,0,0,0,0,0],[64,-8,10,-8,0,0,0,0,0,0,-8,1,0,0,-8,1,0,0
,-2,1,-2,0,4,-2,4,0,0,0,0,0,0,0,0,0,0,0],[64,-8,10,-8,0,0,0,0,0,0,-8,1,0,0,-8,
1,0,0,4,-2,4,0,-2,1,-2,0,0,0,0,0,0,0,0,0,0,0],[72,-9,-9,18,0,-4,2,-1,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,1,-2,-2,4,1,0,0,0],
[TENSOR,[33,2]],[72,18,-9,-9,0,-4,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2
,1,-2,1,1,4,-2,0,0,0],
[TENSOR,[35,2]]],
[( 2, 4)( 7, 8)(19,23)(20,24)(21,25)(22,26)(29,30)(31,33),
( 9,10)(11,15)(12,16)(13,17)(14,18)(35,36)]);
ARC("3^4:2(A4xA4).2","tomfusion",rec(name:="3^4:2(A4xA4).2",map:=[1,12,5,
6,2,4,41,28,21,16,15,8,49,123,9,10,48,107,14,83,13,36,11,71,7,27,3,29,37,
42,105,20,100,18,61,68],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^4:2(A4xA4).2","L4(3)",[1,5,4,6,3,2,13,12,9,9,4,7,14,23,4,7,14,23,5,
19,7,15,6,18,7,16,3,14,15,16,22,8,21,10,17,17],[
"fusion map is unique up to table automorphisms"
]);

MOT("(4xA6):2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct'"
],
[2880,64,72,72,32,20,2880,64,72,72,32,20,1440,32,36,36,16,20,20,96,96,16,12,12
,96,96,16,12,12],
[,[1,1,3,4,2,6,1,1,3,4,2,6,7,7,9,10,8,12,12,1,1,2,3,4,1,1,2,3,4],[1,2,1,1,5,6,
7,8,7,7,11,12,13,14,13,13,17,18,19,20,21,22,20,21,25,26,27,25,26],,[1,2,3,4,5,
1,7,8,9,10,11,7,13,14,15,16,17,13,13,20,21,22,23,24,25,26,27,28,29]],
0,
[(18,19),(20,25)(21,26)(22,27)(23,28)(24,29),
( 3, 4)( 9,10)(15,16)(20,21)(23,24)(25,26)(28,29)],
["ConstructIndexTwoSubdirectProduct","C4","D8","A6","A6.2_1",[40,41,42,43,44,
51,52,53,54,55],(),()]);
ARC("(4xA6):2","tomfusion",rec(name:="(4xA6):2",map:=[1,8,9,10,20,39,2,7,
41,40,18,107,11,21,111,114,28,185,185,4,3,33,51,52,5,6,27,50,53],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("(4xA6):2","D8",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,5,5,
5,5,5]);
ALF("(4xA6):2","A6.2_1",[1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,6,7,8,9,10,
11,7,8,9,10,11]);
ALF("(4xA6):2","L4(3)",[1,2,5,6,10,11,2,3,12,13,8,20,8,10,21,22,9,28,29,2,
3,10,12,16,3,2,10,15,13],[
"fusion map is unique up to table automorphisms"
]);

MOT("(3x2S5).2",
[
"origin: Dixon's Algorithm"
],
[1440,1440,720,720,240,72,36,24,16,48,24,12,36,36,72,72,36,36,36,12,24,24,24,8
,20,20,30,30,60,60],
[,[1,1,3,3,2,1,3,1,1,2,4,15,14,14,16,16,16,14,14,16,11,11,10,10,30,30,27,27,29
,29],[1,2,1,2,5,6,6,8,9,10,10,5,2,1,2,1,6,6,6,8,23,23,23,24,25,26,29,30,29,30]
,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,5,5,3,4,1,2]
],
[[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,-1,1,1,1,-1,-1,-1,1,1,1,1],
[TENSOR,[2,3]],[2,2,-1,-1,0,-2,1,0,0,2,-1,0,-1,-1,2,2,-2,1,1,0,1,1,-2,0,0,0,
-1,-1,2,2],
[TENSOR,[5,2]],[4,4,4,4,-4,-2,-2,2,0,0,0,-1,1,1,1,1,1,1,1,-1,0,0,0,0,1,1,-1,
-1,-1,-1],
[TENSOR,[7,4]],
[TENSOR,[7,3]],
[TENSOR,[7,2]],[4,-4,4,-4,0,0,0,0,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,
-E(20)-E(20)^9+E(20)^13+E(20)^17,E(20)+E(20)^9-E(20)^13-E(20)^17,-1,1,-1,1],
[TENSOR,[11,2]],[5,5,5,5,-5,-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],
[TENSOR,[13,4]],
[TENSOR,[13,3]],
[TENSOR,[13,2]],[6,6,6,6,-6,0,0,0,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1
,1,1],
[TENSOR,[17,2]],[8,-8,-4,4,0,0,0,0,0,0,0,0,-2,2,4,-4,0,0,0,0,0,0,0,0,0,0,1,-1
,-2,2],[8,-8,8,-8,0,0,0,0,0,0,0,0,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2],[8,
-8,-4,4,0,0,0,0,0,0,0,0,1,-1,-2,2,0,-3,3,0,0,0,0,0,0,0,1,-1,-2,2],
[TENSOR,[21,2]],[8,8,-4,-4,0,-4,2,0,0,0,0,0,-1,-1,2,2,2,-1,-1,0,0,0,0,0,0,0,1
,1,-2,-2],
[TENSOR,[23,2]],[10,10,-5,-5,0,-2,1,0,0,2,-1,0,1,1,-2,-2,-2,1,1,0,-1,-1,2,0,0
,0,0,0,0,0],
[TENSOR,[25,2]],[12,12,-6,-6,0,0,0,0,0,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
-1,2,2],[12,-12,12,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2],
[12,-12,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(24)+E(24)^11+E(24)^17-E(24)^19
,E(24)-E(24)^11-E(24)^17+E(24)^19,0,0,0,0,-1,1,2,-2],
[TENSOR,[29,2]]],
[(21,22),(18,19),(25,26)]);
ARC("(3x2S5).2","tomfusion",rec(name:="(3x2S5).2",map:=[1,2,6,17,9,3,19,4,
5,11,53,58,23,8,18,7,20,21,22,33,98,98,37,42,88,88,72,109,16,45],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("(3x2S5).2","U3(5).3.2",[1,2,11,13,23,2,14,22,22,4,15,27,14,11,7,3,7,
13,14,24,19,20,9,25,28,29,16,21,5,10],[
"fusion map is unique up to table automorphisms"
]);

MOT("O8+(2)M2",
[
"2nd maximal subgroup of O8+(2),\n",
"differs from O8+(2)M1 = S6(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["S6(2)"]]);
ALF("O8+(2)M2","O8+(2)",[1,4,2,4,6,8,10,11,12,15,15,13,15,19,25,22,27,25,32,
29,34,35,36,37,39,42,49,49,47,52],[
"fusion S6(2) -> O8+(2) mapped under O8+(2).3"
],"tom:11168");

MOT("O8+(2)M3",
[
"3rd maximal subgroup of O8+(2),\n",
"differs from O8+(2)M1 = S6(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["S6(2)"]]);
ALF("O8+(2)M3","O8+(2)",[1,5,2,5,6,9,10,11,12,16,16,13,16,20,26,23,27,26,33,
30,34,35,36,37,40,43,50,50,47,53],[
"fusion O8+(2)M2 -> O8+(2) mapped under O8+(2).3"
],"tom:11170");

MOT("O8+(2)M5",
[
"5th maximal subgroup of O8+(2),\n",
"differs from O8+(2)M4 = 2^6:A8 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2^6:A8"]]);
ALF("O8+(2)M5","O8+(2)",[1,4,2,2,5,3,6,13,4,6,12,13,15,8,22,25,11,28,30,32,
13,17,16,14,15,17,36,37,19,42,25,45,49,29,31,33,34,35,35,52,52],[
"fusion 2^6:A8 -> O8+(2) mapped under O8+(2).3"
],"tom:11167");

MOT("O8+(2)M6",
[
"6th maximal subgroup of O8+(2),\n",
"differs from O8+(2)M4 = 2^6:A8 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2^6:A8"]]);
ALF("O8+(2)M6","O8+(2)",[1,5,2,2,3,4,6,13,5,6,12,13,16,9,23,26,11,29,28,33,
13,17,14,15,16,17,36,37,20,43,26,46,50,30,32,31,34,35,35,53,53],[
"fusion O8+(2)M5 -> O8+(2) mapped under O8+(2).3"
],"tom:11165");

MOT("O8+(2)M8",
[
"8th maximal subgroup of O8+(2),\n",
"differs from O8+(2)M7 = A9 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A9"]]);
ALF("O8+(2)M8","O8+(2)",[1,4,6,8,10,11,15,17,19,25,34,35,40,38,42,49,52,
52],[
"fusion A9 -> O8+(2) mapped under O8+(2).3"
],"tom:11162");

MOT("O8+(2)M9",
[
"9th maximal subgroup of O8+(2),\n",
"differs from O8+(2)M7 = A9 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A9"]]);
ALF("O8+(2)M9","O8+(2)",[1,5,6,9,10,11,16,17,20,26,34,35,38,39,43,50,53,
53],[
"fusion O8+(2)M8 -> O8+(2) mapped under O8+(2).3"
],"tom:11164");

MOT("(3xU4(2)):2",
[
"10th maximal subgroup of O8+(2),\n",
"origin: Dixon's Algorithm"
],
[155520,77760,108,108,108,324,648,3456,1728,288,576,48,24,32,96,12,36,72,144,
288,8,12,162,324,96,36,1440,216,216,216,1944,1944,1944,36,36,36,10,15,30,27,27
,27,36,108,54],
[,[1,2,7,6,6,6,7,1,2,2,1,11,10,11,11,18,6,7,9,8,20,24,23,24,1,24,1,32,31,33,31
,32,33,30,29,28,39,38,39,40,41,42,7,24,23],[1,1,8,8,8,1,1,8,8,11,11,12,12,14,
15,15,11,11,20,20,21,25,1,1,25,27,27,8,8,8,1,1,1,20,20,20,37,39,39,32,32,32,27
,8,8],,[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,
27,28,29,30,31,32,33,34,35,36,27,2,1,40,41,42,43,44,45]],
0,
[( 4, 5)(29,30)(31,33)(34,35)(41,42)],
[ "ConstructIndexTwoSubdirectProduct", "C3", "S3", "U4(2)", "U4(2).2", 
  [ 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 ], (2,8,12,44,37,25,38,15,36,27,30,
    45,16)(3,11)(4,32,41,26,29)(5,7,20,33,42,22,23,19,31,17,9,39,14,40,43,21,
    6,24,13,18,10,28)(34,35), (3,6,14,19,40,37,29,9,10,11,18,35,26)(4,5)(7,13,
    20,31,16,24,38,30,15,23,34,25,39,36,27,8,12,17,28)(21,32,22,33)(41,42) ]);
ARC("(3xU4(2)):2","tomfusion",rec(name:="(3xU4(2)):2",map:=[1,6,38,40,43,
11,10,2,30,32,4,22,139,23,20,146,49,45,115,15,87,60,13,12,5,47,3,33,36,35,
7,8,9,135,131,133,113,165,28,110,109,111,48,44,46],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("(3xU4(2)):2","O8+(2)",[1,7,21,29,30,11,7,2,21,24,3,14,48,14,14,48,31,
24,44,12,36,34,10,11,6,31,3,27,22,23,8,10,9,46,45,47,41,51,18,38,40,39,24,
28,27],[
"fusion map is unique up to table automorphisms"
],"tom:11158");

MOT("O8+(2)M11",
[
"11th maximal subgroup of O8+(2),\n",
"differs from O8+(2)M10 = (3xU4(2)):2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(3xU4(2)):2"]]);
ALF("O8+(2)M11","O8+(2)",[1,8,22,30,28,11,8,2,22,25,4,15,49,15,15,49,32,
25,45,12,36,34,10,11,6,32,4,27,23,21,9,10,7,44,46,47,42,52,19,39,38,40,25,
29,27],[
"fusion (3xU4(2)):2 -> O8+(2) mapped under O8+(2).3"
],"tom:11157");

MOT("O8+(2)M12",
[
"12th maximal subgroup of O8+(2),\n",
"differs from O8+(2)M10 = (3xU4(2)):2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(3xU4(2)):2"]]);
ALF("O8+(2)M12","O8+(2)",[1,9,23,28,29,11,9,2,23,26,5,16,50,16,16,50,33,
26,46,12,36,34,10,11,6,33,5,27,21,22,7,10,8,45,44,47,43,53,20,40,39,38,26,
30,27],[
"fusion O8+(2)M11 -> O8+(2) mapped under O8+(2).3"
],"tom:11156");

MOT("2^(1+8)_+:(S3xS3xS3)",
[
"13th maximal subgroup of O8+(2),\n",
"origin: Dixon's Algorithm"
],
[110592,110592,3072,2048,1024,4608,512,3072,3072,216,216,36,96,1728,1728,144,
216,216,216,216,144,96,1728,1728,216,216,96,144,1728,1728,256,256,64,128,32,32
,64,64,128,768,768,64,64,24,24,2304,2304,128,192,144,144,24,72,72,72,72,768,
768,64,128,64,24,24,2304,2304,192,128,24,144,144,72,72,72,72,768,768,128,64,64
,24,24,2304,2304,128,192,24,144,144,72,72,72,72],
[,[1,1,1,1,1,2,2,1,1,10,10,11,14,14,14,15,18,18,19,19,23,24,24,24,25,25,30,29,
30,30,4,4,3,1,7,6,9,8,4,1,1,5,8,25,25,1,1,4,8,30,30,27,19,19,18,18,1,1,3,4,5,
18,18,1,1,3,4,13,14,14,19,19,25,25,1,1,4,5,9,19,19,1,1,4,9,22,24,24,25,25,18,
18],[1,2,3,4,5,6,7,8,9,1,2,6,3,1,2,6,2,1,1,2,6,9,2,1,1,2,8,6,2,1,31,32,33,34,
35,36,37,38,39,40,41,42,43,41,40,46,47,48,49,46,47,49,46,47,47,46,57,58,59,60,
61,58,57,64,65,66,67,66,64,65,64,65,65,64,75,76,77,78,79,76,75,82,83,84,85,85,
82,83,82,83,82,83]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1
,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1
],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1
,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,
1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-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,[2,5]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,-1,-1,-1,2,2,2,2,-1,-1,2,2,-1,-1,-1,-1,2,2,
-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,-2,-2,1,1,-2,-2,-2
,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,-1,-1,-1,2,2,-1,-1],
[TENSOR,[9,2]],
[TENSOR,[9,5]],
[TENSOR,[9,4]],[2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,-1,-1,-1,-1,-1
,-1,2,2,2,2,0,0,0,0,0,0,0,0,2,2,2,2,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-2,-2,-2,-2,1,1,1,-2,-2,1,1,0,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1,1,1,-2,-2],
[TENSOR,[13,5]],
[TENSOR,[13,2]],
[TENSOR,[13,3]],[2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,2,2,-1,-1,2,2,2,2,2,2
,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1,1,1,-2,-2,0,0,0,0
,0,0,0,-2,-2,-2,-2,1,1,1,1,1,-2,-2,2,2,2,2,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[17,3]],
[TENSOR,[17,4]],
[TENSOR,[17,5]],[4,4,4,4,4,4,4,4,4,1,1,1,1,1,1,1,4,4,-2,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-4,-4,-4,-4,-1,-1,-1,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[21,3]],[4,4,4,4,4,4,4,4,4,1,1,1,-2,-2,-2,-2,-2,-2,4,4,1,1,1,1,-2,-2,
-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,-1,-1,-1,2,2,2,2],
[TENSOR,[23,2]],[4,4,4,4,4,4,4,4,4,1,1,1,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,
4,4,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,-1,-1,-1,2,2,2,2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[25,4]],[8,8,8,8,8,8,8,8,8,-1,-1,-1,2,2,2,2,-4,-4,-4,-4,2,2,2,2,-4,-4
,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],[12,12,4,-4,-4,8,0,4,4
,3,3,-1,-2,6,6,2,0,0,0,0,2,-2,6,6,0,0,-2,2,6,6,-4,-4,0,4,-2,2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[TENSOR,[28,2]],[16,-16,0,0,0,0,0,0,0,-2,2,0,0,4,-4,0,-1,1,1,-1,0,0,-4,4,1,-1
,0,0,-4,4,-4,4,0,0,0,0,0,0,0,-4,4,0,0,1,-1,4,-4,0,0,-2,2,0,1,-1,-1,1,-4,4,0,0,
0,1,-1,4,-4,0,0,0,-2,2,1,-1,-1,1,4,-4,0,0,0,-1,1,-4,4,0,0,0,2,-2,-1,1,-1,1],
[TENSOR,[30,8]],
[TENSOR,[30,7]],
[TENSOR,[30,6]],
[TENSOR,[30,5]],
[TENSOR,[30,4]],
[TENSOR,[30,3]],
[TENSOR,[30,2]],[18,18,10,2,2,6,-2,-6,-6,0,0,0,1,9,9,-3,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,-2,-2,-2,-2,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,-6,-2,2,2,0,
0,6,6,2,-2,-1,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[38,6]],
[TENSOR,[38,3]],
[TENSOR,[38,2]],[18,18,-6,2,2,6,-2,-6,10,0,0,0,0,0,0,0,0,0,0,0,-3,1,9,9,0,0,0
,0,0,0,-2,-2,2,-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,-6,-6,2,2,-2,0,0,6,6,-2,2,-1,3,3,0,0,0,0],
[TENSOR,[42,7]],
[TENSOR,[42,2]],
[TENSOR,[42,3]],[18,18,-6,2,2,6,-2,10,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
-3,9,9,-2,-2,2,-2,0,0,2,-2,-2,6,6,-2,2,0,0,-6,-6,2,-2,-3,-3,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[46,6]],
[TENSOR,[46,4]],
[TENSOR,[46,2]],[24,24,8,-8,-8,16,0,8,8,-3,-3,1,-4,12,12,4,0,0,0,0,-2,2,-6,-6
,0,0,2,-2,-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],[24,24,8,-8,-8,
16,0,8,8,-3,-3,1,2,-6,-6,-2,0,0,0,0,4,-4,12,12,0,0,2,-2,-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],[24,24,8,-8,-8,16,0,8,8,-3,-3,1,2,-6,-6,-2,0,0,
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[
(57,58)(62,63)(64,65)(69,70)(71,72)(73,74)(75,76)(80,81)(82,83)(87,88)(89,90)
(91,92)
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(40,41)(44,45)(46,47)(50,51)(53,54)(55,56)(75,76)(80,81)(82,83)(87,88)(89,90)
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(31,32)(46,47)(50,51)(53,54)(55,56)(64,65)(69,70)(71,72)(73,74)(82,83)(87,88)
(89,90)(91,92)
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(42,78)(43,79)(44,80)(45,81)(46,82)
(47,83)(48,84)(49,85)(50,87)(51,88)(52,86)(53,89)(54,90)(55,92)(56,91)(71,74)
(72,73)
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(42,61)(43,59)(44,62)(45,63)(46,64)
(47,65)(48,67)(49,66)(50,69)(51,70)(52,68)(53,71)(54,72)(55,73)(56,74)(89,91)
(90,92)
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ALF("2^(1+8)_+:(S3xS3xS3)","O8+(2)",[1,2,3,2,6,12,13,4,5,10,27,47,24,7,21,
44,28,11,11,30,46,26,23,9,11,29,25,45,22,8,12,13,14,6,37,36,16,15,13,6,4,
17,15,32,34,2,4,13,15,22,25,49,28,32,32,30,3,6,14,13,17,34,31,3,2,14,13,
48,24,21,31,29,30,31,6,5,13,17,16,33,34,2,5,13,16,50,23,26,28,33,29,33],[
"fusion map is unique up to table automorphisms"
],"tom:11155");

MOT("3^4:2^3.S4(a)",
[
"14th maximal subgroup of O8+(2),\n",
"origin: Dixon's Algorithm"
],
[15552,1944,648,486,1944,1944,288,72,72,192,72,288,72,16,72,72,288,54,27,27,27
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3,11,12,17,15],[1,1,1,1,1,1,7,7,7,10,12,12,12,14,17,17,17,1,4,1,4,4,10,24,24,
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,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,5,2,-1,-4,-4,4,1,-2,0,0,0,0,0,0,0,0,2,2,-1,-1,
-1,0,-4,2,-1,2,-1,-4,2,2,-2,1,0,0,0,0,0,0],
[TENSOR,[13,2]],[8,-4,2,-1,-4,5,0,0,0,0,0,0,0,0,1,-2,4,2,-1,-1,-1,2,0,-4,2,2,
-1,-1,2,-4,2,0,0,0,0,0,0,-2,1],
[TENSOR,[15,2]],[8,-4,2,-1,5,-4,0,0,0,0,1,4,-2,0,0,0,0,2,-1,-1,2,-1,0,-4,-1,2
,2,-1,2,2,-4,0,0,0,0,1,-2,0,0],
[TENSOR,[17,2]],[8,8,8,8,8,8,0,0,0,-8,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[16,10,4,-2,-8,-8,8,2,-4,0,0,0,0,0,0,0,0,-2,-2,1,1,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,-8,4,-2,-8,10,0,0,0,0,0,0,0,0,2,-4,8,-2
,1,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,-8,4,-2,10,-8,0,0,0,0,2,8,-4,
0,0,0,0,-2,1,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,15,6,-3,-12,-12,-4,
-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,-1,2,-1,-4,2,2,2,-1,0,0,0,0,0,0],
[TENSOR,[23,2]],[24,6,-3,-3,6,6,4,-2,1,0,-2,4,1,0,-2,1,4,0,0,0,0,0,0,-6,0,0,0
,3,-3,-3,-3,0,0,-2,1,0,0,0,0],
[TENSOR,[25,2]],[24,-12,6,-3,-12,15,0,0,0,0,0,0,0,0,-1,2,-4,0,0,0,0,0,0,-4,2,
2,-1,-1,2,-4,2,0,0,0,0,0,0,2,-1],
[TENSOR,[27,2]],[24,-12,6,-3,15,-12,0,0,0,0,-1,-4,2,0,0,0,0,0,0,0,0,0,0,-4,-1
,2,2,-1,2,2,-4,0,0,0,0,-1,2,0,0],
[TENSOR,[29,2]],[24,6,-3,-3,6,6,-4,2,-1,0,2,-4,-1,0,-2,1,4,0,0,0,0,0,0,-2,-2,
-2,4,1,1,-5,1,0,0,2,-1,0,0,0,0],
[TENSOR,[31,2]],[24,6,-3,-3,6,6,-4,2,-1,0,-2,4,1,0,2,-1,-4,0,0,0,0,0,0,-2,4,
-2,-2,1,1,1,-5,0,0,2,-1,0,0,0,0],
[TENSOR,[33,2]],[24,6,-3,-3,6,6,4,-2,1,0,2,-4,-1,0,2,-1,-4,0,0,0,0,0,0,-2,-2,
4,-2,1,-5,1,1,0,0,2,-1,0,0,0,0],
[TENSOR,[35,2]],[32,-4,-4,5,-4,-4,0,0,0,0,0,0,0,0,0,0,0,2,-1,2,-1,-1,0,-8,-2,
-2,-2,1,4,4,4,0,0,0,0,0,0,0,0],
[TENSOR,[37,2]],[64,-8,-8,10,-8,-8,0,0,0,0,0,0,0,0,0,0,0,-2,1,-2,1,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 5, 6)(11,15)(12,17)(13,16)(21,22)(25,27)(30,31)(36,39)(37,38),
( 2, 5)( 7,12)( 8,11)( 9,13)(19,21)(25,26)(29,31)(32,37)(33,36)]);
ARC("3^4:2^3.S4(a)","projectives",["(2x3^4:2^3).S4",[[2,2,2,2,2,2,0,0,0,2,2,2,
2,0,0,0,0,-1,-1,-1,-1,-1,1,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,-E(8)-E(8)^3,0,0,0,0,
-E(8)-E(8)^3,-E(8)-E(8)^3],[4,4,4,4,4,4,0,0,0,4,4,4,4,0,0,0,0,1,1,1,1,1,-1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,4,4,4,0,0,0,-4,0,0,0,0,0,0,0,1,1,1,1,1,1,
0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0],[6,6,6,6,6,6,0,0,0,6,-2,-2,-2,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,-E(8)-E(8)^3,0,0,0,0,E(8)+E(8)^3,
E(8)+E(8)^3],[8,-4,2,-1,5,-4,0,0,0,0,1,4,-2,0,0,0,0,2,-1,-1,2,-1,0,0,-3,0,0,3,
0,0,0,0,0,0,0,-1,2,0,0],[8,8,8,8,8,8,0,0,0,-8,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,-8,4,-2,10,-8,0,0,0,0,2,8,-4,0,0,0,0,-2,1
,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,10,4,-2,-8,-8,0,0,0,0,0,0,0,0,0
,0,0,-2,-2,1,1,1,0,0,0,0,0,0,0,0,0,-2*E(8)-2*E(8)^3,E(8)+E(8)^3,0,0,0,0,0,0],[
16,-8,4,-2,-8,10,0,0,0,0,0,0,0,0,0,0,0,-2,1,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,-2*E(8)-2*E(8)^3,E(8)+E(8)^3],[24,-12,6,-3,15,-12,0,0,0,0,-1,-4,2,0,0,0,0,0
,0,0,0,0,0,0,-3,0,0,3,0,0,0,0,0,0,0,1,-2,0,0],[32,20,8,-4,-16,-16,0,0,0,0,0,0,
0,0,0,0,0,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[32,-4,-4,5,-4,-4,0,
0,0,0,0,0,0,0,0,0,0,2,-1,2,-1,-1,0,0,-6,0,0,-3,0,0,0,0,0,0,0,0,0,0,0],[32,-16,
8,-4,-16,20,0,0,0,0,0,0,0,0,0,0,0,2,-1,-1,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0],[48,12,-6,-6,12,12,0,0,0,0,-4,8,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[48,12,-6,-6,12,12,0,0,0,0,4,-8,-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],[64,-8,-8,10,-8,-8,0,0,0,0,0,0,0,0,0,0,0,-2,1,-2,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("3^4:2^3.S4(a)","O8+(2)",[1,8,11,10,7,9,4,25,32,6,24,3,31,17,26,33,5,11,
39,10,38,40,34,2,21,22,23,27,29,30,28,15,49,6,34,48,14,16,50],[
"fusion map is unique up to table automorphisms"
],"tom:11077");
ARC("3^4:2^3.S4(a)","tomfusion",rec(name:="3^4:2^3.S4(a)",map:=[1,9,12,10,
11,14,7,44,62,6,66,2,57,17,51,45,3,13,103,8,112,106,65,4,38,56,47,67,68,
70,52,20,160,5,55,135,35,34,120],text:=[
"fusion map is unique up to table automorphisms"
]));

MOT("2x2.S6(2)",
[
"1st maximal subgroup of 2^2.O8+(2)"
],
0,
0,
0,
[(36,37)(79,80),
(44,45)(50,51)(52,53)(54,55)(56,57)(62,63)(66,67)(72,73)(75,76)(77,78)(79,80)
(83,84)(85,86)
],
["ConstructDirectProduct",[["Cyclic",2],["2.S6(2)"]]]);
ALF("2x2.S6(2)","2^2.O8+(2)",[1,2,7,5,6,12,13,14,25,26,29,30,33,34,38,39,
37,38,45,46,64,58,69,70,63,77,73,82,83,84,87,88,89,92,93,105,105,126,127,
122,123,132,133,3,4,6,5,7,12,15,16,27,28,31,32,35,36,39,38,37,39,47,48,63,
57,71,72,64,76,73,82,85,86,87,90,91,94,95,104,104,127,126,124,125,134,135],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2x2.S6(2)","2xS6(2)",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,
15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30,31,
31,32,33,34,35,36,36,37,37,38,38,39,39,40,41,42,43,44,44,45,46,47,47,48,
49,50,51,52,52,53,54,54,55,55,56,56,57,58,59,59,60,60]);
ALF("2x2.S6(2)","S6(2)",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,15,
16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30,1,1,2,3,
4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,15,16,17,17,18,19,20,21,22,22,23,24,
24,25,25,26,26,27,28,29,29,30,30]);

MOT("2^2.O8+(2)M2",
[
"2nd maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M1 = 2x2.S6(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2x2.S6(2)"]]);
ALF("2^2.O8+(2)M2","2^2.O8+(2)",[1,3,9,5,8,12,17,19,25,27,29,31,33,35,40,41,
37,40,49,51,66,60,69,71,65,79,74,82,83,85,87,88,90,96,98,107,107,128,129,
122,124,136,138,4,2,8,5,9,12,20,18,28,26,32,30,36,34,41,40,37,41,52,50,65,
59,72,70,66,78,74,82,86,84,87,91,89,99,97,106,106,129,128,125,123,139,137],[
"fusion 2x2.S6(2) -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);
ALF("2^2.O8+(2)M2","O8+(2)M2",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,
15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30,1,1,2,3,
4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,15,16,17,17,18,19,20,21,22,22,23,24,
24,25,25,26,26,27,28,29,29,30,30]);

MOT("2^2.O8+(2)M3",
[
"3rd maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M1 = 2x2.S6(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2x2.S6(2)"]]);
ALF("2^2.O8+(2)M3","2^2.O8+(2)",[1,4,11,5,10,12,21,24,25,28,29,32,33,36,42,
43,37,42,53,56,68,62,69,72,67,81,75,82,83,86,87,88,91,100,103,109,109,130,
131,122,125,140,143,2,3,10,5,11,12,22,23,26,27,30,31,34,35,43,42,37,43,54,
55,67,61,70,71,68,80,75,82,84,85,87,89,90,101,102,108,108,131,130,123,124,
141,142], [
"fusion 2^2.O8+(2)M2 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);
ALF("2^2.O8+(2)M3","2.O8+(2)M3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]);
ALF("2^2.O8+(2)M3","O8+(2)M3",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,
14,14,15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,
30,1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,15,16,17,17,18,19,20,21,
22,22,23,24,24,25,25,26,26,27,28,29,29,30,30]);

MOT("(2x2^(1+6)_+).A8",
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[5160960,5160960,5160960,5160960,92160,92160,36864,3072,6144,6144,6144,6144,
3072,256,3072,3072,512,6144,6144,6144,6144,512,384,384,11520,11520,11520,11520
,1152,1152,576,576,288,288,288,288,72,72,144,144,64,64,128,128,128,128,64,64,
32,32,128,128,128,128,240,240,240,240,40,40,96,96,192,192,192,192,48,48,24,48,
48,48,48,24,28,28,28,28,28,28,28,28,60,60,60,60,60,60,60,60],
[,[1,1,1,1,2,2,1,1,4,4,3,3,1,7,2,2,1,7,7,7,7,7,5,5,25,25,25,25,25,25,26,26,34,
34,34,34,34,34,33,33,8,13,10,10,12,12,15,15,17,21,22,22,22,22,56,56,56,56,55,
55,26,26,30,30,30,30,31,31,34,36,36,35,35,34,76,76,76,76,80,80,80,80,84,84,84,
84,88,88,88,88],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,1,2,3,4,7,7,5,6,2,1,4,3,7,7,6,5,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,60,15,16,19,18,21,20,24,23,8,11,12,9,10,13,79,80,81,82,75,76,77
,78,55,56,57,58,55,56,57,58],,[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
,46,47,48,49,50,51,52,53,54,2,1,4,3,6,5,61,62,63,64,65,66,67,68,69,70,71,72,73
,74,79,80,81,82,75,76,77,78,26,25,28,27,26,25,28,27],,[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
,64,65,66,67,68,69,70,71,72,73,74,2,1,4,3,2,1,4,3,87,88,89,90,83,84,85,86]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1],[7,7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,3,3,3,3
,3,3,4,4,4,4,4,4,4,4,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,2,2,2,2
,2,2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1
],[14,14,14,14,14,14,14,6,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1
,-1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,-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,-1,-1,-1,-1,-1,-1,-1,-1],[20,20,20,20,
20,20,20,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,-1,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0],[21,21,21,21,21,21,21,-3,-3,-3,-3,-3,-3,
-3,1,1,1,1,1,1,1,1,1,1,6,6,6,6,6,6,6,6,0,0,0,0,0,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1
,-1,-1,-1,-1,1,1,1,1,1,1,-2,-2,-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],[21,21,21,21,21,21,21,-3,-3,-3,-3,-3,-3,-3,1,1,1,1,1,1,1,1,1,1
,-3,-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1
,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[6,7]],[28,28,28,28,28,28,28,-4,-4,-4,-4,-4,-4,-4,4,4,4,4,4,4,4,4,4,4
,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2
,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1],[35,35,35,
35,35,35,35,3,3,3,3,3,3,3,-5,-5,-5,-5,-5,-5,-5,-5,-5,-5,5,5,5,5,5,5,5,5,2,2,2,
2,2,2,2,2,-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,
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E(15)+E(15)^2+E(15)^4+E(15)^8],
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0,0,0,0,0,0,0,0,0,0,0]],
[(83,87)(84,88)(85,89)(86,90),(75,79)(76,80)(77,81)(78,82),
( 8,13)(37,38)(41,42)(69,74),
( 3, 4)( 9,11)(10,12)(18,19)(27,28)(35,36)(37,38)(43,45)(44,46)(51,52)
(57,58)(63,64)(70,72)(71,73)(77,78)(81,82)(85,86)(89,90)
]);
ALF("(2x2^(1+6)_+).A8","P31/G1/L1/V1/ext2",[1,1,5,5,2,4,3,6,7,7,10,10,9,8,
11,18,13,12,12,17,17,14,15,16,19,19,20,20,23,24,21,22,25,25,26,26,30,29,
27,28,31,34,32,32,33,33,35,40,38,37,36,36,39,39,41,41,42,42,43,44,45,50,
46,46,49,49,47,48,51,54,54,52,52,53,55,55,56,56,57,57,58,58,61,61,62,62,
59,59,60,60]);
ALF("(2x2^(1+6)_+).A8","2^(1+6)_+.A8",[1,2,1,2,3,3,4,5,6,6,7,8,9,10,11,11,
12,13,14,13,14,15,16,16,17,18,17,18,19,19,20,20,21,22,21,22,23,24,25,25,
26,27,28,28,29,30,31,31,32,33,34,35,34,35,36,37,36,37,38,38,39,39,40,41,
40,41,42,42,43,44,45,46,46,47,48,49,48,49,50,51,50,51,54,55,54,55,52,53,
52,53]);
ALF("(2x2^(1+6)_+).A8","2^6:A8",[1,1,1,1,2,2,3,4,5,5,6,6,7,8,9,9,10,11,11,
11,11,12,13,13,14,14,14,14,15,15,16,16,17,17,17,17,18,19,20,20,21,22,23,
23,24,24,25,25,26,27,28,28,28,28,29,29,29,29,30,30,31,31,32,32,32,32,33,
33,34,35,35,36,36,37,38,38,38,38,39,39,39,39,41,41,41,41,40,40,40,40]);
ALF("(2x2^(1+6)_+).A8","2^2.O8+(2)",[1,2,4,3,6,7,5,5,9,8,11,10,12,37,6,7,
12,35,36,34,33,37,38,39,13,14,16,15,58,57,63,64,30,29,31,32,75,74,77,76,
37,44,40,41,42,43,38,39,44,87,91,90,88,89,46,45,47,48,105,104,63,64,113,
112,110,111,127,126,73,81,80,79,78,82,84,83,85,86,84,83,85,86,133,132,134,
135,133,132,134,135],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2^2.O8+(2)M5",
[
"5th maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M4 = (2x2^(1+6)_+).A8 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(2x2^(1+6)_+).A8"]]);
ALF("2^2.O8+(2)M5","2^2.O8+(2)",[1,3,2,4,8,9,5,5,11,10,7,6,12,37,8,9,
12,36,34,35,33,37,40,41,17,19,18,20,60,59,65,66,31,29,32,30,73,75,79,78,
37,44,42,43,38,39,40,41,44,87,89,91,88,90,51,49,52,50,107,106,65,66,115,
117,114,116,129,128,74,77,76,81,80,82,85,83,86,84,85,83,86,84,138,136,139,
137,138,136,139,137],[
"fusion (2x2^(1+6)_+).A8 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);
ALF("2^2.O8+(2)M5","2^(1+6)_+.A8",[1,2,1,2,3,3,4,5,6,6,7,8,9,10,11,11,12,
13,14,13,14,15,16,16,17,18,17,18,19,19,20,20,21,22,21,22,23,24,25,25,26,
27,28,28,29,30,31,31,32,33,34,35,34,35,36,37,36,37,38,38,39,39,40,41,40,
41,42,42,43,44,45,46,46,47,48,49,48,49,50,51,50,51,52,53,52,53,54,55,54,
55]);
ALF("2^2.O8+(2)M5","O8+(2)M5",[1,1,1,1,2,2,3,4,5,5,6,6,7,8,9,9,10,11,11,11,
11,12,13,13,14,14,14,14,15,15,16,16,17,17,17,17,18,19,20,20,21,22,23,23,
24,24,25,25,26,27,28,28,28,28,29,29,29,29,30,30,31,31,32,32,32,32,33,33,
34,35,35,36,36,37,38,38,38,38,39,39,39,39,40,40,40,40,41,41,41,41]);

MOT("2^2.O8+(2)M6",
[
"6th maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M4 = (2x2^(1+6)_+).A8 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(2x2^(1+6)_+).A8"]]);
ALF("2^2.O8+(2)M6","2^2.O8+(2)",[1,4,3,2,10,11,5,5,7,6,9,8,12,37,10,
11,12,34,35,36,33,37,42,43,21,24,23,22,62,61,67,68,32,29,30,31,74,73,81,
80,37,44,38,39,40,41,42,43,44,87,90,89,88,91,56,53,54,55,109,108,67,68,
120,119,118,121,131,130,75,79,78,77,76,82,86,83,84,85,86,83,84,85,143,140,
141,142,143,140,141,142],[
"fusion 2^2.O8+(2)M5 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);
ALF("2^2.O8+(2)M6","2.O8+(2)M6",[1,2,2,1,3,3,4,5,7,8,6,6,9,10,11,11,12,
14,13,13,14,15,16,16,17,18,18,17,19,19,20,20,21,22,22,21,24,23,25,25,26,
27,29,30,28,28,31,31,32,33,35,34,34,35,36,37,37,36,38,38,39,39,41,40,40,
41,42,42,43,46,46,44,45,47,48,49,49,48,50,51,51,50,52,53,53,52,54,55,55,
54]);
ALF("2^2.O8+(2)M6","O8+(2)M6",[1,1,1,1,2,2,3,4,5,5,6,6,7,8,9,9,10,11,11,11,
11,12,13,13,14,14,14,14,15,15,16,16,17,17,17,17,18,19,20,20,21,22,23,23,
24,24,25,25,26,27,28,28,28,28,29,29,29,29,30,30,31,31,32,32,32,32,33,33,
34,35,35,36,36,37,38,38,38,38,39,39,39,39,40,40,40,40,41,41,41,41]);

MOT("2x2.A9",
[
"7th maximal subgroup of 2^2.O8+(2)"
],
0,
0,
0,
[(27,29)(28,30)(57,59)(58,60),(25,26)(55,56),(16,17)(46,47),
(16,17)(25,26)(27,29)(28,30)(46,47)(55,56)(57,59)(58,60),
(20,22)(21,23)(50,52)(51,53),
(25,26)(31,32)(35,36)(37,38)(39,40)(43,44)(46,47)(48,49)(50,51)(52,53)(57,58)
(59,60)
],
["ConstructDirectProduct",[["Cyclic",2],["2.A9"]]]);
ALF("2x2.A9","2xA9",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,12,13,13,14,
14,15,16,16,17,17,18,18,19,19,20,21,22,22,23,23,24,24,25,26,27,27,28,29,
29,30,30,31,31,32,32,33,34,34,35,35,36,36]);
ALF("2x2.A9","A9",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,12,13,13,14,14,
15,16,16,17,17,18,18,1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,12,13,13,14,
14,15,16,16,17,17,18,18]);
ALF("2x2.A9","2^2.O8+(2)",[1,2,6,12,13,14,25,26,29,30,38,44,45,46,63,82,
82,83,84,96,97,100,101,104,126,126,132,133,132,133,3,4,7,12,15,16,27,28,
31,32,39,44,47,48,64,82,82,85,86,98,99,102,103,105,127,127,134,135,134,
135],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2^2.O8+(2)M8",
[
"8th maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M7 = 2x2.A9 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2x2.A9"]]);
ALF("2^2.O8+(2)M8","2^2.O8+(2)",[1,3,8,12,17,19,25,27,29,31,40,44,49,51,65,
82,82,83,85,100,102,92,94,106,128,128,136,138,136,138,4,2,9,12,20,18,28,
26,32,30,41,44,52,50,66,82,82,86,84,103,101,95,93,107,129,129,139,137,139,
137],[
"fusion 2x2.A9 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);
ALF("2^2.O8+(2)M8","O8+(2)M8",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,12,
13,13,14,14,15,16,16,17,17,18,18,1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,
12,13,13,14,14,15,16,16,17,17,18,18]);

MOT("2^2.O8+(2)M9",
[
"9th maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M7 = 2x2.A9 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2x2.A9"]]);
ALF("2^2.O8+(2)M9","2^2.O8+(2)",[1,4,10,12,21,24,25,28,29,32,42,44,53,56,
67,82,82,83,86,92,95,96,99,108,130,130,140,143,140,143,2,3,11,12,22,23,26,
27,30,31,43,44,54,55,68,82,82,84,85,93,94,97,98,109,131,131,141,142,141,
142],[
"fusion 2^2.O8+(2)M8 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);
ALF("2^2.O8+(2)M9","2.O8+(2)M9",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,2,1,3,4,6,5,8,7,10,9,11,12,14,13,
15,17,16,19,18,21,20,23,22,24,26,25,28,27,30,29]);
ALF("2^2.O8+(2)M9","O8+(2)M9",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,12,
13,13,14,14,15,16,16,17,17,18,18,1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,
12,13,13,14,14,15,16,16,17,17,18,18]);

MOT("2x(3x2.U4(2)):2",
[
"10th maximal subgroup of 2^2.O8+(2)"
],
0,
0,
0,
[(73,76)(74,75)(77,78)(79,82)(80,81)(85,87)(86,88)(90,95)(91,93)(92,94)(96,
101)(97,99)(98,100)(104,105)(107,112)(108,110)(109,111)(113,116)(114,115)(119,
122)(120,121)(125,126)(132,133)(137,138)(139,144)(140,142)(141,143),(18,20)
(22,23)(24,25)(27,29)(32,33)(35,36)(38,40)(57,58)(67,68)(70,72)(90,92)(94,95)
(96,97)(99,101)(104,105)(107,108)(110,112)(129,130)(139,140)(142,144),(5,6)
(77,78),(5,77)(6,78)(11,83)(12,84)(17,89)(53,125)(54,126)(60,132)(61,133)(62,
134)(63,135)(64,136)(65,137)(66,138)],
["ConstructDirectProduct",[["Cyclic",2],["(3x2.U4(2)):2"]]]);
ALF("2x(3x2.U4(2)):2","2x(3xU4(2)):2",[1,2,2,1,37,37,39,38,38,39,27,22,23,
24,23,24,25,29,28,30,28,30,29,31,33,32,33,32,31,9,8,45,45,44,35,34,36,34,
36,35,20,19,19,20,18,17,6,7,7,6,11,10,21,21,13,12,5,4,3,15,15,26,43,14,16,
16,41,42,40,42,40,41,46,47,47,46,82,82,84,83,83,84,72,67,68,69,68,69,70,
74,73,75,73,75,74,76,78,77,78,77,76,54,53,90,90,89,80,79,81,79,81,80,65,
64,64,65,63,62,51,52,52,51,56,55,66,66,58,57,50,49,48,60,60,71,88,59,61,
61,86,87,85,87,85,86]);
ALF("2x(3x2.U4(2)):2","(3xU4(2)):2",[1,2,2,1,37,37,39,38,38,39,27,22,23,
24,23,24,25,29,28,30,28,30,29,31,33,32,33,32,31,9,8,45,45,44,35,34,36,34,
36,35,20,19,19,20,18,17,6,7,7,6,11,10,21,21,13,12,5,4,3,15,15,26,43,14,16,
16,41,42,40,42,40,41,1,2,2,1,37,37,39,38,38,39,27,22,23,24,23,24,25,29,28,
30,28,30,29,31,33,32,33,32,31,9,8,45,45,44,35,34,36,34,36,35,20,19,19,20,
18,17,6,7,7,6,11,10,21,21,13,12,5,4,3,15,15,26,43,14,16,16,41,42,40,42,40,
41]);
ALF("2x(3x2.U4(2)):2","2^2.O8+(2)",[1,13,14,2,104,104,45,132,133,46,6,82,
25,29,26,30,12,59,69,61,70,62,60,18,22,26,21,25,17,57,5,72,71,73,114,118,
122,119,123,115,34,111,110,33,63,76,29,13,14,30,6,63,87,87,126,38,75,74,
58,39,39,76,63,38,127,127,100,96,92,97,93,101,3,15,16,4,105,105,47,134,
135,48,7,82,27,31,28,32,12,59,71,62,72,61,60,20,24,28,23,27,19,58,5,70,69,
73,116,120,124,121,125,117,36,113,112,35,64,77,31,15,16,32,7,64,87,87,127,
39,75,74,57,38,38,77,64,39,126,126,102,98,94,99,95,103],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^2.O8+(2)M11",
[
"11th maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M10 = 2x(3x2.U4(2)):2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2x(3x2.U4(2)):2"]]);
ALF("2^2.O8+(2)M11","O8+(2)M11",[1,2,2,1,37,37,39,38,38,39,27,22,23,24,23,
24,25,30,28,29,28,29,30,33,31,32,31,32,33,9,8,45,45,44,34,35,36,35,36,34,
20,19,19,20,18,17,6,7,7,6,11,10,21,21,13,12,4,5,3,15,15,26,43,14,16,16,42,
41,40,41,40,42,1,2,2,1,37,37,39,38,38,39,27,22,23,24,23,24,25,30,28,29,28,
29,30,33,31,32,31,32,33,9,8,45,45,44,34,35,36,35,36,34,20,19,19,20,18,17,
6,7,7,6,11,10,21,21,13,12,4,5,3,15,15,26,43,14,16,16,42,41,40,41,40,42]);
ALF("2^2.O8+(2)M11","(3x2.U4(2)):2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
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]);
ALF("2^2.O8+(2)M11","2^2.O8+(2)",[1,17,19,3,106,106,49,136,138,51,8,82,25,
29,27,31,12,61,69,57,71,58,62,23,15,27,13,25,21,59,5,70,72,74,118,110,122,
112,124,120,35,116,114,33,65,78,29,17,19,31,8,65,87,87,128,40,73,75,60,41,
41,78,65,40,129,129,92,100,96,102,98,94,4,20,18,2,107,107,52,139,137,50,9,
82,28,32,26,30,12,61,72,58,70,57,62,22,14,26,16,28,24,60,5,71,69,74,121,
113,125,111,123,119,34,115,117,36,66,79,32,20,18,30,9,66,87,87,129,41,73,
75,59,40,40,79,66,41,128,128,95,103,99,101,97,93],[
"fusion 2x(3x2.U4(2)):2 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);

MOT("2^2.O8+(2)M12",
[
"12th maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M10 = 2x(3x2.U4(2)):2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2x(3x2.U4(2)):2"]]);
ALF("2^2.O8+(2)M12","O8+(2)M12",[1,2,2,1,37,37,39,38,38,39,27,22,23,24,23,
24,25,30,28,29,28,29,30,33,31,32,31,32,33,9,8,45,45,44,34,35,36,35,36,34,
20,19,19,20,18,17,6,7,7,6,11,10,21,21,13,12,4,5,3,15,15,26,43,14,16,16,42,
41,40,41,40,42,1,2,2,1,37,37,39,38,38,39,27,22,23,24,23,24,25,30,28,29,28,
29,30,33,31,32,31,32,33,9,8,45,45,44,34,35,36,35,36,34,20,19,19,20,18,17,
6,7,7,6,11,10,21,21,13,12,4,5,3,15,15,26,43,14,16,16,42,41,40,41,40,42]);
ALF("2^2.O8+(2)M12","2.O8+(2)M12",[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,
65,66,67,68,69,70,71,72,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
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]);
ALF("2^2.O8+(2)M12","2^2.O8+(2)",[1,17,19,3,106,106,49,136,138,51,8,82,25,
29,27,31,12,61,69,57,71,58,62,23,15,27,13,25,21,59,5,70,72,74,118,110,122,
112,124,120,35,116,114,33,65,78,29,17,19,31,8,65,87,87,128,40,73,75,60,41,
41,78,65,40,129,129,92,100,96,102,98,94,4,20,18,2,107,107,52,139,137,50,9,
82,28,32,26,30,12,61,72,58,70,57,62,22,14,26,16,28,24,60,5,71,69,74,121,
113,125,111,123,119,34,115,117,36,66,79,32,20,18,30,9,66,87,87,129,41,73,
75,59,40,40,79,66,41,128,128,95,103,99,101,97,93],[
"fusion 2x(3x2.U4(2)):2 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);

MOT("2^2.(2^(1+8)_+:(S3xS3xS3))",
[
"13th maximal subgroup of 2^2.O8+(2),\n",
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[442368,442368,442368,442368,110592,6144,6144,2048,1024,18432,18432,18432,
18432,512,6144,6144,6144,6144,864,864,864,864,864,864,864,864,144,144,144,144,
192,192,6912,6912,6912,6912,3456,3456,576,576,576,576,216,864,864,864,864,864,
864,864,864,216,576,576,576,576,192,192,3456,3456,6912,6912,6912,6912,864,864,
864,864,216,192,192,576,576,576,576,3456,3456,6912,6912,6912,6912,1024,1024,
1024,1024,256,128,128,128,128,128,128,128,32,128,128,128,128,128,768,1536,1536
,64,128,128,48,48,24,2304,4608,4608,128,384,384,288,288,288,288,48,48,72,144,
144,144,144,72,1536,1536,768,128,128,128,64,24,48,48,4608,4608,2304,384,384,
128,48,48,288,288,288,288,144,144,72,72,144,144,768,1536,1536,128,64,128,128,
48,48,24,2304,4608,4608,128,384,384,48,48,288,288,288,288,72,144,144,72,144,
144],
[,[1,1,1,1,1,2,2,1,1,5,5,5,5,5,3,3,4,4,19,19,19,19,19,19,19,19,23,23,23,23,33,
33,34,34,34,34,34,34,38,38,38,38,46,46,46,46,46,48,48,48,48,48,60,60,60,60,61,
61,64,64,64,64,64,64,66,66,66,66,66,78,78,77,77,77,77,80,80,80,80,80,80,8,8,8,
8,8,6,6,1,14,14,14,14,10,17,17,15,15,8,1,3,3,9,15,15,68,68,66,1,3,3,8,15,15,80
,80,78,78,70,70,48,50,50,44,44,46,2,2,1,6,6,8,9,46,47,47,2,2,1,6,6,8,31,31,33,
33,34,34,49,49,48,66,65,65,1,4,4,8,9,17,17,51,51,48,1,4,4,8,17,17,57,57,64,64,
61,61,66,67,67,46,45,45],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4
,5,5,5,5,10,11,12,13,6,7,2,1,4,3,5,5,11,10,13,12,5,3,4,1,2,1,2,3,4,5,13,12,11,
10,17,18,5,5,4,3,2,1,2,1,4,3,5,15,16,12,13,10,11,5,5,3,4,1,2,82,83,84,85,86,87
,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,101,102,100,109,
110,111,112,113,114,109,109,110,111,113,114,109,110,111,111,110,109,127,128,
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0],[96,-96,-96,96,0,0,0,0,0,16,-16,-16,16,0,0,0,-16,16,6,-6,-6,6,6,-6,-6,
6,-2,2,2,-2,0,0,-12,12,12,-12,0,0,2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,-2,2,2,-2,2,-2
,6,-6,-6,6,6,-6,0,0,0,0,0,0,0,2,-2,-2,2,0,0,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[144,-144,-144,144,0,0,0,0,0,-24,24,24,-24,0,0,0,8,
-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,-3,-3
,3,-1,1,9,-9,-9,9,9,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-24,24,0,
4,-4,1,-1,-3,3,-3,3,0,0,0,0,0,0],
[TENSOR,[181,2]]],
[
(156,157)(160,161)(162,163)(166,167)(169,170)(171,172)(173,174)(175,176)(178,
179)(181,182)
,
(127,128)(130,131)(135,136)(137,138)(140,141)(143,144)(145,146)(147,148)(149,
150)(153,154)
,
(101,102)(104,105)(106,107)(110,111)(113,114)(115,116)(117,118)(119,120)(122,
123)(124,125)
,
( 82, 83)( 84, 85)( 90, 91)( 92, 93)( 95, 96)( 97, 98)(110,111)(113,114)(115,
116)(117,118)(119,120)(122,123)
(124,125)(166,167)(169,170)(171,172)(173,174)(175,176)(178,179)(181,182)
,
( 82, 84)( 83, 85)( 87, 88)( 90, 92)( 91, 93)( 95, 96)(137,138)(140,141)(143,
144)(145,146)(147,148)(149,150)
(153,154)(166,167)(169,170)(171,172)(173,174)(175,176)(178,179)(181,182)
,
(  3,  4)( 12, 13)( 15, 17)( 16, 18)( 21, 22)( 25, 26)( 29, 30)( 35, 36)( 41,
42)( 44, 45)( 48, 66)( 49, 65)
( 50, 67)( 51, 68)( 52, 69)( 53, 72)( 54, 73)( 55, 75)( 56, 74)( 57, 70)( 58,
71)( 59, 76)( 60, 77)( 61, 78)
( 62, 79)( 63, 81)( 64, 80)( 84, 85)( 92, 93)( 95, 97)( 96, 98)( 99,158)(100,
155)(101,156)(102,157)(103,159)
(104,160)(105,161)(106,162)(107,163)(108,164)(109,165)(110,166)(111,167)(112,
168)(113,169)(114,170)(115,173)
(116,174)(117,175)(118,176)(119,171)(120,172)(121,177)(122,179)(123,178)(124,
182)(125,181)(126,180)(149,154)
(150,153)(151,152)
,
(  2,  3)(  6, 15)(  7, 16)( 11, 12)( 20, 21)( 24, 25)( 28, 29)( 31, 70)( 32,
71)( 33, 78)( 34, 80)( 35, 79)
( 36, 81)( 37, 76)( 38, 77)( 39, 72)( 40, 74)( 41, 73)( 42, 75)( 43, 69)( 44,
65)( 45, 67)( 46, 66)( 47, 68)
( 49, 50)( 54, 55)( 62, 63)( 83, 84)( 87, 97)( 88, 98)( 91, 92)( 99,132)(100,
129)(101,127)(102,128)(103,133)
(104,130)(105,131)(106,135)(107,136)(108,134)(109,139)(110,137)(111,138)(112,
142)(113,140)(114,141)(115,147)
(116,148)(117,145)(118,146)(119,143)(120,144)(121,151)(122,150)(123,149)(124,
154)(125,153)(126,152)(177,180)
(178,182)(179,181)
]);
ALF("2^2.(2^(1+8)_+:(S3xS3xS3))","2.2^(1+8)_+:(S3xS3xS3)",[1,1,2,2,3,4,5,
6,7,8,8,9,9,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,20,21,
21,22,22,24,23,26,26,25,25,27,29,29,28,28,30,30,31,31,32,33,33,34,34,35,
35,36,36,38,38,37,37,39,39,40,40,41,42,42,43,43,44,44,45,45,47,47,46,46,
48,48,49,49,50,51,52,53,54,54,55,55,56,57,57,58,58,59,60,61,61,62,63,63,
64,64,65,66,67,67,68,69,69,70,70,71,71,72,72,73,74,74,75,75,76,77,78,79,
80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,106,107,108,109,109,110,110,111,112,113,113,114,115,115,
116,116,117,117,118,118,119,120,120,121,122,122]);
ALF("2^2.(2^(1+8)_+:(S3xS3xS3))","2^2.O8+(2)",[1,2,3,4,5,6,7,5,12,33,34,
35,36,37,8,9,10,11,25,26,27,28,69,70,71,72,122,123,124,125,63,64,14,13,16,
15,58,57,111,110,113,112,73,31,32,29,30,29,30,31,32,75,121,120,119,118,67,
68,62,61,24,23,22,21,30,29,32,31,74,65,66,116,117,114,115,60,59,19,20,17,
18,33,34,35,36,37,38,39,12,88,89,90,91,87,42,43,40,41,37,12,8,9,44,40,41,
78,79,82,5,8,9,37,40,41,59,60,65,66,128,129,73,78,79,79,78,75,6,7,12,38,
39,37,44,82,76,77,6,7,5,38,39,37,126,127,63,64,57,58,77,76,74,75,76,77,12,
10,11,37,44,42,43,80,81,82,5,10,11,37,42,43,130,131,61,62,67,68,73,81,80,
74,80,81],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.(2^(1+8)_+:(S3xS3xS3))","2^(1+8)_+:(S3xS3xS3)",[1,1,1,1,2,3,3,4,5,
6,6,6,6,7,8,8,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,14,14,14,14,
15,15,16,16,16,16,17,18,18,18,18,19,19,19,19,20,21,21,21,21,22,22,23,23,
24,24,24,24,25,25,25,25,26,27,27,28,28,28,28,29,29,30,30,30,30,31,31,31,
31,32,33,33,34,35,35,35,35,36,37,37,38,38,39,40,41,41,42,43,43,44,44,45,
46,47,47,48,49,49,50,50,51,51,52,52,53,54,54,55,55,56,57,57,58,59,59,60,
61,62,63,63,64,64,65,66,66,67,68,68,69,69,70,70,71,71,72,73,74,74,75,76,
76,77,78,79,79,80,80,81,82,83,83,84,85,85,86,86,87,87,88,88,89,90,90,91,
92,92]);

MOT("(2^2x3^4).2^3.S4",
[
"14th maximal subgroup of 2^2.O8+(2),\n",
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[62208,62208,62208,62208,7776,7776,7776,7776,2592,2592,2592,2592,1944,1944,
1944,1944,7776,7776,7776,7776,7776,7776,7776,7776,576,576,144,144,144,144,768,
768,768,768,144,144,576,576,144,144,16,144,144,144,144,576,576,216,216,216,216
,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,24,24,24,24,
432,216,216,216,216,216,216,216,216,216,216,216,216,216,96,96,96,96,48,48,48,
48,48,24,48,48,48,48,96,96,96,96,96,96,96,96,48,48,48,48],
[,[1,1,1,1,5,5,5,5,9,9,9,9,13,13,13,13,17,17,17,17,21,21,21,21,4,4,8,8,12,12,1
,1,1,1,18,18,2,2,10,10,34,23,23,11,11,3,3,48,48,48,48,52,52,52,52,56,56,56,56,
60,60,60,60,64,64,64,64,48,48,48,48,1,17,17,5,5,21,21,13,13,13,13,9,9,9,25,25,
25,25,27,27,27,27,1,9,35,35,35,35,37,37,37,37,46,46,46,46,42,42,42,42],[1,2,3,
4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,25,26,25,26,25,26,31,32,33,34,37,38,
37,38,37,38,41,46,47,46,47,46,47,1,2,3,4,13,14,15,16,1,2,3,4,13,14,15,16,13,14
,15,16,34,33,32,31,72,72,72,72,72,72,72,72,72,72,72,72,72,72,86,87,88,89,86,87
,88,89,94,94,100,101,102,103,100,101,102,103,104,105,106,107,104,105,106,107]]
,
0,
[
( 86, 89)( 87, 88)( 90, 93)( 91, 92)( 96, 97)( 98, 99)(100,101)(102,103)
(104,106)(105,107)(108,110)(109,111)
,
( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 86, 87)( 88, 89)( 90, 91)( 92, 93)
( 96, 97)( 98, 99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)
,
( 73, 74)( 77, 78)( 79, 82)( 80, 81)( 96, 98)( 97, 99)(100,102)(101,103)
(104,105)(106,107)(108,109)(110,111)
,
(  3,  4)(  5, 21)(  6, 22)(  7, 24)(  8, 23)( 11, 12)( 15, 16)( 19, 20)
( 25, 46)( 26, 47)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 31, 32)( 50, 51)
( 52, 64)( 53, 65)( 54, 67)( 55, 66)( 58, 59)( 62, 63)( 70, 71)( 75, 77)
( 76, 78)( 81, 82)( 83, 84)( 86,104)( 87,105)( 88,107)( 89,106)( 90,108)
( 91,109)( 92,111)( 93,110)( 98, 99)(102,103)
,
(  2,  3)(  6,  7)( 10, 11)( 14, 15)( 17, 21)( 18, 23)( 19, 22)( 20, 24)
( 32, 33)( 35, 42)( 36, 43)( 37, 46)( 38, 47)( 39, 44)( 40, 45)( 49, 50)
( 53, 54)( 57, 58)( 60, 64)( 61, 66)( 62, 65)( 63, 67)( 69, 70)( 73, 77)
( 74, 78)( 80, 81)( 84, 85)( 87, 88)( 91, 92)( 96,108)( 97,110)( 98,109)
( 99,111)(100,104)(101,106)(102,105)(103,107)
],
[ "ConstructV4G", "(2x3^4:2^3).S4", (2,3,4)(5,17,21)(6,19,24)(7,20,22)(8,18,
    23)(10,11,12)(14,15,16)(25,37,46)(26,38,47)(27,35,42)(28,36,43)(29,39,
    44)(30,40,45)(31,33,32)(49,50,51)(52,60,64)(53,62,67)(54,63,65)(55,61,
    66)(57,58,59)(69,70,71)(73,77,75)(74,78,76)(80,81,82)(83,85,84)(86,100,
    104)(87,102,107)(88,103,105)(89,101,106)(90,96,108)(91,98,111)(92,99,
    109)(93,97,110) ]);
ALF("(2^2x3^4).2^3.S4","(2x3^4:2^3).S4",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,
8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,19,20,21,22,23,
24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,
36,37,37,38,38,39,39,40,41,42,43,43,44,44,45,45,46,46,47,48,49,50,50,51,
51,52,52,53,53,54,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,63]);
ALF("(2^2x3^4).2^3.S4","3^4:2^3.S4(a)",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,
5,5,5,6,6,6,6,7,7,8,8,9,9,10,10,10,10,11,11,12,12,13,13,14,15,15,16,16,17,
17,18,18,18,18,19,19,19,19,20,20,20,20,21,21,21,21,22,22,22,22,23,23,23,
23,24,25,25,26,26,27,27,28,28,28,28,29,30,31,32,32,32,32,33,33,33,33,34,
35,36,36,36,36,37,37,37,37,38,38,38,38,39,39,39,39]);
ALF("(2^2x3^4).2^3.S4","2^2.O8+(2)",[1,2,4,3,17,18,20,19,29,30,32,31,25,
26,28,27,13,14,16,15,21,22,24,23,8,9,65,66,78,79,12,12,12,12,63,64,6,7,76,
77,44,67,68,80,81,10,11,29,30,32,31,96,97,99,98,25,26,28,27,92,93,95,94,
100,101,103,102,82,82,82,82,5,57,58,59,60,61,62,69,70,72,71,74,75,73,40,
41,41,40,128,129,129,128,12,82,126,126,127,127,38,38,39,39,42,43,42,43,
130,131,130,131],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("(2x2.(A5xA5)):2^2",
[
"15th maximal subgroup of 2^2.O8+(2),\n",
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[57600,57600,57600,57600,288,288,128,128,144,144,144,144,144,144,144,144,64,64
,64,64,200,200,200,200,200,200,200,200,960,960,1440,1440,1440,1440,1200,1200,
1200,1200,72,72,48,48,48,48,40,40,60,60,60,60,48,48,48,48,960,960,960,960,32,
32,48,48,48,48,40,40,40,40,960,960,960,960,48,48,48,48,32,32,40,40,40,40],
[,[1,1,1,1,2,2,1,1,9,9,9,9,10,10,10,10,7,7,7,7,23,23,23,23,28,28,28,28,2,2,32,
32,32,32,35,35,35,35,31,31,30,30,31,31,36,36,48,48,48,48,43,43,43,43,4,4,4,4,8
,8,12,12,12,12,22,22,22,22,3,3,3,3,11,11,11,11,8,8,26,26,26,26],[1,2,3,4,5,6,7
,8,1,2,3,4,5,5,6,6,18,17,20,19,21,22,23,24,25,26,27,28,29,30,2,1,4,3,35,36,37,
38,5,6,41,42,30,29,45,46,36,35,38,37,41,41,42,42,58,57,56,55,60,59,57,58,55,56
,68,67,66,65,71,72,69,70,71,72,69,70,78,77,81,82,79,80],,[1,2,3,4,5,6,7,8,9,10
,11,12,13,14,15,16,17,18,19,20,3,4,1,2,4,3,2,1,29,30,31,32,33,34,1,2,3,4,39,40
,41,42,43,44,30,29,31,32,33,34,51,52,53,54,55,56,57,58,59,60,61,62,63,64,57,58
,55,56,69,70,71,72,73,74,75,76,77,78,72,71,70,69]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1],[1,1,1,1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,-1,-1,1,1,1,1,1,
1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,
-1,-1,1,1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,
-E(4),-E(4),E(4),E(4),-E(4),E(4),-E(4),-E(4),E(4),E(4),E(4),E(4),-E(4),-E(4),
E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),-E(4),E(4),-E(4),-E(4),-E(4),E(4),E(4)],
[TENSOR,[5,4]],
[TENSOR,[2,6]],
[TENSOR,[2,5]],[8,8,-8,-8,-4,4,0,0,2,2,-2,-2,2,2,-2,-2,0,0,0,0,2,2,-2,-2,2,2,
-2,-2,-4,4,5,5,-5,-5,3,3,-3,-3,-1,1,2,-2,1,-1,-1,1,0,0,0,0,-1,-1,1,1,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[9,2]],
[TENSOR,[9,7]],
[TENSOR,[9,5]],[10,10,-10,-10,-2,2,2,-2,-2,-2,2,2,-2,-2,2,2,-2,-2,2,2,0,0,0,0
,0,0,0,0,-6,6,4,4,-4,-4,5,5,-5,-5,-2,2,0,0,0,0,1,-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],
[TENSOR,[13,2]],
[TENSOR,[13,7]],
[TENSOR,[13,5]],[12,12,12,12,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,
2,4,4,6,6,6,6,7,7,7,7,0,0,0,0,-2,-2,-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],
[TENSOR,[17,5]],[16,16,16,16,-4,-4,0,0,1,1,1,1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,
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[TENSOR,[19,4]],
[TENSOR,[19,3]],
[TENSOR,[19,2]],
[TENSOR,[19,8]],
[TENSOR,[19,7]],
[TENSOR,[19,6]],
[TENSOR,[19,5]],[18,18,18,18,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,3,3,
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0,0,0,0,0,6,6,6,6,0,0,0,0,-2,-2,1,1,1,1],
[TENSOR,[27,3]],[18,18,18,18,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,-2,-2,-2
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0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,2]],
[TENSOR,[27,6]],
[TENSOR,[27,5]],
[TENSOR,[29,6]],
[TENSOR,[29,5]],[25,25,25,25,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,
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,-5,-1,-1,1,1,1,1,0,0,0,0,5,5,5,5,-1,-1,-1,-1,1,1,0,0,0,0],
[TENSOR,[35,4]],
[TENSOR,[35,3]],
[TENSOR,[35,2]],
[TENSOR,[35,8]],
[TENSOR,[35,7]],
[TENSOR,[35,6]],
[TENSOR,[35,5]],[40,40,-40,-40,-4,4,0,0,-2,-2,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,0
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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],
[TENSOR,[43,2]],
[TENSOR,[43,7]],
[TENSOR,[43,5]],[48,48,48,48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,
-2,-2,-2,-8,-8,6,6,6,6,-2,-2,-2,-2,0,0,0,0,-2,-2,2,2,1,1,1,1,0,0,0,0,0,0,0,0,0
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[TENSOR,[47,5]],[60,60,60,60,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-4,-4,-6,-6,-6,-6,5,5,5,5,0,0,0,0,2,2,1,1,-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],
[TENSOR,[49,5]],[8,-8,8,-8,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,-2,2,-2,2,-3,3,
-3,3,0,0,4,-4,4,-4,-2,2,-2,2,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0
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[TENSOR,[51,3]],[8,-8,8,-8,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,3,-3,3,-3,2,-2,2
,-2,0,0,4,-4,4,-4,-2,2,-2,2,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,-4*E(4),4*E(4),
-4*E(4),4*E(4),0,0,-2*E(4),2*E(4),-2*E(4),2*E(4),E(4),-E(4),E(4),-E(4),0,0,0,0
,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[53,2]],[16,-16,16,-16,0,0,0,0,1,-1,1,-1,-3*E(4),3*E(4),-3*E(4),
3*E(4),0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,-4,4,-4,4,-4,4,-4,4,0,0,0,0,0,0,0,0,1,
-1,1,-1,0,0,0,0,-4*E(4),4*E(4),-4*E(4),4*E(4),0,0,E(4),-E(4),E(4),-E(4),E(4),
-E(4),E(4),-E(4),-4,4,-4,4,-1,1,-1,1,0,0,-1,1,-1,1],
[TENSOR,[55,2]],
[TENSOR,[55,4]],
[TENSOR,[55,3]],[32,-32,32,-32,0,0,0,0,-4,4,-4,4,0,0,0,0,0,0,0,0,2,-2,2,-2,-2
,2,-2,2,0,0,4,-4,4,-4,-8,8,-8,8,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[36,-36,36,-36,0,0,0,0,0,0,0,0,0,
0,0,0,-2*E(4),2*E(4),-2*E(4),2*E(4),1,-1,1,-1,-1,1,-1,1,0,0,0,0,0,0,6,-6,6,-6,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6*E(4),6*E(4),-6*E(4),6*E(4),0,0,0,0,0,0,
-E(4),E(4),-E(4),E(4),-6,6,-6,6,0,0,0,0,0,0,1,-1,1,-1],
[TENSOR,[60,2]],
[TENSOR,[60,4]],
[TENSOR,[60,3]],[48,-48,48,-48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,2,-2
,2,-2,0,0,12,-12,12,-12,-2,2,-2,2,0,0,0,0,0,0,0,0,2,-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],[48,-48,48,-48,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,-2,2,-2,2,2,-2,2,-2,0,0,-6,6,-6,6,-2,2,-2,2,0,0,0,0,0,0,0,0,-1
,1,-1,1,-E(24)-E(24)^11+E(24)^17+E(24)^19,E(24)+E(24)^11-E(24)^17-E(24)^19,
-E(24)-E(24)^11+E(24)^17+E(24)^19,E(24)+E(24)^11-E(24)^17-E(24)^19,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[65,2]],
[TENSOR,[53,5]],
[TENSOR,[53,6]],
[TENSOR,[51,6]],
[TENSOR,[51,5]],
[TENSOR,[55,7]],
[TENSOR,[55,5]],
[TENSOR,[55,8]],
[TENSOR,[55,6]],
[TENSOR,[59,5]],
[TENSOR,[60,7]],
[TENSOR,[60,5]],
[TENSOR,[60,8]],
[TENSOR,[60,6]],
[TENSOR,[64,5]],
[TENSOR,[65,5]],
[TENSOR,[65,7]]],
[(51,52)(53,54),
(55,56)(57,58)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(79,80)
(81,82)
,
(55,57)(56,58)(59,60)(61,63)(62,64)(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)
(77,78)(79,81)
(80,82)
,(13,14)(15,16)(17,18)(19,20)(69,70)(71,72)(73,74)(75,76)(79,80)(81,82),
( 5, 6)(13,15)(14,16)(17,19)(18,20)(39,40)(41,42)(51,53)(52,54)(69,71)(70,72)
(73,75)(74,76)
(77,78)(79,81)(80,82)
,
( 3, 4)(11,12)(15,16)(17,18)(21,25)(22,26)(23,28)(24,27)(33,34)(37,38)(49,50)
(53,54)
(55,69,56,70)(57,72,58,71)(59,77)(60,78)(61,74,62,73)(63,75,64,76)(65,79,66,80
)(67,82,68,81)
]);
ALF("(2x2.(A5xA5)):2^2","2^2.O8+(2)",[1,2,3,4,6,7,12,12,29,30,31,32,76,76,
77,77,44,44,44,44,55,56,53,54,52,51,50,49,7,6,14,13,16,15,45,46,47,48,63,
64,39,38,63,64,104,105,133,132,135,134,127,127,126,126,10,11,11,10,44,44,
81,80,80,81,109,108,108,109,8,9,8,9,78,79,78,79,44,44,107,106,107,106],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(2x2.(A5xA5)):2^2","(A5xA5).(2x4)",[1,1,2,2,3,4,5,6,7,7,8,8,9,9,10,
10,12,12,11,11,14,14,13,13,16,16,15,15,18,17,19,19,20,20,21,21,22,22,23,
24,26,25,27,28,29,30,31,31,32,32,34,34,33,33,35,35,36,36,37,38,39,39,40,
40,42,42,41,41,43,43,44,44,45,45,46,46,47,48,50,50,49,49]);
ALF("(2x2.(A5xA5)):2^2","(A5xA5):2^2",[1,1,1,1,2,2,3,3,4,4,4,4,5,5,5,5,6,
6,6,6,7,7,7,7,8,8,8,8,9,9,10,10,10,10,11,11,11,11,12,12,13,13,14,14,15,15,
16,16,16,16,17,17,17,17,18,18,18,18,19,19,20,20,20,20,21,21,21,21,22,22,
22,22,23,23,23,23,24,24,25,25,25,25]);

MOT("2^2.O8+(2)M16",
[
"16th maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M15 = (2x2.(A5xA5)):2^2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(2x2.(A5xA5)):2^2"]]);
ALF("2^2.O8+(2)M16","2.(A5xA5).2^2",[1,2,2,1,3,3,4,4,5,6,6,5,7,8,8,7,10,9,
9,10,12,11,11,12,13,14,14,13,15,15,17,16,16,17,18,19,19,18,20,20,21,21,22,
22,23,23,25,24,24,25,26,27,27,26,28,29,29,28,30,30,32,31,31,32,33,34,34,
33,36,35,35,36,37,38,38,37,39,39,41,40,40,41]);
ALF("2^2.O8+(2)M16","O8+(2)M16",[1,1,1,1,2,2,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,
7,7,7,8,8,8,8,9,9,10,10,10,10,11,11,11,11,12,12,13,13,14,14,15,15,16,16,
16,16,17,17,17,17,18,18,18,18,19,19,20,20,20,20,21,21,21,21,22,22,22,22,
23,23,23,23,24,24,25,25,25,25]);
ALF("2^2.O8+(2)M16","2^2.O8+(2)",[1,3,4,2,8,9,12,12,29,31,32,30,78,78,79,
79,44,44,44,44,48,46,45,47,54,56,55,53,9,8,19,17,18,20,49,51,52,50,65,66,
41,40,65,66,106,107,138,136,137,139,129,129,128,128,6,7,7,6,44,44,77,76,
76,77,105,104,104,105,10,11,10,11,80,81,80,81,44,44,109,108,109,108],[
"fusion (2x2.(A5xA5)):2^2 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);

MOT("2^2.O8+(2)M17",
[
"17th maximal subgroup of 2^2.O8+(2),\n",
"differs from 2^2.O8+(2)M15 = (2x2.(A5xA5)):2^2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(2x2.(A5xA5)):2^2"]]);
ALF("2^2.O8+(2)M17","2.O8+(2)M17",[1,2,1,2,3,3,4,4,5,6,5,6,7,8,7,8,9,10,9,
10,13,14,13,14,12,11,12,11,15,15,17,16,17,16,18,19,18,19,20,20,21,21,22,
22,23,23,25,24,25,24,26,27,26,27,35,36,35,36,39,39,37,38,37,38,40,41,40,
41,28,29,28,29,31,32,31,32,30,30,33,34,33,34]);
ALF("2^2.O8+(2)M17","O8+(2)M17",[1,1,1,1,2,2,3,3,4,4,4,4,5,5,5,5,6,6,6,6,
8,8,8,8,7,7,7,7,9,9,10,10,10,10,11,11,11,11,12,12,13,13,14,14,15,15,16,16,
16,16,17,17,17,17,22,22,22,22,24,24,23,23,23,23,25,25,25,25,18,18,18,18,
20,20,20,20,19,19,21,21,21,21]);
ALF("2^2.O8+(2)M17","2^2.O8+(2)",[1,4,2,3,10,11,12,12,29,32,30,31,80,80,
81,81,44,44,44,44,50,51,49,52,47,46,48,45,11,10,24,21,23,22,53,56,54,55,
67,68,43,42,67,68,108,109,143,140,142,141,131,131,130,130,8,9,9,8,44,44,
79,78,78,79,107,106,106,107,6,7,6,7,76,77,76,77,44,44,105,104,105,104],[
"fusion 2^2.O8+(2)M16 -> 2^2.O8+(2) mapped under 2^2.O8+(2).3"
]);

MOT("(4^2x2)(2xS4)",
[
"origin: Dixon's Algorithm"
],
[1536,512,256,256,128,384,64,64,64,64,12,12,32,64,64,32,64,64,16,16,96,96,64,
64,64,64,12,12,64,64,32,64,64,32,16,16],
[,[1,1,2,2,2,1,2,2,1,1,11,11,5,1,2,5,2,1,10,10,1,1,5,5,5,5,11,11,2,1,5,2,1,5,7
,7],[1,2,3,4,5,6,7,8,9,10,1,6,13,14,15,16,17,18,19,20,21,22,23,24,25,26,21,22,
29,30,31,32,33,34,35,36]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,
1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,1,1,1,-1,-1,
-1,1,1,-1],[1,1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,1
,-1,-1,-1,1,1,1,-1,-1,1],[1,1,-1,-1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,-1
,1,-1,-1,1,1,-1,1,-1,-1,1,1,1,-1,-1,1],[1,1,-1,-1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,
-1,1,1,1,-1,1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,-1,1,1,-1],
[TENSOR,[2,5]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,2,-2,-2,2,-2,2,-2,-2,2,-1,1,0,0,0,0,0,0,0,0,-2,2,-2,-2,2,2,
1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[9,6]],
[TENSOR,[9,3]],
[TENSOR,[9,2]],[3,3,-3,-3,3,-3,-1,1,1,-1,0,0,-1,1,1,1,-1,-1,1,-1,-3,3,1,1,-1,
-1,0,0,1,1,-1,-1,-1,1,-1,1],
[TENSOR,[13,8]],
[TENSOR,[13,7]],
[TENSOR,[13,6]],
[TENSOR,[13,5]],
[TENSOR,[13,4]],
[TENSOR,[13,3]],
[TENSOR,[13,2]],[6,6,-2,-2,-2,6,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,-2,-2,2,-2,-2,2,0,0],
[TENSOR,[21,7]],
[TENSOR,[21,3]],
[TENSOR,[21,2]],[6,6,-2,-2,-2,6,-2,2,-2,2,0,0,-2,2,2,-2,2,2,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],
[TENSOR,[25,6]],
[TENSOR,[25,4]],
[TENSOR,[25,2]],[12,-4,-4,4,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,-2,2,-2,2,0
,0,-2,2,0,2,-2,0,0,0],
[TENSOR,[29,8]],
[TENSOR,[29,7]],
[TENSOR,[29,6]],
[TENSOR,[29,3]],
[TENSOR,[29,2]],
[TENSOR,[29,5]],
[TENSOR,[29,4]]],
[(13,16)(14,18)(15,17)(19,20)(23,24)(25,26)(29,32)(30,33)(31,34)(35,36),
(13,16)(14,18)(15,17)(19,20)(21,22)(23,25)(24,26)(27,28)]);
ARC("(4^2x2)(2xS4)","tomfusion",rec(name:="(4^2x2)(2xS4)",map:=[1,11,45,
47,44,10,50,43,8,3,12,54,166,2,49,167,41,9,23,18,7,5,168,165,170,172,53,
57,48,4,169,42,6,164,180,179],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("(4^2x2)(2xS4)","U4(3).(2^2)_{133}",[1,2,17,18,6,15,7,18,16,2,5,21,12,
15,18,22,6,2,7,18,27,36,30,31,40,39,29,38,28,27,40,37,36,31,32,41],[
"fusion map is unique up to table automorphisms"
]);

MOT("(4^2x2)S4",
[
"origin: Dixon's Algorithm"
],
[768,256,32,32,64,6,32,32,8,16,48,32,32,6,32,32,8,16],
[,[1,1,1,2,2,6,2,1,3,5,1,5,5,6,2,1,4,5],[1,2,3,4,5,1,7,8,9,10,11,12,13,11,15,
16,17,18]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,
1,1,1],[1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,-1,0,0,0,0,-2,-2,-2,1,0,0,0,0],
[TENSOR,[5,2]],[3,3,-1,-1,3,0,-1,-1,1,-1,-3,1,1,0,1,1,-1,1],
[TENSOR,[7,4]],
[TENSOR,[7,3]],
[TENSOR,[7,2]],[6,6,2,-2,-2,0,-2,-2,0,2,0,0,0,0,0,0,0,0],
[TENSOR,[11,2]],[6,6,-2,2,-2,0,0,0,0,0,0,0,0,0,-2,-2,0,2],
[TENSOR,[13,3]],[12,-4,0,0,0,0,-2,2,0,0,0,-2,2,0,2,-2,0,0],
[TENSOR,[15,4]],
[TENSOR,[15,3]],
[TENSOR,[15,2]]],
[]);
ARC("(4^2x2)S4","tomfusion",rec(name:="(4^2x2)S4",map:=[1,2,4,17,9,7,13,6,
21,49,3,34,29,25,15,5,57,50],text:=[
"fusion map is unique"
]));
ALF("(4^2x2)S4","U4(3).2_3",[1,2,2,7,6,5,6,2,7,12,16,19,20,18,17,16,21,20],[
"fusion map is unique"
]);
ALF("(4^2x2)S4","Ly",[1,2,2,5,5,4,5,2,5,12,2,12,13,10,5,2,13,13],[
"determined uniquely by factorization through 3.McL.2"
]);

MOT("(4^2x3):S3",
[
"origin: Dixon's Algorithm"
],
[288,96,96,96,8,8,8,8,48,48,48,48,48,144,48,9,9,9],
[,[1,1,2,2,3,4,1,2,15,15,15,2,15,14,14,16,17,18],[1,2,4,3,6,5,7,8,4,12,3,12,12
,1,2,1,1,1]],
[[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],[2,2,2,2,0,0,0,0,2,2,2,2,2,2,2,-1,-1,-1],[2,2,2,2,0,0,0,0,-1,-1,-1,2,-1,-1,
-1,2,-1,-1],[2,2,2,2,0,0,0,0,-1,-1,-1,2,-1,-1,-1,-1,-1,2],[2,2,2,2,0,0,0,0,-1,
-1,-1,2,-1,-1,-1,-1,2,-1],[3,3,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,3,3,0,0,0],
[TENSOR,[7,2]],[3,-1,-1-2*E(4),-1+2*E(4),-E(4),E(4),-1,1,-1-2*E(4),1,
-1+2*E(4),1,1,3,-1,0,0,0],
[GALOIS,[9,3]],
[TENSOR,[9,2]],
[TENSOR,[10,2]],[6,6,-2,-2,0,0,0,0,1,1,1,-2,1,-3,-3,0,0,0],[6,-2,2,2,0,0,0,0,
2,-2,2,-2,-2,6,-2,0,0,0],[6,-2,-2+4*E(4),-2-4*E(4),0,0,0,0,1-2*E(4),-1,
1+2*E(4),2,-1,-3,1,0,0,0],
[GALOIS,[15,3]],[6,-2,2,2,0,0,0,0,-1,-E(12)^4-2*E(12)^7-E(12)^8+2*E(12)^11,-1
,-2,-E(12)^4+2*E(12)^7-E(12)^8-2*E(12)^11,-3,1,0,0,0],
[GALOIS,[17,5]]],
[(17,18),(16,17),(10,13),( 3, 4)( 5, 6)( 9,11)]);
ARC("(4^2x3):S3","tomfusion",rec(name:="(4^2x3):S3",map:=[1,2,10,10,23,23,
3,11,26,27,26,9,27,4,13,6,5,7],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("(4^2x3):S3","U3(11)",[1,2,4,5,10,11,2,6,18,20,19,6,21,3,9,3,3,3],[
"fusion map is unique up to table automorphisms"
]);

MOT("(7:3x3):2",
[
"origin: Dixon's Algorithm"
],
[126,6,6,18,18,6,21,9,9,21,21,63],
[,[1,4,5,5,4,1,7,9,8,11,10,12],[1,6,6,1,1,6,7,1,1,7,7,1],,,,[1,2,3,4,5,6,1,8,9
,12,12,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,-1,1,1,-1,1,1,1,1,1,1],[1,-E(3),-E(3)^2,
E(3)^2,E(3),-1,1,E(3)^2,E(3),1,1,1],
[GALOIS,[3,2]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,0,0,2,2,0,2,-1,-1,-1,-1,-1],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[6,0,0,0,0,0,-1,0,0,-1,-1,6],[6,0,0,0,0,0,-1,0,0,
E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19,
E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,-3],
[GALOIS,[11,2]]],
[(10,11),(2,3)(4,5)(8,9)]);
ARC("(7:3x3):2","tomfusion",rec(name:="(7:3x3):2",map:=[1,7,7,5,5,2,8,4,4,
12,12,3],text:=[
"fusion map is unique"
]));
ALF("(7:3x3):2","U3(5).3.2",[1,24,24,3,3,22,8,12,12,17,18,12],[
"fusion map is unique up to table automorphisms"
]);
ALF("(7:3x3):2","S3x7:6",[1,17,21,4,6,19,2,11,13,9,9,8],[
"fusion map is unique up to table automorphisms"
]);
ALF("(7:3x3):2","G2(4)",[1,14,14,5,5,3,15,5,5,31,32,4],[
"fusion map is unique up to table aut."
]);
ALF("(7:3x3):2","3.A7.2",[1,20,20,6,6,17,13,6,6,14,15,2],[
"fusion map is unique up to table aut."
]);
ALN("(7:3x3):2",["G2(4)N7"]);

MOT("(7xL2(7)):2",
[
"origin: Dixon's Algorithm"
],
[2352,1176,1176,1176,6,12,42,21,21,21,49,49,49,49,49,49,49,56,56,56,112,8,8,28
,28,28,56],
[,[1,4,2,3,7,1,7,10,8,9,11,14,15,16,17,12,13,4,3,2,1,27,27,19,20,18,21],[1,3,4
,2,6,6,1,3,4,2,11,16,17,12,13,14,15,20,18,19,21,23,22,26,24,25,27],,,,[1,1,1,1
,5,6,7,7,7,7,1,1,1,1,1,1,1,21,21,21,21,22,23,27,27,27,27]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,-1,-1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,1],[2,E(7)^3+E(7)^4,E(7)^2+E(7)^5,
E(7)+E(7)^6,0,0,2,E(7)^3+E(7)^4,E(7)^2+E(7)^5,E(7)+E(7)^6,2,E(7)^3+E(7)^4,
E(7)^2+E(7)^5,E(7)+E(7)^6,E(7)^3+E(7)^4,E(7)^2+E(7)^5,E(7)+E(7)^6,
E(7)^3+E(7)^4,E(7)+E(7)^6,E(7)^2+E(7)^5,2,0,0,E(7)^3+E(7)^4,E(7)+E(7)^6,
E(7)^2+E(7)^5,2],
[GALOIS,[3,3]],
[GALOIS,[3,2]],[6,6,6,6,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-2,-2,-2,-2,0,0,2,2,
2,2],[6,6,6,6,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,-E(8)+E(8)^3,
E(8)-E(8)^3,0,0,0,0],
[TENSOR,[7,2]],[6,3*E(7)^3+3*E(7)^4,3*E(7)^2+3*E(7)^5,3*E(7)+3*E(7)^6,0,0,0,0
,0,0,-1,-2*E(7)-E(7)^2-E(7)^3-E(7)^4-E(7)^5-2*E(7)^6,
E(7)+2*E(7)^3+2*E(7)^4+E(7)^6,-E(7)-2*E(7)^2-E(7)^3-E(7)^4-2*E(7)^5-E(7)^6,
2*E(7)+E(7)^2+E(7)^5+2*E(7)^6,-E(7)-E(7)^2-2*E(7)^3-2*E(7)^4-E(7)^5-E(7)^6,
2*E(7)^2+E(7)^3+E(7)^4+2*E(7)^5,-E(7)^3-E(7)^4,-E(7)-E(7)^6,-E(7)^2-E(7)^5,-2,
0,0,E(7)^3+E(7)^4,E(7)+E(7)^6,E(7)^2+E(7)^5,2],
[GALOIS,[9,3]],
[GALOIS,[9,2]],[6,3*E(7)^3+3*E(7)^4,3*E(7)^2+3*E(7)^5,3*E(7)+3*E(7)^6,0,0,0,0
,0,0,-1,2*E(7)+E(7)^2+E(7)^5+2*E(7)^6,
-E(7)-E(7)^2-2*E(7)^3-2*E(7)^4-E(7)^5-E(7)^6,2*E(7)^2+E(7)^3+E(7)^4+2*E(7)^5,
-2*E(7)-E(7)^2-E(7)^3-E(7)^4-E(7)^5-2*E(7)^6,E(7)+2*E(7)^3+2*E(7)^4+E(7)^6,
-E(7)-2*E(7)^2-E(7)^3-E(7)^4-2*E(7)^5-E(7)^6,-E(7)^3-E(7)^4,-E(7)-E(7)^6,
-E(7)^2-E(7)^5,-2,0,0,E(7)^3+E(7)^4,E(7)+E(7)^6,E(7)^2+E(7)^5,2],
[GALOIS,[12,3]],
[GALOIS,[12,2]],[7,7,7,7,-1,-1,1,1,1,1,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,-1,-1,-1
,-1],
[TENSOR,[15,2]],[8,8,8,8,-1,2,-1,-1,-1,-1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[17,2]],[12,6*E(7)^3+6*E(7)^4,6*E(7)^2+6*E(7)^5,6*E(7)+6*E(7)^6,0,0,0
,0,0,0,-2,-E(7)^3-E(7)^4,-E(7)^2-E(7)^5,-E(7)-E(7)^6,-E(7)^3-E(7)^4,
-E(7)^2-E(7)^5,-E(7)-E(7)^6,2*E(7)^3+2*E(7)^4,2*E(7)+2*E(7)^6,
2*E(7)^2+2*E(7)^5,4,0,0,0,0,0,0],
[GALOIS,[19,3]],
[GALOIS,[19,2]],[14,7*E(7)^3+7*E(7)^4,7*E(7)^2+7*E(7)^5,7*E(7)+7*E(7)^6,0,0,2
,E(7)^3+E(7)^4,E(7)^2+E(7)^5,E(7)+E(7)^6,0,0,0,0,0,0,0,-E(7)^3-E(7)^4,
-E(7)-E(7)^6,-E(7)^2-E(7)^5,-2,0,0,-E(7)^3-E(7)^4,-E(7)-E(7)^6,-E(7)^2-E(7)^5,
-2],
[GALOIS,[22,3]],
[GALOIS,[22,2]],[16,8*E(7)^3+8*E(7)^4,8*E(7)^2+8*E(7)^5,8*E(7)+8*E(7)^6,0,0,
-2,-E(7)^3-E(7)^4,-E(7)^2-E(7)^5,-E(7)-E(7)^6,2,E(7)^3+E(7)^4,E(7)^2+E(7)^5,
E(7)+E(7)^6,E(7)^3+E(7)^4,E(7)^2+E(7)^5,E(7)+E(7)^6,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,3]],
[GALOIS,[25,2]]],
[(22,23),(12,15)(13,16)(14,17),
( 2, 3, 4)( 8, 9,10)(12,13,14,15,16,17)(18,20,19)(24,26,25)]);
ARC("(7xL2(7)):2","tomfusion",rec(name:="(7xL2(7)):2",map:=[1,11,11,11,10,
3,4,27,27,27,12,14,13,14,13,14,13,20,20,20,2,16,16,30,30,30,6],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("(7xL2(7)):2","3D4(2)",[1,11,13,12,10,3,4,30,32,31,14,12,14,13,14,11,
14,24,25,26,2,15,15,33,34,35,6],[
"fusion map is unique up to table automorphisms"
]);

MOT("(9x3).S3",
[
"origin: Dixon's Algorithm"
],
[162,9,6,9,6,9,6,27,54,54,27,27,81],
[,[1,2,1,4,9,6,10,11,10,9,12,8,13],[1,1,3,1,3,1,3,13,1,1,13,13,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,-1,1,-1,1,1,1,1,1,1],[2,-1,0,-1,0,-1,0,
2,2,2,2,2,2],[2,2,0,-1,0,-1,0,-1,2,2,-1,-1,2],[2,-1,0,-1,0,2,0,-1,2,2,-1,-1,2]
,[2,-1,0,2,0,-1,0,-1,2,2,-1,-1,2],[3,0,-1,0,-E(3),0,-E(3)^2,0,3*E(3)^2,3*E(3),
0,0,3],
[GALOIS,[7,2]],
[TENSOR,[8,2]],
[TENSOR,[7,2]],[6,0,0,0,0,0,0,2*E(9)^2+E(9)^4+E(9)^5+2*E(9)^7,0,0,
-E(9)^2+E(9)^4+E(9)^5-E(9)^7,-E(9)^2-2*E(9)^4-2*E(9)^5-E(9)^7,-3],
[GALOIS,[11,2]],
[GALOIS,[11,4]]],
[( 8,11,12),( 5, 7)( 9,10),(4,6),(2,4)]);
ARC("(9x3).S3","tomfusion",rec(name:="(9x3).S3",map:=[1,6,2,7,11,5,11,17,
4,4,17,17,3],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("(9x3).S3","U3(8)",[1,5,2,5,9,5,10,14,4,3,15,16,5],[
"fusion map is unique up to table automorphisms"
]);

MOT("(A5xA5):2^2",
[
"origin: Dixon's Algorithm"
],
[14400,144,64,36,36,16,50,50,480,360,300,36,24,24,20,15,12,240,16,12,10,240,12
,16,10],
[,[1,1,1,4,4,3,7,8,1,10,11,10,9,10,11,16,14,1,3,4,7,1,4,3,8],[1,2,3,1,2,6,7,8,
9,1,11,2,13,9,15,11,13,18,19,18,21,22,22,24,25],,[1,2,3,4,5,6,1,1,9,10,1,12,13
,14,9,10,17,18,19,20,18,22,23,24,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,1,1,-1,-1,1,1,1,1,1
,-1,-1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1],[1,-1,1,1,-1,-1,1,1,1,1,1,-1,-1,1,1,1,-1,
1,1,1,1,-1,-1,-1,-1],
[TENSOR,[2,3]],[8,-4,0,2,2,0,-2,-2,4,5,3,-1,-2,1,-1,0,1,0,0,0,0,0,0,0,0],
[TENSOR,[5,2]],[10,-2,2,-2,-2,2,0,0,6,4,5,-2,0,0,1,-1,0,0,0,0,0,0,0,0,0],
[TENSOR,[7,2]],[12,0,-4,0,0,0,2,2,4,6,7,0,0,-2,-1,1,0,0,0,0,0,0,0,0,0],[16,-4
,0,1,-1,0,1,1,0,4,-4,2,0,0,0,-1,0,-4,0,-1,1,4,1,0,-1],
[TENSOR,[10,4]],
[TENSOR,[10,3]],
[TENSOR,[10,2]],[18,0,2,0,0,0,-2,3,-6,0,3,0,0,0,-1,0,0,0,0,0,0,6,0,-2,1],
[TENSOR,[14,3]],[18,0,2,0,0,0,3,-2,-6,0,3,0,0,0,-1,0,0,-6,2,0,-1,0,0,0,0],
[TENSOR,[16,2]],[25,-1,1,1,-1,-1,0,0,5,-5,0,-1,1,-1,0,0,1,-5,-1,1,0,5,-1,1,0]
,
[TENSOR,[18,4]],
[TENSOR,[18,3]],
[TENSOR,[18,2]],[40,-4,0,-2,2,0,0,0,4,1,-5,-1,2,1,-1,1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[22,2]],[48,0,0,0,0,0,-2,-2,-8,6,-2,0,0,-2,2,1,0,0,0,0,0,0,0,0,0],[60
,0,-4,0,0,0,0,0,-4,-6,5,0,0,2,1,-1,0,0,0,0,0,0,0,0,0]],
[( 7, 8)(18,22)(19,24)(20,23)(21,25)]);
ARC("(A5xA5):2^2","tomfusion",rec(name:="(A5xA5):2^2",map:=[1,5,6,8,27,19,
24,25,2,7,23,29,13,32,68,93,85,3,20,35,72,4,36,17,71],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("(A5xA5):2^2","O8+(2)",[1,3,6,11,31,17,20,19,3,7,18,24,14,24,41,51,48,
5,17,33,43,4,32,17,42],[
"fusion map is unique up to table automorphisms"
],"tom:11076");
ALF("(A5xA5):2^2","S4(4).2",[1,20,4,5,24,23,9,11,3,6,10,25,22,13,15,17,30,
2,8,12,14,20,24,23,28],[
"fusion map is unique up to table automorphisms"
]);
ALF("(A5xA5):2^2","s5wrs2",[1,11,3,5,15,13,7,7,2,4,6,14,12,8,9,10,16,29,
30,31,32,29,31,30,32],[
"fusion map is unique"
]);

MOT("S4(4).2M7",
[
"7th maximal subgroup of S4(4).2"
],
0,
0,
0,
0,
["ConstructPermuted",["(A5xA5):2^2"]]);
ALF("S4(4).2M7","S4(4).2",[1,20,4,6,25,23,10,11,2,5,9,24,21,12,14,16,29,3,
8,13,15,20,25,23,28],[
"fusion (A5xA5):2^2 -> S4(4).2 mapped under S4(4).4"
]);

MOT("O8+(2)M16",
[
"16th maximal subgroup of O8+(2),\n",
"differs from O8+(2)M15 = (A5xA5):2^2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(A5xA5):2^2"]]);
ARC("O8+(2)M16","projectives",["2.(A5xA5).2^2",[[8,0,0,2,0,0,3,-2,0,-4,-2,0,0,
0,0,1,0,-4,0,2,-1,0,0,0,0],[8,0,0,2,0,0,-2,3,0,-4,-2,0,0,0,0,1,0,0,0,0,0,
-4*E(4),-2*E(4),0,E(4)],[16,0,0,1,-3*E(4),0,1,1,0,4,-4,0,0,0,0,-1,0,-4,0,-1,-1
,-4*E(4),E(4),0,E(4)],[32,0,0,-4,0,0,2,2,0,-4,-8,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
[36,0,0,0,0,-2*E(4),1,1,0,0,6,0,0,0,0,0,0,-6,0,0,1,-6*E(4),0,0,-E(4)],[48,0,0,
0,0,0,-2,-2,0,-12,-2,0,0,0,0,-2,0,0,0,0,0,0,0,0,0],[48,0,0,0,0,0,-2,-2,0,6,-2,
0,0,0,0,1,-E(24)-E(24)^11+E(24)^17+E(24)^19,0,0,0,0,0,0,0,0]],]);
ALF("O8+(2)M16","O8+(2)",[1,4,6,11,32,17,18,20,4,8,19,25,15,25,42,52,49,3,
17,31,41,5,33,17,43],[
"fusion (A5xA5):2^2 -> O8+(2) mapped under O8+(2).3"
]);

MOT("O8+(2)M17",
[
"17th maximal subgroup of O8+(2),\n",
"differs from O8+(2)M15 = (A5xA5):2^2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(A5xA5):2^2"]]);
ALF("O8+(2)M17","O8+(2)",[1,5,6,11,33,17,18,19,5,9,20,26,16,26,43,53,50,3,
17,31,41,4,32,17,42],[
"equals the map from O8+(2)M15, mapped under an outer autom."
]);

MOT("2.O8+(2)M3",
[
"3rd maximal subgroup of 2.O8+(2),\n",
"differs from 2.O8+(2)M2 = 2.S6(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2.S6(2)"]]);
ALF("2.O8+(2)M3","2.O8+(2)",[1,2,7,3,7,8,13,14,15,16,17,18,19,20,25,25,21,
25,31,32,40,36,41,42,40,49,45,50,51,52,53,54,55,60,61,65,65,77,77,72,73,82,
83],[
"fusion 2.S6(2) -> 2.O8+(2) mapped under 2.O8+(2).2"
]);
ALF("2.O8+(2)M3","O8+(2)M3",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14,
15,16,17,17,18,19,20,21,22,22,23,24,24,25,25,26,26,27,28,29,29,30,30]);

MOT("2.O8+(2)M6",
[
"6th maximal subgroup of 2.O8+(2),\n",
"differs from 2.O8+(2)M5 = 2^(1+6)_+.A8 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2^(1+6)_+.A8"]]);
ALF("2.O8+(2)M6","2.O8+(2)",[1,2,7,3,3,6,5,4,8,21,7,8,20,19,21,25,13,14,
36,40,18,17,43,44,49,21,26,24,22,23,25,26,53,54,55,32,31,65,40,70,71,77,
45,47,46,48,50,52,51,52,51,83,82,83,82],[
"fusion 2^(1+6)_+.A8 -> 2.O8+(2) mapped under 2.O8+(2).2"
]);
ALF("2.O8+(2)M6","O8+(2)M6",[1,1,2,3,4,6,5,5,7,8,9,10,11,11,12,13,14,14,
15,16,17,17,19,18,20,21,22,24,23,23,25,26,27,28,28,29,29,30,31,32,32,33,
34,36,36,35,37,38,38,39,39,40,40,41,41]);

MOT("2xA9",
[
"7th maximal subgroup of 2.O8+(2)"
],
0,
0,
0,
[(17,18)(35,36),(13,14)(31,32)],
["ConstructDirectProduct",[["Cyclic",2],["A9"]]]);
ALF("2xA9","2.O8+(2)",[1,4,8,9,15,17,22,26,27,37,50,51,58,60,62,74,78,78,
2,5,8,10,16,18,23,26,28,38,50,52,59,61,63,75,79,79],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2.O8+(2)M9",
[
"9th maximal subgroup of 2.O8+(2),\n",
"differs from 2.O8+(2)M8 = 2.A9 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2.A9"]]);
ALF("2.O8+(2)M9","2.O8+(2)",[1,2,7,8,13,14,15,16,17,18,25,26,31,32,40,50,
50,51,52,56,57,58,59,65,77,77,82,83,82,83],[
"equals the map from 2.O8+(2)M8, mapped under an outer autom."
]);
ALF("2.O8+(2)M9","O8+(2)M9",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,12,13,
13,14,14,15,16,16,17,17,18,18]);

MOT("2x(3xU4(2)):2",
[
"10th maximal subgroup of 2.O8+(2)",
],
0,
0,
0,
[(4,5)(29,30)(31,33)(34,35)(41,42)(49,50)(74,75)(76,78)(79,80)(86,87),(14,59)
(15,60)(16,61)(21,66)(22,67)(25,70)(26,71)(27,72)(37,82)(43,88)],
["ConstructDirectProduct",[["Cyclic",2],["(3xU4(2)):2"]]]);
ALF("2x(3xU4(2)):2","(3xU4(2)):2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]);
ALF("2x(3xU4(2)):2","2.O8+(2)",[1,9,34,44,45,17,9,3,33,37,4,22,74,22,23,
75,46,37,66,19,53,50,15,17,8,46,4,41,35,36,11,15,13,70,68,72,62,78,27,56,
60,58,37,43,42,2,10,33,44,45,18,10,3,34,38,5,23,75,23,22,74,47,38,67,20,
53,50,16,18,8,47,5,42,35,36,12,16,14,71,69,73,63,79,28,57,61,59,38,43,41],[
"fusion map is unique up to table automorphisms"
]);

MOT("(3x2.U4(2)):2",
[
"11th maximal subgroup of 2.O8+(2),\n",
"origin: Dixon's Algorithm"
],
[311040,155520,155520,311040,20,20,60,30,30,60,1440,12,324,648,324,648,96,432,
432,432,432,432,432,3888,3888,3888,3888,3888,3888,1728,3456,108,108,108,72,72,
72,72,72,72,576,288,288,576,72,36,648,1296,1296,648,576,288,16,16,24,48,108,
108,108,192,192,36,36,32,24,24,54,54,54,54,54,54],
[,[1,2,2,1,10,10,7,8,8,7,4,14,13,14,13,14,1,29,28,27,28,27,29,29,27,28,27,28,
29,2,1,13,13,14,18,20,19,20,19,18,31,30,30,31,49,50,47,48,48,47,4,3,44,44,52,
51,47,47,48,51,51,16,49,51,45,45,67,68,69,68,69,67],[1,1,4,4,5,6,7,7,10,10,11,
17,1,1,4,4,17,31,31,31,31,31,31,4,4,4,1,1,1,31,31,31,31,31,44,44,44,41,41,41,
41,41,44,44,51,51,1,1,4,4,51,51,53,54,56,56,31,31,31,60,61,11,11,64,61,60,28,
28,28,26,26,26],,[1,2,3,4,11,11,1,2,3,4,11,12,13,14,15,16,17,18,19,20,21,22,23
,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
,50,51,52,54,53,55,56,57,58,59,61,60,62,63,64,66,65,67,68,69,70,71,72]],
0,
[(53,54)(60,61)(65,66),(5,6),
(18,20)(22,23)(24,25)(27,29)(32,33)(35,36)(38,40)(57,58)(67,68)(70,72)],
[ "ConstructIndexTwoSubdirectProduct", "C3", "S3", "2.U4(2)", "2.U4(2).2", 
  [ 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114 ], 
  (2,4,51,68,54,72,65,62,61,60,17,19,34,50,46,58,40,8,49,33,47,57,38,42,22,71,
    66,12,41,9,14,7,48,32,24,39,55,36,15,10,16,21,69,5,28,52,67,53,70,6,26,3,
    31,25)(11,44,20,45,18,59)(13,56,35)(23,37,43)(27,30,29)(63,64), 
  (3,11,21,43,19,63,31,53,56,68,65,34,64,35,50,41,10,13,24,59,7,15,29,30,37,
    58,72,71,70,66,52,54,61,32,45,27,23,47,36,49,42,12,20,44,18,55,62,33,46,
    26,8,14,25,60,6,17,39)(9,16,28,22,48,38,57,69,67,51,40) ]);
ALF("(3x2.U4(2)):2","2.O8+(2)",[1,11,12,2,64,64,29,80,81,30,6,50,15,17,16,
18,8,33,41,36,42,36,34,10,14,16,13,15,9,35,3,42,41,44,66,70,72,71,73,67,
20,69,68,19,39,48,17,11,12,18,6,39,53,53,76,24,45,43,35,24,24,48,39,24,76,
76,60,56,58,57,59,61],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(3x2.U4(2)):2","O8+(2)M11",[1,2,2,1,37,37,39,38,38,39,27,22,23,24,23,
24,25,30,28,29,28,29,30,33,31,32,31,32,33,9,8,45,45,44,34,35,36,35,36,34,
20,19,19,20,18,17,6,7,7,6,11,10,21,21,13,12,4,5,3,15,15,26,43,14,16,16,42,
41,40,41,40,42]);

MOT("2.O8+(2)M12",
[
"12th maximal subgroup of 2.O8+(2),\n",
"differs from 2.O8+(2)M11 = (3x2.U4(2)):2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["(3x2.U4(2)):2"]]);
ALF("2.O8+(2)M12","2.O8+(2)",[1,13,14,2,65,65,31,82,83,32,7,50,15,17,16,18,
8,35,41,33,42,34,35,12,10,16,9,15,11,36,3,41,42,45,68,66,72,67,73,69,20,
71,70,19,40,49,17,13,14,18,7,40,53,53,77,25,43,44,36,25,25,49,40,25,77,77,
56,58,60,59,61,57],[
"equals the map from 2.O8+(2)M11, mapped under an outer autom."
]);
ALF("2.O8+(2)M12","O8+(2)M12",[1,2,2,1,37,37,39,38,38,39,27,22,23,24,23,24,
25,30,28,29,28,29,30,33,31,32,31,32,33,9,8,45,45,44,34,35,36,35,36,34,20,
19,19,20,18,17,6,7,7,6,11,10,21,21,13,12,4,5,3,15,15,26,43,14,16,16,42,41,
40,41,40,42]);

MOT("2.2^(1+8)_+:(S3xS3xS3)",
[
"13th maximal subgroup of 2.O8+(2),\n",
"origin: Dixon's Algorithm"
],
[221184,221184,110592,6144,6144,2048,1024,9216,9216,512,3072,3072,432,432,432,
432,72,72,192,192,3456,3456,3456,3456,288,288,216,432,432,432,432,216,288,288,
96,1728,3456,3456,432,432,216,96,288,288,1728,3456,3456,512,512,256,128,128,
128,64,64,32,64,64,128,768,768,64,64,24,24,2304,2304,128,192,144,144,24,72,72,
72,72,1536,1536,768,128,128,128,64,24,48,48,4608,4608,2304,384,384,128,48,48,
288,288,288,288,144,144,72,72,144,144,768,768,128,64,64,24,24,2304,2304,128,
192,24,144,144,72,72,72,72],
[,[1,1,1,1,1,1,1,3,3,3,2,2,13,13,13,13,15,15,21,21,21,21,21,21,23,23,28,28,28,
30,30,30,36,36,38,37,37,37,39,39,39,47,45,45,46,46,46,6,6,6,4,4,1,10,10,8,12,
11,6,1,2,7,11,40,39,1,2,6,11,46,47,42,30,31,29,28,1,1,1,4,4,6,7,28,28,28,1,1,1
,4,4,6,19,19,21,21,21,21,30,30,30,39,39,39,1,2,6,7,12,31,30,1,2,6,12,35,37,38,
39,40,28,29],[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,3,8,9,4,5,1,2,3,3,9,8,3,1,2,1,2
,3,9,8,12,3,1,2,1,2,3,11,9,8,3,1,2,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,61,60,66,67,68,69,66,67,69,66,67,67,66,77,78,79,80,81,82,83,79,77,78,87,
88,89,90,91,92,90,91,87,88,89,89,88,87,89,89,87,88,105,106,107,108,109,106,105
,112,113,114,115,115,112,113,112,113,112,113]],
0,
[
( 11, 12)( 30, 39)( 31, 40)( 32, 41)( 33, 43)( 34, 44)( 35, 42)( 36, 45)
( 37, 46)( 38, 47)( 57, 58)( 59,107)( 60,105)( 61,106)( 62,108)( 63,109)
( 64,110)( 65,111)( 66,112)( 67,113)( 68,114)( 69,115)( 70,117)( 71,118)
( 72,116)( 73,119)( 74,120)( 75,122)( 76,121)( 99,104)(100,103)(101,102)
,( 48, 49)( 51, 52)( 54, 55)( 77, 78)( 80, 81)( 85, 86),
( 48, 49)( 51, 52)( 54, 55)( 87, 88)( 90, 91)( 93, 94)( 95, 96)( 97, 98)
( 99,100)(103,104)
],
["ConstructProj",[["2^(1+8)_+:(S3xS3xS3)",[]],["2.2^(1+8)_+:(S3xS3xS3)",[]]]
]);
ALF("2.2^(1+8)_+:(S3xS3xS3)","2^(1+8)_+:(S3xS3xS3)",[1,1,2,3,3,4,5,6,6,
7,8,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,18,18,19,19,20,21,21,
22,23,24,24,25,25,26,27,28,28,29,30,30,31,31,32,33,33,34,35,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,57,58,59,59,60,
61,62,63,63,64,64,65,66,66,67,68,68,69,69,70,70,71,71,72,73,74,74,75,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92]);
ALF("2.2^(1+8)_+:(S3xS3xS3)","2.O8+(2)",[1,2,3,4,5,3,8,19,20,21,6,7,15,16,
41,42,72,73,37,38,9,10,33,34,67,66,43,17,18,17,18,45,71,70,40,36,13,14,17,
18,44,39,69,68,35,11,12,19,20,21,22,23,8,54,55,53,25,24,21,8,6,26,24,48,
50,3,6,21,24,35,39,76,43,48,48,45,4,5,8,22,23,21,26,50,46,47,4,5,3,22,23,
21,74,75,37,38,33,34,47,46,44,45,46,47,8,7,21,26,25,49,50,3,7,21,25,77,36,
40,43,49,44,49],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("(2x3^4:2^3).S4",
[
"14th maximal subgroup of 2.O8+(2),\n",
"origin: Dixon's Algorithm"
],
[31104,31104,3888,3888,1296,1296,972,972,3888,3888,3888,3888,288,72,72,384,384
,144,144,576,576,144,144,16,72,72,288,108,108,54,54,54,54,54,54,54,54,12,12,
432,216,216,108,108,108,108,216,216,216,48,48,24,24,48,24,24,24,48,48,48,48,24
,24],
[,[1,1,3,3,5,5,7,7,9,9,11,11,2,4,6,1,1,9,9,1,1,5,5,17,12,6,2,28,28,30,30,32,32
,34,34,36,36,28,28,1,9,9,3,11,7,7,5,5,5,13,13,14,14,1,5,18,18,20,20,27,27,25,
25],[1,2,1,2,1,2,1,2,1,2,1,2,13,13,13,16,17,20,21,20,21,20,21,24,27,27,27,1,2,
7,8,1,2,7,8,7,8,17,16,40,40,40,40,40,40,40,40,40,40,50,51,50,51,54,54,58,59,58
,59,60,61,60,61]],
0,
[(41,42)(45,46)(56,57)(58,59),(50,51)(52,53)(60,61)(62,63),
( 3,11)( 4,12)(13,27)(14,25)(15,26)(30,36)(31,37)(43,44)(47,48)(50,60)(51,61)
(52,62)(53,63)
],
["ConstructProj",[["3^4:2^3.S4(a)",[]],["(2x3^4:2^3).S4",[]]]]);
ALF("(2x3^4:2^3).S4","2.O8+(2)",[1,2,11,12,17,18,15,16,9,10,13,14,6,39,48,
8,8,37,38,4,5,46,47,26,40,49,7,17,18,58,59,15,16,56,57,60,61,50,50,3,33,
34,35,36,41,42,44,45,43,24,24,76,76,8,50,74,75,22,23,25,25,77,77],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(2x3^4:2^3).S4","3^4:2^3.S4(a)",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,10,10,
11,11,12,12,13,13,14,15,16,17,18,18,19,19,20,20,21,21,22,22,23,23,24,25,
25,26,27,28,28,29,30,31,32,32,33,33,34,35,36,36,37,37,38,38,39,39]);

MOT("(A5xA5).(2x4)",
[
"15th maximal subgroup of 2.O8+(2)"
],
0,
0,
0,
[(3,4)(9,10)(11,12)(23,24)(25,26)(33,34)(43,44)(45,46)(47,48)(49,50),(3,4)(9,
10)(11,12)(23,24)(25,26)(33,34)(35,36)(37,38)(39,40)(41,42),(13,15)(14,16)(35,
43)(36,44)(37,47)(38,48)(39,45)(40,46)(41,49)(42,50)],
["ConstructIsoclinic",[["(A5xA5):2^2"],["Cyclic",2]],[1..34]]);
ALF("(A5xA5).(2x4)","(A5xA5):2^2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,
22,23,23,24,24,25,25]);
ALF("(A5xA5).(2x4)","2.O8+(2)",[1,2,4,5,8,8,17,18,46,47,26,26,31,32,29,30,
4,5,9,10,27,28,37,38,22,23,37,38,62,63,78,79,74,75,7,7,26,26,49,49,65,65,
6,6,48,48,26,26,64,64],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2.(A5xA5).2^2",
[
"16th maximal subgroup of 2.O8+(2),\n",
"origin: Dixon's Algorithm"
],
[28800,28800,144,64,72,72,72,72,32,32,100,100,100,100,480,720,720,600,600,36,
24,24,20,30,30,24,24,480,480,16,24,24,20,20,480,480,24,24,16,20,20],
[,[1,1,2,1,5,5,6,6,4,4,11,11,13,13,2,16,16,18,18,17,15,17,19,24,24,22,22,1,1,4
,5,5,11,11,2,2,6,6,4,14,14],[1,2,3,4,1,2,3,3,10,9,11,12,13,14,15,1,2,18,19,3,
21,15,23,18,19,21,21,28,29,30,28,29,33,34,36,35,35,36,39,41,40],,[1,2,3,4,5,6,
7,8,9,10,1,2,1,2,15,16,17,1,2,20,21,22,15,16,17,26,27,28,29,30,31,32,29,28,35,
36,37,38,39,35,36]],
0,
[(26,27),( 7, 8)( 9,10)(35,36)(37,38)(40,41),
(28,29)(31,32)(33,34)(35,36)(37,38)(40,41)],
["ConstructProj",[["O8+(2)M16",[]],["2.(A5xA5).2^2",[]]]]);
ALF("2.(A5xA5).2^2","O8+(2)M16",[1,1,2,3,4,4,5,5,6,6,7,7,8,8,9,10,10,11,
11,12,13,14,15,16,16,17,17,18,18,19,20,20,21,21,22,22,23,23,24,25,25]);
ALF("2.(A5xA5).2^2","2.O8+(2)",[1,2,6,8,17,18,48,48,26,26,27,28,31,32,6,
11,12,29,30,39,24,39,64,80,81,76,76,4,5,26,46,47,63,62,7,7,49,49,26,65,65],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2.O8+(2)M17",
[
"17th maximal subgroup of 2.O8+(2),\n",
"differs from 2.O8+(2)M16 = 2.(A5xA5).2^2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2.(A5xA5).2^2"]]);
ALF("2.O8+(2)M17","O8+(2)M17",[1,1,2,3,4,4,5,5,6,6,7,7,8,8,9,10,10,11,11,
12,13,14,15,16,16,17,17,18,18,19,20,20,21,21,22,22,23,23,24,25,25]);
ALF("2.O8+(2)M17","2.O8+(2)",[1,2,7,8,17,18,49,49,26,26,27,28,29,30,7,13,
14,31,32,40,25,40,65,82,83,77,77,4,5,26,46,47,63,62,6,6,48,48,26,64,64],[
"fusion 2.(A5xA5).2^2 -> 2.O8+(2) mapped under 2.O8+(2).2"
]);

MOT("(A8xA4):2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct'"
],
[483840,161280,60480,4608,1536,576,2304,768,288,4320,1440,540,432,144,54,384,
128,48,192,64,24,360,120,45,288,96,36,144,48,18,84,28,21,21,180,60,45,45,2880,
2880,192,192,192,192,64,64,72,72,72,72,24,24,16,16,20,20,24,24],
[,[1,1,3,1,1,3,1,1,3,10,10,12,13,13,15,4,4,6,7,7,9,22,22,24,10,10,12,13,13,15,
31,31,34,33,35,35,38,37,1,2,1,2,7,8,7,8,10,11,13,14,13,14,16,17,22,23,25,26],[
1,2,1,4,5,4,7,8,7,1,2,1,1,2,1,16,17,16,19,20,19,22,23,22,7,8,7,4,5,4,31,32,31,
31,22,23,22,22,39,40,41,42,43,44,45,46,39,40,39,40,41,42,53,54,55,56,43,44],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,2,3,25,26,27,28,29,30,
31,32,33,34,10,11,12,12,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,39,40,
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,
27,28,29,30,1,2,3,3,35,36,38,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58]],
0,
[(37,38),(33,34)],
["ConstructIndexTwoSubdirectProduct","A8","A8.2","a4","Symm(4)",[64,65,69,70,
74,75,79,80,84,85,89,90,94,95,99,100,104,105,109,110],(),()]);
ARC("(A8xA4):2","tomfusion",rec(name:="(A8xA4):2",map:=[1,5,10,7,8,74,3,6,
70,9,65,11,13,83,12,57,58,326,24,29,313,60,261,365,67,69,71,86,88,80,90,
362,712,712,364,903,366,366,2,43,4,44,22,48,33,54,61,286,62,349,77,341,
248,251,259,709,299,302],text:=[
"fusion map is unique"
]));
ALF("(A8xA4):2","A8.2",[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,
9,9,10,10,10,11,11,11,11,12,12,12,12,13,13,14,14,15,15,16,16,17,17,18,18,
19,19,20,20,21,21,22,22],[
"fusion map is unique"
]);
ALF("(A8xA4):2","Symm(4)",[1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,
2,3,1,2,3,1,2,3,3,1,2,3,3,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5]);
ALF("(A8xA4):2","A12",[1,2,5,4,3,16,2,4,15,5,15,6,6,17,8,10,12,34,9,11,32,
13,28,37,15,16,17,19,18,21,22,36,40,40,37,41,38,38,2,9,4,11,9,10,11,12,15,
32,17,33,19,35,23,24,28,39,32,34]);
ALF("(A8xA4):2","HN",[1,2,4,3,2,15,2,3,14,4,14,4,4,14,5,6,6,31,7,7,30,9,
22,34,14,15,14,15,14,16,17,33,44,44,34,48,34,34,2,7,3,7,7,6,7,6,14,30,14,
30,15,30,19,19,22,41,30,31],[
"fusion map is unique"
]);
ALF("(A8xA4):2","S8xS4",[1,2,3,6,7,8,11,12,13,16,17,18,21,22,23,26,27,28,
31,32,33,36,37,38,41,42,43,46,47,48,51,52,53,53,56,57,58,58,64,65,69,70,
74,75,79,80,84,85,89,90,94,95,99,100,104,105,109,110],[
"fusion map is unique"
]);

MOT("(A7xA5):2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct'"
],
[302400,20160,15120,12600,2880,192,144,120,4320,288,216,180,1080,72,54,45,480,
32,24,20,600,40,30,25,1440,96,72,60,420,28,21,35,35,1440,480,720,288,96,144,
144,48,72,72,24,36,36,12,18,60,20,30,72,24,36],
[,[1,1,3,4,1,1,3,4,9,9,11,12,13,13,15,16,5,5,7,8,21,21,23,24,9,9,11,12,29,29,
31,33,32,1,2,3,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,25,26,27],[1,2,1,4,5,6,5,
8,1,2,1,4,1,2,1,4,17,18,17,20,21,22,21,24,5,6,5,8,29,30,29,32,33,34,35,34,37,
38,37,40,41,40,34,35,34,37,38,37,49,50,49,40,41,40],,[1,2,3,1,5,6,7,5,9,10,11,
9,13,14,15,13,17,18,19,17,1,2,3,1,25,26,27,25,29,30,31,29,29,34,35,36,37,38,39
,40,41,42,43,44,45,46,47,48,34,35,36,52,53,54],,[1,2,3,4,5,6,7,8,9,10,11,12,13
,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,2,3,4,4,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54]],
0,
[(32,33)],
["ConstructIndexTwoSubdirectProduct","A7","A7.2","A5","A5.2",[61,62,63,68,69,
70,75,76,77,82,83,84,89,90,91,96,97,98,103,104,105],(),()]);
ARC("(A7xA5):2","tomfusion",rec(name:="(A7xA5):2",map:=[1,4,7,35,3,5,39,
113,8,48,9,208,10,58,11,209,23,25,134,285,37,114,207,36,51,53,56,450,66,
205,302,470,470,2,27,41,6,30,44,18,32,131,46,159,45,59,194,60,112,289,442,
173,176,182],text:=[
"fusion map is unique"
]));
ALF("(A7xA5):2","A7.2",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,
7,7,7,8,8,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,
15]);
ALF("(A7xA5):2","A5.2",[1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,
2,3,4,1,2,3,4,4,5,6,7,5,6,7,5,6,7,5,6,7,5,6,7,5,6,7,5,6,7]);
ALF("(A7xA5):2","A12",[1,2,5,13,2,4,15,28,5,15,6,37,6,17,8,38,9,11,32,39,
13,28,37,14,15,16,17,41,22,36,40,42,43,2,9,15,4,11,16,9,10,32,15,32,17,19,
35,21,28,39,41,32,34,33],[
"fusion map is unique up to table automorphisms"
]);

MOT("(S3xS3xA5):2",
[
"origin: Dixon's Algorithm"
],
[4320,1080,1080,480,720,360,72,36,24,48,24,72,72,288,32,36,18,24,54,216,54,18,
36,12,12,24,8,30,60,60,30,90,45,90,180,20],
[,[1,2,3,1,1,3,1,2,4,1,3,3,2,1,1,20,21,20,19,20,21,19,20,18,13,14,15,34,35,35,
32,34,33,32,35,35],[1,1,1,4,5,5,7,7,9,10,10,14,14,14,15,5,5,4,1,1,1,7,7,9,26,
26,27,30,30,29,29,35,35,35,35,36],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,6,5,5,6,3,2,3,1,4]],
[[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,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,
1,1,1,1],[1,1,1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,1,1,-1,-1,-1
,-1,-1,1,1,1,1,1],
[TENSOR,[2,3]],[2,2,2,-2,0,0,0,0,0,0,0,2,2,2,-2,0,0,-2,2,2,2,0,0,0,0,0,0,0,0,
0,0,2,2,2,2,-2],[4,-2,1,0,2,-1,0,0,0,2,-1,1,-2,4,0,2,-1,0,-2,4,1,0,0,0,0,0,0,
-1,2,2,-1,1,-2,1,4,0],
[TENSOR,[6,2]],[4,1,-2,0,0,0,-2,1,0,0,0,-2,1,4,0,0,0,0,1,4,-2,1,-2,0,1,-2,0,0
,0,0,0,-2,1,-2,4,0],
[TENSOR,[8,2]],[4,4,4,4,-4,-4,-2,-2,2,0,0,0,0,0,0,-1,-1,1,1,1,1,1,1,-1,0,0,0,
1,1,1,1,-1,-1,-1,-1,-1],
[TENSOR,[10,4]],
[TENSOR,[10,3]],
[TENSOR,[10,2]],[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,-1,0,0,0,0,0,0,0,0,0],
[TENSOR,[14,4]],
[TENSOR,[14,3]],
[TENSOR,[14,2]],[6,6,6,6,-6,-6,0,0,0,2,2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,
-1,-1,-1,-1,1,1,1,1,1],
[TENSOR,[18,2]],[6,6,6,-6,0,0,0,0,0,0,0,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,
-E(5)+E(5)^2+E(5)^3-E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,
E(5)-E(5)^2-E(5)^3+E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,1,1,1,1,-1],
[TENSOR,[20,2]],[8,8,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,2,0,0,0,0,0,0,0,0,
0,0,-2,-2,-2,-2,2],[10,10,10,-10,0,0,0,0,0,0,0,2,2,2,-2,0,0,2,-2,-2,-2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0],[12,-6,3,0,-6,3,0,0,0,2,-1,-1,2,-4,0,0,0,0,0,0,0,0,0,0
,0,0,0,-E(5)-E(5)^4,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,-E(5)^2-E(5)^3,
E(5)-2*E(5)^2-2*E(5)^3+E(5)^4,-1,-2*E(5)+E(5)^2+E(5)^3-2*E(5)^4,2,0],
[GALOIS,[24,2]],
[TENSOR,[25,2]],
[TENSOR,[24,2]],[16,-8,4,0,8,-4,0,0,0,0,0,0,0,0,0,2,-1,0,-2,4,1,0,0,0,0,0,0,1
,-2,-2,1,-1,2,-1,-4,0],
[TENSOR,[28,2]],[16,4,-8,0,0,0,-4,2,0,0,0,0,0,0,0,0,0,0,1,4,-2,-1,2,0,0,0,0,0
,0,0,0,2,-1,2,-4,0],
[TENSOR,[30,2]],[20,-10,5,0,10,-5,0,0,0,2,-1,1,-2,4,0,-2,1,0,2,-4,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[32,2]],[20,5,-10,0,0,0,-2,1,0,0,0,-2,1,4,0,0,0,0,-1,-4,2,1,-2,0,-1,2
,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[34,2]],[24,6,-12,0,0,0,0,0,0,0,0,4,-2,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,-2,1,-2,4,0]],
[(28,31)(29,30)(32,34)]);
ARC("(S3xS3xA5):2","tomfusion",rec(name:="(S3xS3xA5):2",map:=[1,9,8,3,2,
31,5,39,15,6,46,36,37,4,7,42,50,48,11,10,12,51,40,110,98,16,26,192,76,76,
192,118,119,118,29,78],text:=[
"fusion map is unique"
]));
ALF("(S3xS3xA5):2","O8-(2)",[1,5,6,3,2,14,3,15,10,4,18,17,15,3,4,13,16,15,
6,5,7,17,15,27,27,10,11,38,23,24,39,29,31,30,12,25],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^{3+6}:(L3(2)x3)",
[
"3rd maximal subgroup of O8-(2),\n",
"origin: Dixon's Algorithm"
],
[258048,36864,3072,3072,768,4032,576,4032,576,1536,1536,256,768,512,512,64,64,
96,96,48,96,96,48,72,72,24,24,72,72,12,72,72,12,96,96,32,32,24,24,24,24,21,21,
21,21,21,21],
[,[1,1,1,1,2,8,8,6,6,1,1,1,2,2,2,4,3,8,8,9,6,6,7,24,24,24,24,31,31,32,28,28,29
,10,11,15,14,21,22,18,19,42,44,43,45,47,46],[1,2,3,4,5,1,2,1,2,10,11,12,13,14,
15,16,17,11,10,13,11,10,13,1,2,4,3,1,2,5,1,2,5,34,35,36,37,35,34,35,34,45,45,
45,42,42,42],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,1,6,8,1,6,8]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1],[1,1,1,1,1,E(3),E(3),E(3)^2,E(3)^2,1,1,1,1,1,1,1,1,E(3),
E(3),E(3),E(3)^2,E(3)^2,E(3)^2,1,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,1,1
,1,1,E(3),E(3),E(3)^2,E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2],
[TENSOR,[2,2]],[3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0
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E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6],
[TENSOR,[4,2]],
[TENSOR,[4,3]],
[GALOIS,[4,3]],
[TENSOR,[7,2]],
[TENSOR,[7,3]],[6,6,6,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1],
[TENSOR,[10,2]],
[TENSOR,[10,3]],[7,7,7,7,7,7,7,7,7,-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,-1,0,0,0,0,0,0],
[TENSOR,[13,2]],
[TENSOR,[13,3]],[8,8,8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,1,1],
[TENSOR,[16,2]],
[TENSOR,[16,3]],[21,21,5,5,-3,0,0,0,0,9,9,1,9,1,1,-3,1,0,0,0,0,0,0,3,3,-1,-1,
0,0,0,0,0,0,3,3,-1,-1,0,0,0,0,0,0,0,0,0,0],[21,21,5,5,-3,0,0,0,0,-3,-3,5,-3,5,
5,1,-3,0,0,0,0,0,0,3,3,-1,-1,0,0,0,0,0,0,-3,-3,1,1,0,0,0,0,0,0,0,0,0,0],[42,42
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0,0,0,0,0,0,0,0,0,0],[42,42,-6,-6,2,0,0,0,0,6,6,-2,6,-2,-2,2,-2,0,0,0,0,0,0,0,
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[TENSOR,[22,3]],
[TENSOR,[22,2]],[63,63,15,15,-9,0,0,0,0,3,3,-5,3,-5,-5,-1,3,0,0,0,0,0,0,0,0,0
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[TENSOR,[28,3]],
[TENSOR,[28,2]],
[TENSOR,[29,3]],
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[TENSOR,[34,3]],
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[TENSOR,[39,3]],
[TENSOR,[39,2]],
[TENSOR,[40,3]],
[TENSOR,[40,2]],[168,-24,-8,8,0,0,0,0,0,0,0,-8,0,8,8,0,0,0,0,0,0,0,0,-3,3,-1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[252,-36,-12,12,0,0,0,0,0,-12,12,4,
0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0],[252,
-36,-12,12,0,0,0,0,0,12,-12,4,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2
,-2,0,0,0,0,0,0,0,0,0,0]],
[(10,11)(14,15)(18,19)(21,22)(34,35)(36,37)(38,39)(40,41),
(42,45)(43,46)(44,47),
( 6, 8)( 7, 9)(18,21)(19,22)(20,23)(28,31)(29,32)(30,33)(38,40)(39,41)(43,44)
(46,47)
]);
ALF("2^{3+6}:(L3(2)x3)","3xL3(2)",[1,1,1,1,1,2,2,3,3,4,4,4,4,4,4,4,4,5,5,
5,6,6,6,7,7,7,7,8,8,8,9,9,9,10,10,10,10,11,11,12,12,13,14,15,16,17,18]);
ALF("2^{3+6}:(L3(2)x3)","O8-(2)",[1,2,3,4,9,5,13,5,13,2,3,4,8,9,8,11,10,
15,13,26,15,13,26,6,14,18,17,7,16,28,7,16,28,8,10,20,21,27,26,27,26,19,36,
37,19,37,36],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^{1+8}_+:(S3xA5)",
[
"4th maximal subgroup of O8-(2),\n",
"origin: Dixon's Algorithm"
],
[184320,184320,6144,3072,1024,1536,1536,768,768,128,64,64,576,576,96,96,96,48,
60,60,60,60,360,360,24,24,72,72,12,30,30,30,30,3840,3840,384,192,128,256,256,
64,64,64,32,32,48,48,24,24,24,20,20,20,20],
[,[1,1,1,1,1,2,2,1,1,3,5,4,13,13,13,13,13,14,21,21,19,19,23,23,23,23,27,27,28,
32,32,30,30,1,1,3,4,1,3,3,5,5,4,7,6,13,13,15,17,16,21,21,19,19],[1,2,3,4,5,6,7
,8,9,10,11,12,1,2,4,3,3,6,21,22,19,20,1,2,9,8,1,2,7,21,22,19,20,34,35,36,37,38
,39,40,41,42,43,44,45,34,35,37,36,36,53,54,51,52],,[1,2,3,4,5,6,7,8,9,10,11,12
,13,14,15,17,16,18,1,2,1,2,23,24,25,26,27,28,29,23,24,23,24,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,50,49,35,34,35,34]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,0,0,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,3,3,-1,-1,0,0,0,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,3,3,3,3,-1,-1,-1,-1,-1
,-1,-1,-1,0,0,0,0,0,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3],
[GALOIS,[2,2]],[4,4,4,4,4,4,4,0,0,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1,4,4,0,0,1,1,1
,-1,-1,-1,-1,4,4,4,4,0,0,0,0,0,0,0,0,1,1,1,1,1,-1,-1,-1,-1],[5,5,5,5,5,5,5,1,1
,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,5,5,1,1,-1,-1,-1,0,0,0,0,5,5,5,5,1,1,1,1,1,1,
1,1,-1,-1,-1,-1,-1,0,0,0,0],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1],
[TENSOR,[2,6]],
[TENSOR,[3,6]],
[TENSOR,[4,6]],
[TENSOR,[5,6]],[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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,6,6,-2,
-2,-2,-2,-2,0,0,0,0,0,0,-2*E(5)-2*E(5)^4,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,
-2*E(5)^2-2*E(5)^3,-3,-3,1,1,0,0,0,E(5)+E(5)^4,E(5)+E(5)^4,E(5)^2+E(5)^3,
E(5)^2+E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[12,2]],[8,8,8,8,8,8,8,0,0,0,0,0,2,2,2,2,2,2,-2,-2,-2,-2,-4,-4,0,0,-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],[10,10,10,10,10,10,
10,2,2,2,2,2,-2,-2,-2,-2,-2,-2,0,0,0,0,-5,-5,-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],[15,15,-1,7,-1,-5,3,3,3,3,-1,-1,6,6,-2,2,2,-2,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-5,-5,3,-1,-1,-1,-1,-1,-1,-1,1,1,-2,-2,2,0,0,0,0,0
,0],
[TENSOR,[16,6]],[15,15,-1,7,-1,-5,3,3,3,3,-1,-1,-3,-3,1,-E(3)+3*E(3)^2,
3*E(3)-E(3)^2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-5,-5,3,-1,-1,-1,-1,-1,-1,-1,1,1
,1,1,-1,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0],
[GALOIS,[18,2]],
[TENSOR,[18,6]],
[TENSOR,[19,6]],[30,30,14,6,-2,2,-6,-6,-6,2,2,-2,3,3,3,-1,-1,-1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,-10,-10,-2,2,2,2,2,-2,-2,2,0,0,-1,-1,-1,1,1,0,0,0,0],[30,30,
14,6,-2,2,-6,6,6,-2,-2,2,3,3,3,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-10,-10,
-2,2,-2,-2,-2,2,2,-2,0,0,-1,-1,-1,1,1,0,0,0,0],
[TENSOR,[22,6]],
[TENSOR,[23,6]],[45,45,-3,21,-3,-15,9,-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,-15,-15,9,-3,1,1,1,1,1,1,-1,-1,0,0,0,0,0,0,0,0,0],
[TENSOR,[26,6]],[60,60,28,12,-4,4,-12,0,0,0,0,0,-3,-3,-3,1,1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,-20,-20,-4,4,0,0,0,0,0,0,0,0,1,1,1,-1,-1,0,0,0,0],
[TENSOR,[28,6]],[60,60,-20,4,-4,8,0,0,0,0,0,0,6,6,-2,-2,-2,2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-4,4,4,0,0,0,-2,2,0,0,0,0,0,0,0,0,0],
[TENSOR,[30,6]],[60,60,12,-12,-4,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,
3,-1,0,0,0,0,0,0,0,0,4,-4,-4,0,0,0,-2,2,0,0,0,0,0,0,0,0,0],
[TENSOR,[32,6]],[90,90,-6,-6,10,-6,-6,6,6,-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,-4,-4,-4,0,0,4,0,0,0,0,0,0,0,0,0,0,0],[90,90,-6,-6,10,
-6,-6,-6,-6,2,-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,-4,
4,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[35,6]],
[TENSOR,[34,6]],[120,120,-40,8,-8,16,0,0,0,0,0,0,-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],[120,120,24,-24,-8
,0,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[16,-16,0,0,0,0,0,4,-4,0,0,0,4,-4,0,0,0,0,1,-1,1,-1,1
,-1,-1,1,-2,2,0,1,-1,1,-1,4,-4,0,0,0,-4,4,0,0,0,0,0,-2,2,0,0,0,1,-1,1,-1],
[TENSOR,[40,6]],[32,-32,0,0,0,0,0,8,-8,0,0,0,8,-8,0,0,0,0,2,-2,2,-2,-1,1,1,-1
,2,-2,0,-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],[48,-48,0,0,0,0,0
,-4,4,0,0,0,0,0,0,0,0,0,-E(5)-E(5)^4,E(5)+E(5)^4,-E(5)^2-E(5)^3,E(5)^2+E(5)^3,
3,-3,1,-1,0,0,0,-E(5)-E(5)^4,E(5)+E(5)^4,-E(5)^2-E(5)^3,E(5)^2+E(5)^3,-12,12,0
,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,E(5)+E(5)^4,-E(5)-E(5)^4,E(5)^2+E(5)^3,
-E(5)^2-E(5)^3],
[GALOIS,[43,2]],
[TENSOR,[43,6]],
[TENSOR,[44,6]],[64,-64,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,0,0,-1,1,-1,1,4,-4,0,0,
-2,2,0,-1,1,-1,1,16,-16,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,-1,1,-1,1],
[TENSOR,[47,6]],[80,-80,0,0,0,0,0,4,-4,0,0,0,-4,4,0,0,0,0,0,0,0,0,5,-5,-1,1,2
,-2,0,0,0,0,0,20,-20,0,0,0,-4,4,0,0,0,0,0,2,-2,0,0,0,0,0,0,0],
[TENSOR,[49,6]],[96,-96,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,-2*E(5)^2-2*E(5)^3,
2*E(5)^2+2*E(5)^3,-2*E(5)-2*E(5)^4,2*E(5)+2*E(5)^4,-3,3,-1,1,0,0,0,
E(5)^2+E(5)^3,-E(5)^2-E(5)^3,E(5)+E(5)^4,-E(5)-E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[51,2]],[128,-128,0,0,0,0,0,0,0,0,0,0,8,-8,0,0,0,0,-2,2,-2,2,-4,4,0,0
,2,-2,0,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,-160,0,0,0,0
,0,8,-8,0,0,0,-8,8,0,0,0,0,0,0,0,0,-5,5,1,-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]],
[(41,42),(16,17)(49,50),(34,35)(39,40)(46,47)(51,52)(53,54),
(19,21)(20,22)(30,32)(31,33)(51,53)(52,54)]);
ALF("2^{1+8}_+:(S3xA5)","O8-(2)",[1,2,2,3,4,8,9,3,4,9,11,10,5,13,15,13,13,
26,12,23,12,24,6,14,18,17,7,16,28,29,38,30,39,2,3,8,10,4,9,8,11,11,10,21,
20,13,15,27,26,26,25,24,25,23],[
"fusion map is unique up to table automorphisms"
]);

MOT("10^2:S3",
[
"origin: Dixon's Algorithm"
],
[600,200,200,200,200,100,100,200,100,100,100,100,200,100,100,100,200,100,100,
200,100,200,3,20,20,20,20,20,20,20,20,20,20],
[,[1,3,4,5,2,7,6,2,6,6,7,4,5,6,3,7,1,5,2,4,7,3,23,1,4,5,2,3,20,22,17,8,13],[1,
5,2,3,4,7,6,13,16,11,14,15,20,21,19,9,17,12,18,22,10,8,1,24,28,25,26,27,30,32,
31,33,29],,[1,1,1,1,1,1,1,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,23,24,
24,24,24,24,31,31,31,31,31]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-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,-1,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,-1,-1,-1,-1,-1,1,1,1,1,1],
[TENSOR,[4,2]],[3,2*E(5)^3+E(5)^4,2*E(5)+E(5)^3,E(5)+2*E(5)^2,E(5)^2+2*E(5)^4
,-E(5)^2-E(5)^3,-E(5)-E(5)^4,E(5)^2+2*E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,2*E(5)+E(5)^3,E(5)+2*E(5)^2,-E(5)-E(5)^4,2*E(5)^3+E(5)^4,
-E(5)^2-E(5)^3,3,E(5)+2*E(5)^2,E(5)^2+2*E(5)^4,2*E(5)+E(5)^3,-E(5)^2-E(5)^3,
2*E(5)^3+E(5)^4,0,-1,-E(5)^3,-E(5),-E(5)^2,-E(5)^4,-E(5)^4,-E(5)^2,-1,-E(5),
-E(5)^3],
[GALOIS,[6,3]],
[GALOIS,[6,4]],
[GALOIS,[6,2]],
[TENSOR,[6,2]],
[TENSOR,[7,2]],
[TENSOR,[8,2]],
[TENSOR,[9,2]],[3,2*E(5)^3+E(5)^4,2*E(5)+E(5)^3,E(5)+2*E(5)^2,E(5)^2+2*E(5)^4
,-E(5)^2-E(5)^3,-E(5)-E(5)^4,E(5)^2-2*E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,
E(5)+2*E(5)^3+E(5)^4,E(5)^2+E(5)^3+2*E(5)^4,-E(5)^3,E(5)-2*E(5)^2,
E(5)+2*E(5)^2+E(5)^4,-E(5)^4,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,-1,-E(5),-E(5)^2,
-2*E(5)+E(5)^3,2*E(5)+E(5)^2+E(5)^3,-2*E(5)^3+E(5)^4,0,-1,-E(5)^3,-E(5),
-E(5)^2,-E(5)^4,E(5)^4,E(5)^2,1,E(5),E(5)^3],
[GALOIS,[14,3]],
[GALOIS,[14,4]],
[GALOIS,[14,2]],
[TENSOR,[14,2]],
[TENSOR,[15,2]],
[TENSOR,[16,2]],
[TENSOR,[17,2]],[6,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,
-2*E(5)^2-2*E(5)^3,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4
,-2*E(5)^2-2*E(5)^3,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,
2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,-2*E(5)^2-2*E(5)^3
,-2*E(5)-2*E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,-2*E(5)-2*E(5)^4,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,6,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,
-2*E(5)^2-2*E(5)^3,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,-2*E(5)-2*E(5)^4,0,0,0,0,0,0,
0,0,0,0,0],
[GALOIS,[22,2]],[6,4*E(5)+2*E(5)^3,2*E(5)+4*E(5)^2,2*E(5)^2+4*E(5)^4,
4*E(5)^3+2*E(5)^4,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)^4,-2,-2*E(5),
-2*E(5)^3,-2*E(5)^2,-2*E(5)^2,-2*E(5)^4,-2*E(5),-2,-2,-2*E(5)^4,-2*E(5)^3,
-2*E(5),-2*E(5)^2,-2*E(5)^3,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[24,2]],
[GALOIS,[24,3]],
[GALOIS,[24,4]],[6,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,
-2*E(5)^2-2*E(5)^3,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4
,2*E(5)^2+2*E(5)^3+4*E(5)^4,-E(5)^2-E(5)^3,-2*E(5)-E(5)^2+E(5)^3,
-E(5)-2*E(5)^3+E(5)^4,-2*E(5),2*E(5)+4*E(5)^2+2*E(5)^4,E(5)^2-E(5)^3-2*E(5)^4,
-2*E(5)^3,-E(5)-E(5)^4,-2,-2*E(5)^2,-2*E(5)^4,4*E(5)+2*E(5)^2+2*E(5)^3,
E(5)-2*E(5)^2-E(5)^4,2*E(5)+4*E(5)^3+2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[28,4]],
[GALOIS,[28,3]],
[GALOIS,[28,2]],[6,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,
-2*E(5)^2-2*E(5)^3,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4
,-4*E(5)-2*E(5)^2-2*E(5)^3-4*E(5)^4,-2*E(5)+E(5)^2+E(5)^3-2*E(5)^4,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,-2,-2*E(5)-4*E(5)^2-4*E(5)^3-2*E(5)^4,
-E(5)^2-E(5)^3,-2,E(5)-2*E(5)^2-2*E(5)^3+E(5)^4,-2,-2,-2,
-4*E(5)-2*E(5)^2-2*E(5)^3-4*E(5)^4,-E(5)-E(5)^4,
-2*E(5)-4*E(5)^2-4*E(5)^3-2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[32,2]]],
[
( 2, 3, 4, 5)( 6, 7)( 8,22,20,13)( 9,16)(10,21,14,11)(12,18,19,15)
(25,26,27,28)(29,33,32,30)
]);
ARC("10^2:S3","tomfusion",rec(name:="10^2:S3",map:=[1,8,8,8,8,9,9,12,13,
15,15,16,12,15,16,13,2,16,16,12,15,12,4,3,17,17,17,17,23,23,6,23,23],text:=[
"fusion map is unique"
]));
ALF("10^2:S3","U3(9)",[1,6,8,7,9,11,10,18,19,26,27,23,16,25,21,20,2,22,24,
17,28,15,4,2,23,22,24,21,37,40,5,38,39],[
"fusion map is unique up to table automorphisms"
]);
ALF("10^2:S3","L3(11)",[1,5,6,7,8,9,10,16,24,27,26,21,19,29,20,25,2,22,23,
18,28,17,3,2,21,22,23,20,44,47,4,46,45],[
"fusion map is unique up to table automorphisms"
]);

MOT("11^(1+2)+:40",
[
"origin: Dixon's Algorithm"
],
[53240,5324,121,121,121,40,40,40,40,440,44,40,40,40,40,40,44,440,40,40,40,40,
44,440,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40],
[,[1,2,3,4,5,7,8,9,6,1,2,7,8,9,6,15,11,10,13,12,14,15,11,10,13,12,14,16,19,20,
21,18,16,19,20,21,18,27,22,25,24,26,27,22,25,24,26],,,[1,2,3,4,5,1,1,1,1,10,11
,10,10,10,10,18,17,18,18,18,18,24,23,24,24,24,24,37,37,37,37,37,32,32,32,32,32
,46,46,46,46,46,41,41,41,41,41],,,,,,[1,1,1,1,1,6,7,8,9,10,10,12,13,14,15,22,
24,24,25,26,27,16,18,18,19,20,21,39,40,42,38,41,44,45,47,43,46,31,28,29,32,30,
36,33,34,37,35]],
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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,
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[TENSOR,[2,3]],
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0,0],[110,-11,0,0,0,0,0,0,0,-10,1,0,0,0,0,0,-1,10,0,0,0,0,-1,10,0,0,0,0,0,0,0,
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[TENSOR,[44,5]],
[TENSOR,[44,3]]],
[(4,5),(3,4),
(28,33)(29,34)(30,35)(31,36)(32,37)(38,43)(39,44)(40,45)(41,46)(42,47),
(16,22)(17,23)(18,24)(19,25)(20,26)(21,27)(28,39)(29,40)(30,42)(31,38)(32,41)
(33,44)(34,45)(35,47)(36,43)(37,46)
,
( 6, 7, 8, 9)(12,13,14,15)(16,20,19,21)(22,26,25,27)(28,30,29,31)(33,35,34,36)
(38,39,42,40)(43,44,47,45)
]);
ARC("11^(1+2)+:40","tomfusion",rec(name:="11^(1+2)+:40",map:=[1,7,9,10,8,
4,4,4,4,2,15,6,6,6,6,11,17,3,11,11,11,11,17,3,11,11,11,16,16,16,16,5,16,
16,16,16,5,16,16,16,5,16,16,16,16,5,16],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("11^(1+2)+:40","U3(11)",[1,14,15,16,17,7,8,7,8,2,26,12,13,12,13,22,47,
4,22,24,24,23,48,5,23,25,25,41,45,39,43,10,45,41,43,39,10,44,42,46,11,40,
40,46,42,11,44],[
"fusion map is unique up to table automorphisms"
]);

MOT("11^2:(5x2L2(11).2)",
[
"origin: Dixon's Algorithm,\n",
"constructions: AGL(2,11)"
],
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120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,
120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,110,1100,100,100,
100,100,100,110,1100,100,100,100,100,110,1100,100,100,100,110,1100,100,100,100
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110,1100,100,100,100,100,100,100,100,110,1100,100,100,110,110,121,1210,110,110
,110,110,110,110,110],
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104,107,95,93,96,97,94,91,92,92,94,95,97,93,3,6,2,1,5,4,126,121,123,124,122,
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117,118,118,118,124,124,123,124,124,124,130,130,130,130,130],,,,,,[1,1,3,4,5,6
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1,1,1,1,1,1,1,1,1,1,1],
[GALOIS,[77,2]],
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-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,
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[GALOIS,[101,2]],
[TENSOR,[102,2]],
[TENSOR,[101,2]],
[TENSOR,[102,7]],
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[TENSOR,[102,6]],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-10,0,0,0,0,0,0,0]],
[
( 22, 29)( 23, 31)( 24, 30)( 25, 28)( 26, 27)( 32, 39)( 33, 41)( 34, 40)
( 35, 38)( 36, 37)( 57, 64)( 58, 66)( 59, 65)( 60, 63)( 61, 62)
,
( 22, 33)( 23, 34)( 24, 36)( 25, 32)( 26, 35)( 27, 38)( 28, 39)( 29, 41)
( 30, 37)( 31, 40)( 42, 49)( 43, 51)( 44, 50)( 45, 48)( 46, 47)( 57, 64)
( 58, 66)( 59, 65)( 60, 63)( 61, 62)
,
(  3,  4,  5,  6)(  7, 11, 10,  8)( 12, 15, 14, 16)( 17, 19, 18, 20)
( 23, 24, 25, 26)( 27, 31, 30, 28)( 32, 35, 34, 36)( 37, 39, 38, 40)
( 42, 45, 44, 46)( 47, 49, 48, 50)( 53, 54, 55, 56)( 57, 58, 61, 59)
( 62, 65, 64, 66)( 67, 85, 74, 80)( 68, 86, 75, 81)( 69, 88, 73, 83)
( 70, 89, 77, 82)( 71, 90, 76, 84)( 72, 87, 78, 79)( 91,105, 96,108)
( 92,106, 97,109)( 93,107, 94,104)( 95,103)( 98,110,100,113)( 99,112)
(101,114,102,111)(115,120,119,116)(121,126,125,122)(127,128,131,129)
]);
ARC("11^2:(5x2L2(11).2)","tomfusion",rec(name:="11^2:(5x2L2(11).2)",map:=[
1,28,7,7,7,7,16,16,2,16,16,54,11,54,54,54,33,33,33,33,4,52,127,127,127,
127,127,127,52,127,127,127,52,127,127,127,127,127,127,127,52,80,30,80,80,
80,80,80,80,80,30,6,36,36,36,36,58,58,58,15,58,58,15,58,58,58,95,25,24,21,
26,23,24,95,25,26,21,23,23,95,25,21,24,26,95,25,23,24,21,26,68,10,9,9,8,
68,10,20,18,20,19,19,8,9,68,10,9,68,10,20,19,18,20,19,17,17,43,3,17,17,67,
67,29,27,67,67,87,87,87,42,87],text:=[
"fusion map determined by the groups"
]));
ALF("11^2:(5x2L2(11).2)","L3(11)",[1,30,5,6,7,8,16,19,2,18,17,53,11,55,54,
56,36,34,37,35,3,49,87,82,86,92,90,85,51,84,89,91,50,81,94,95,88,83,96,93,
52,70,32,75,72,73,69,76,74,71,33,4,44,45,46,47,62,60,57,15,58,61,14,59,63,
64,80,19,26,29,20,25,28,78,17,22,27,25,24,79,18,28,29,23,77,16,24,27,26,
21,68,8,10,10,9,66,6,21,25,23,29,27,10,9,65,5,9,67,7,22,28,24,20,26,23,22,
48,2,21,20,68,67,31,30,66,65,78,79,77,48,80],[
"fusion map is unique up to table automorphisms"
]);
ALN("11^2:(5x2L2(11).2)",["AGL(2,11)"]);

MOT("11^2:60",
[
"origin: Dixon's Algorithm"
],
[7260,121,121,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,
60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,
60,60,60,60,60,60,60,60,60,60,60,60],
[,[1,2,3,5,4,9,11,10,12,14,13,15,17,16,6,8,7,10,9,11,13,12,14,7,6,8,4,1,5,16,
15,17,18,20,19,24,26,25,27,29,28,30,32,31,21,23,22,25,24,26,28,27,29,22,21,23,
19,18,20,31,30,32],[1,2,3,1,1,15,15,15,6,6,6,9,9,9,12,12,12,25,25,25,19,19,19,
31,31,31,28,28,28,22,22,22,48,48,48,60,60,60,51,51,51,54,54,54,57,57,57,44,44,
44,41,41,41,35,35,35,38,38,38,47,47,47],,[1,2,3,5,4,1,5,4,1,5,4,1,5,4,1,5,4,29
,28,27,29,28,27,29,28,27,29,28,27,29,28,27,40,39,41,40,39,41,40,39,41,40,39,41
,40,39,41,51,53,52,51,53,52,51,53,52,51,53,52,51,53,52],,,,,,[1,1,1,5,4,6,8,7,
9,11,10,12,14,13,15,17,16,20,19,18,23,22,21,26,25,24,29,28,27,32,31,30,59,58,
57,50,49,48,53,52,51,62,61,60,56,55,54,38,37,36,41,40,39,47,46,45,35,34,33,44,
43,42]],
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[TENSOR,[2,47]],
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[TENSOR,[2,49]],
[TENSOR,[2,50]],
[TENSOR,[2,51]],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(2,3),
(33,58)(34,59)(35,57)(36,49)(37,50)(38,48)(39,52)(40,53)(41,51)(42,61)(43,62)
(44,60)(45,55)(46,56)(47,54)
,
( 6, 9,12,15)( 7,10,13,16)( 8,11,14,17)(18,21,30,24)(19,22,31,25)(20,23,32,26)
(33,45,42,36)(34,46,43,37)(35,47,44,38)(48,57,54,60)(49,58,55,61)(50,59,56,62)
,
( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(18,20)(21,23)(24,26)(27,29)(30,32)(33,34)
(36,37)(39,40)(42,43)(45,46)(49,50)(52,53)(55,56)(58,59)(61,62)
]);
ARC("11^2:60","tomfusion",rec(name:="11^2:60",map:=[1,9,8,3,3,5,11,11,5,
11,11,5,11,11,5,11,11,15,7,15,15,7,15,15,7,15,6,2,6,15,7,15,18,18,12,18,
18,12,10,10,4,18,18,12,18,18,12,12,18,18,4,10,10,12,18,18,12,18,18,12,18,
18],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("11^2:60","L2(121)",[1,2,3,23,23,15,11,31,27,7,19,15,31,11,27,19,7,5,
21,25,17,9,29,29,9,17,13,33,13,25,21,5,4,22,24,16,10,30,28,8,18,14,32,12,
26,20,6,6,20,26,18,8,28,30,10,16,12,32,14,24,22,4],[
"fusion map is unique up to table automorphisms"
]);

MOT("2(A4xA4).4.2",
[
"origin: Dixon's Algorithm"
],
[2304,2304,192,128,36,36,24,144,144,48,16,12,12,16,32,32,24,24,12,96,32,32,96,
8,16,16],
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10,11,10,10,14,15,16,20,20,23,20,21,22,23,24,25,26]],
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[TENSOR,[16,4]],
[TENSOR,[16,3]],
[TENSOR,[16,2]],[12,12,4,-4,0,0,1,-3,-3,0,0,0,0,0,0,0,-1,-1,1,2,2,-2,-2,0,0,0
],
[TENSOR,[20,2]],[16,-16,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,
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,0,0],
[TENSOR,[22,2]],[16,-16,0,0,1,-1,0,-4,4,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,
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[TENSOR,[24,2]],[18,18,-6,2,0,0,0,0,0,0,0,0,0,2,-2,-2,0,0,0,0,0,0,0,0,0,0]],
[(17,18),(12,13),(25,26)]);
ARC("2(A4xA4).4.2","tomfusion",rec(name:="2(A4xA4).4.2",map:=[1,2,8,3,7,
21,59,20,6,4,16,24,24,46,15,13,121,121,63,26,33,5,10,50,43,42],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2(A4xA4).4.2","U4(3).2_3",[1,2,6,2,4,10,15,9,3,2,7,10,10,12,7,6,24,
25,23,19,20,16,17,21,19,20],[
"fusion map is unique up to table automorphisms"
]);
ALF("2(A4xA4).4.2","McL.2",[1,2,5,2,4,9,16,8,3,2,5,9,9,11,5,5,32,33,26,23,
24,20,21,24,23,24],[
"fusion map is unique up to table aut."
]);

MOT("2(A4xA4).4.2^2",
[
"origin: Dixon's Algorithm"
],
[4608,4608,384,256,288,288,48,72,72,64,64,192,192,24,24,64,32,64,96,32,12,16,
32,32,96,32,12,16,32,32,64,32,128,128,24,24,64,192,64,192,36,48,144,384,2304,
256],
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,7,1,2,3,3,9,5,6,1,2,2],[1,2,3,4,1,2,3,1,2,10,11,12,13,12,13,16,17,18,19,20,19
,22,23,24,25,26,25,28,29,30,31,32,33,34,38,40,37,38,39,40,45,44,45,44,45,46]],
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[TENSOR,[11,4]],
[TENSOR,[11,3]],
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[TENSOR,[15,7]],
[TENSOR,[15,3]],
[TENSOR,[15,2]],[6,6,2,-2,3,3,-1,0,0,2,0,-4,-2,-1,1,2,0,-2,0,0,0,0,0,0,0,0,0,
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[TENSOR,[19,2]],
[TENSOR,[20,2]],
[TENSOR,[19,7]],
[TENSOR,[20,7]],
[TENSOR,[19,3]],
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[TENSOR,[27,3]],
[TENSOR,[27,4]],
[TENSOR,[27,5]],[9,9,-3,1,0,0,0,0,0,-1,1,-3,3,0,0,1,-1,1,-3,1,0,1,-1,-1,-3,1,
0,1,-1,-1,1,-1,1,1,0,0,1,-3,-1,3,0,0,0,-3,9,1],
[TENSOR,[31,8]],
[TENSOR,[31,7]],
[TENSOR,[31,6]],
[TENSOR,[31,5]],
[TENSOR,[31,4]],
[TENSOR,[31,3]],
[TENSOR,[31,2]],[12,12,4,-4,-3,-3,1,0,0,-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,-1,1,2,2,-2,-2,0,1,-3,4,12,-4],
[TENSOR,[39,7]],
[TENSOR,[39,3]],
[TENSOR,[39,2]],[18,18,-6,2,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,0,0,0,0,0,0,0,0,0,0
,0,0,2,-2,2,2,0,0,0,0,0,0,0,0,0,6,-18,-2],
[TENSOR,[43,3]],[32,-32,0,0,-4,4,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[32,-32,0,0,8,-8,0,2,-2,0,0,0,0,0,0,0,0,
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[(29,30)(33,34),(23,24)(29,30),(19,25)(20,26)(21,27)(22,28)(23,29)(24,30),
(10,39)(11,37)(12,38)(13,40)(14,35)(15,36)(22,28)(23,29)(24,30)]);
ARC("2(A4xA4).4.2^2","tomfusion",rec(name:="2(A4xA4).4.2^2",map:=[1,9,40,
5,11,55,181,10,50,155,8,42,152,184,455,39,154,29,3,23,45,148,113,111,2,30,
44,151,112,114,4,153,24,32,183,461,7,41,157,160,174,51,186,6,43,38],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2(A4xA4).4.2^2","U4(3).(2^2)_{133}",[1,2,6,2,3,9,14,4,10,31,27,28,30,
34,35,7,12,6,2,7,10,32,30,31,16,18,20,41,39,40,16,22,18,17,43,44,36,37,40,
39,25,19,24,15,17,18],[
"fusion map is unique up to table automorphisms"
]);

MOT("2(L2(11)x2).2",
[
"origin: Dixon's Algorithm"
],
[5280,5280,5280,5280,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,
48,48,48,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,44,44,44,44],
[,[1,1,2,2,2,1,15,15,16,16,16,16,15,15,21,21,22,22,22,22,21,21,6,6,6,6,35,35,
36,36,42,42,41,41,40,40,39,39,37,37,38,38,3,4,45,45,46,46],[1,2,4,3,5,6,24,23,
25,26,24,23,25,26,6,6,5,5,3,4,1,2,26,25,24,23,34,33,32,31,29,30,27,28,41,42,39
,40,37,38,35,36,44,43,45,46,48,47],,[1,2,3,4,5,6,11,12,13,14,7,8,9,10,16,15,18
,17,19,20,21,22,23,24,25,26,44,44,43,43,44,44,43,43,4,3,1,2,1,2,3,4,43,44,45,
46,47,48],,,,,,[1,2,4,3,5,6,9,10,7,8,13,14,11,12,16,15,17,18,20,19,21,22,26,25
,24,23,30,29,28,27,34,33,32,31,36,35,37,38,39,40,42,41,44,43,1,2,4,3]],
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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,
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-E(4),-E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),-E(4),-1,-1,1,1,1,1,-1,-1,
-E(4),E(4),1,1,-1,-1],
[TENSOR,[2,3]],[10,10,10,10,2,2,0,0,0,0,0,0,0,0,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0
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[TENSOR,[5,3]],[10,10,10,10,-2,-2,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,2,2
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[TENSOR,[7,2]],[10,-10,-10*E(4),10*E(4),0,0,-1-E(4),1+E(4),-1+E(4),1-E(4),
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-1-E(4),1+E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,E(4),-E(4)],
[TENSOR,[9,3]],
[TENSOR,[9,2]],
[TENSOR,[9,4]],
[TENSOR,[7,4]],
[TENSOR,[7,3]],[10,-10,-10*E(4),10*E(4),0,0,-E(12)^4-E(12)^11,
E(12)^4+E(12)^11,E(12)^7-E(12)^8,-E(12)^7+E(12)^8,-E(12)^7-E(12)^8,
E(12)^7+E(12)^8,-E(12)^4+E(12)^11,E(12)^4-E(12)^11,E(3)-E(3)^2,-E(3)+E(3)^2,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11,E(4),-E(4),1,-1,1-E(4),-1+E(4),-1-E(4),
1+E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,E(4),-E(4)],
[GALOIS,[15,5]],
[TENSOR,[16,3]],
[TENSOR,[15,3]],
[TENSOR,[16,2]],
[TENSOR,[15,2]],
[TENSOR,[15,4]],
[TENSOR,[16,4]],[10,10,-10,-10,2,-2,-E(3)+E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,
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1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1],
[TENSOR,[23,2]],
[TENSOR,[23,4]],
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[TENSOR,[27,2]],
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,E(4)],
[TENSOR,[31,3]],[12,-12,-12*E(4),12*E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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-E(4),E(4)],
[GALOIS,[33,13]],
[TENSOR,[34,2]],
[TENSOR,[33,2]],
[TENSOR,[33,4]],
[TENSOR,[34,3]],
[TENSOR,[34,4]],
[TENSOR,[33,3]],[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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-E(20)^13-E(20)^17,E(20)^13+E(20)^17,E(20)^13+E(20)^17,-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)+E(5)^4,E(5)+E(5)^4,
-E(5)-E(5)^4,-E(5)-E(5)^4,2*E(4),-2*E(4),1,1,-1,-1],
[GALOIS,[41,13]],
[TENSOR,[42,2]],
[TENSOR,[41,2]],
[TENSOR,[41,4]],
[TENSOR,[42,4]],
[TENSOR,[42,3]],
[TENSOR,[41,3]]],
[(27,28)(29,30)(31,32)(33,34),
(27,31,28,32)(29,33,30,34)(35,42)(36,41)(37,39)(38,40),
( 7, 8)( 9,10)(11,12)(13,14)(23,24)(25,26),
( 7,11)( 8,12)( 9,13)(10,14)(15,16)(17,18),
( 3, 4)( 7, 9)( 8,10)(11,13)(12,14)(15,16)(19,20)(23,26)(24,25)(27,29)(28,30)
(31,33)(32,34)(35,36)(41,42)(43,44)(47,48)
]);
ARC("2(L2(11)x2).2","tomfusion",rec(name:="2(L2(11)x2).2",map:=[1,2,5,5,6,
3,25,28,25,28,25,28,25,28,12,12,23,23,22,22,4,11,8,9,9,8,46,46,46,46,46,
46,46,46,33,33,10,19,10,19,33,33,16,16,21,35,48,48],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2(L2(11)x2).2","U3(11)",[1,2,4,5,6,2,18,20,19,20,18,21,19,21,9,9,20,
21,19,18,3,9,6,5,4,6,40,44,43,39,42,46,45,41,25,24,8,13,7,12,22,23,10,11,
14,26,47,48],[
"fusion map is unique up to table automorphisms"
]);

MOT("2(L2(7)x4).2",
[
"origin: Dixon's Algorithm"
],
[2688,2688,2688,2688,2688,2688,2688,2688,48,48,48,48,48,48,48,48,48,48,48,48,
48,48,48,48,48,48,48,48,56,56,56,56,56,56,56,56,64,64,64,64,64,64,64,64,64,64,
64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64],
[,[1,1,2,2,4,4,3,3,23,23,24,24,21,21,22,22,5,6,8,7,25,25,26,26,28,28,27,27,32,
32,31,31,30,30,29,29,4,3,2,1,53,53,54,54,56,56,55,55,39,39,39,39,40,40,40,40,
53,53,54,54,56,56,55,55],[1,2,4,3,8,7,6,5,18,18,17,17,19,19,20,20,19,20,17,18,
8,7,6,5,3,4,1,2,30,29,31,32,35,36,33,34,38,37,39,40,63,64,61,62,60,59,58,57,50
,49,51,52,55,56,53,54,48,47,46,45,43,44,41,42],,,,[1,2,4,3,7,8,5,6,14,13,15,16
,10,9,11,12,20,19,18,17,23,24,21,22,26,25,27,28,3,4,1,2,6,5,7,8,38,37,39,40,48
,47,46,45,44,43,42,41,49,50,52,51,55,56,53,54,63,64,61,62,59,60,57,58]],
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ARC("2(L2(7)x4).2","tomfusion",rec(name:="2(L2(7)x4).2",map:=[1,2,5,5,13,
13,13,13,59,59,59,59,59,59,59,59,35,35,35,35,42,42,42,42,26,26,4,10,45,45,
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24,22,20,21,20,21,24,22],text:=[
"fusion map determined by the groups"
]));
ALF("2(L2(7)x4).2","U3(7)",[1,2,4,5,11,13,10,12,47,51,53,49,52,48,54,50,
24,26,25,23,28,30,27,29,21,20,3,7,32,31,8,22,57,55,56,58,15,14,6,2,12,14,
16,18,19,16,15,13,17,16,19,18,4,6,5,6,10,14,17,19,17,18,11,15],[
"fusion map is unique up to table automorphisms"
]);

MOT("2.(2.(A4xA4).2.2)",
[
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],
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ARC("2.(2.(A4xA4).2.2)","tomfusion",rec(name:="2.(2.(A4xA4).2.2)",map:=[1,
2,3,17,11,12,7,21,23,22,77,76,8,24,26,9,25,27,6,67,67,50,52,52,86,34,59,4,
16,37,79,57,14,5],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2.(2.(A4xA4).2.2)","2.U4(2).2",[1,2,3,4,12,11,5,6,17,16,24,23,7,8,18,
9,10,19,26,33,34,29,28,27,20,18,13,3,4,32,31,29,25,26],[
"fusion map is unique up to table automorphisms"
]);

MOT("2.(2^5:S6)",
[
"origin: Dixon's Algorithm"
],
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,288],
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,1,1,-3,-3,-3,1,-3,-3,1,9,9,0,0,0,-1,-1,1,0,0,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,
0,0],
[TENSOR,[37,2]],[45,45,45,-3,-3,-3,-3,1,-3,-3,1,1,1,1,-3,-3,5,-3,-3,0,0,0,1,1
,-1,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[39,2]],[64,-64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,
0,0,0,-1,1,-E(20)-E(20)^9+E(20)^13+E(20)^17,E(20)+E(20)^9-E(20)^13-E(20)^17,0,
0,0,0,0,0,0,-4,4],
[GALOIS,[41,11]],[72,-72,0,0,0,0,0,0,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0],[80,-80,0,0,0,0,0,0,0,0,-8,8,0,0,0,0,0,0,0
,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4]],
[(34,35),( 6, 7)(26,27)(28,29),(15,16)(18,19)(23,24)(28,29)(36,37)(38,39)]);
ARC("2.(2^5:S6)","tomfusion",rec(name:="2.(2^5:S6)",map:=[1,2,10,3,12,5,4,
26,7,21,18,19,22,146,57,60,6,13,14,184,9,37,118,139,163,46,47,144,143,125,
148,35,172,530,530,189,185,548,542,40,180,175,36,8],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2.(2^5:S6)","2^5:S6",[1,1,4,2,3,22,23,21,8,9,6,6,5,7,24,25,28,26,27,
11,10,10,30,31,29,33,32,17,18,16,16,19,19,20,20,37,36,35,34,15,13,14,12,
12]);
ALF("2.(2^5:S6)","2.S6(2)",[1,2,3,4,5,4,6,17,6,5,13,14,17,18,15,16,6,5,3,
26,11,12,18,16,31,27,28,15,18,32,33,19,20,36,37,21,25,39,38,22,25,21,8,7],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(2^5:S6)","Co3",[1,2,7,2,8,2,3,8,3,8,8,7,8,19,17,18,3,7,8,28,5,13,
17,19,19,13,14,19,18,17,18,9,22,33,34,27,26,41,40,12,27,26,11,4],[
"fusion map is unique up to table aut."
]);

MOT("2x3^(1+2)_+:2S4",
0,
0,
0,
0,
[(15,16)(33,34),(15,33)(16,34)(17,35)(18,36),(8,9,10)(12,13,14)(26,27,28)(30,
31,32)],
["ConstructDirectProduct",[["Cyclic",2],["3^(1+2)+:2S4"]]]);
ARC("2x3^(1+2)_+:2S4","tomfusion",rec(name:="2.(3^(1+2)+:2S4)",map:=[1,7,
11,3,21,13,70,8,9,10,66,36,31,32,56,56,5,45,2,19,27,4,20,14,69,25,24,26,
127,29,28,34,58,58,6,44],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2x3^(1+2)_+:2S4","2.U4(2).2",[1,5,9,3,17,11,23,5,9,7,21,16,19,18,33,
34,26,32,2,6,10,3,16,12,24,6,10,8,22,17,19,18,34,33,26,32],[
"fusion map is unique up to table automorphisms"
]);
ALF("2x3^(1+2)_+:2S4","2.S6(2)",[1,9,11,4,23,13,40,7,9,11,34,22,24,27,31,
31,6,28,2,10,12,4,24,14,41,8,10,12,35,22,23,27,31,31,6,28],[
"fusion map is unique up to table aut."
]);
ALF("2x3^(1+2)_+:2S4","2^(1+6).3^(1+2).2S4",[1,5,7,10,14,16,19,21,29,26,
30,32,39,36,48,51,40,45,2,6,8,11,15,17,20,22,28,27,31,33,38,37,49,52,40,
45]);

MOT("2.(3^3:(S4x2))",
[
"origin: Dixon's Algorithm"
],
[2592,432,216,324,432,2592,216,324,24,48,36,18,18,36,96,96,36,36,144,12,12,12,
24,48,24,48,24,36,36,36,72,36,16,16],
[,[1,2,3,4,2,1,3,4,5,6,11,12,12,11,1,1,7,5,6,11,11,3,1,10,9,10,9,4,4,2,1,3,10,
10],[1,1,1,1,6,6,6,6,10,10,1,4,8,6,15,16,19,19,19,15,16,23,23,24,24,26,26,31,
31,31,31,31,33,34]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,
1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1],[1
,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-2,-2,-2,-2,-2,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0],
[TENSOR,[5,2]],[2,2,2,2,-2,-2,-2,-2,0,0,-1,-1,1,1,2,-2,0,0,0,-1,1,0,0,
-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,0,0,0,0,0,-E(8)-E(8)^3,
E(8)+E(8)^3],
[TENSOR,[7,4]],
[TENSOR,[7,3]],
[TENSOR,[7,2]],[3,3,3,3,3,3,3,3,-1,-1,0,0,0,0,-3,-3,1,1,1,0,0,-1,-1,1,1,1,1,1
,1,1,1,1,-1,-1],
[TENSOR,[11,4]],
[TENSOR,[11,3]],
[TENSOR,[11,2]],[4,4,4,4,-4,-4,-4,-4,0,0,1,1,-1,-1,4,-4,0,0,0,1,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0],
[TENSOR,[15,2]],[6,3,0,-3,3,6,0,-3,-1,2,0,0,0,0,0,0,-2,1,4,0,0,0,0,-2,1,-2,1,
1,1,1,-2,-2,0,0],
[TENSOR,[17,4]],
[TENSOR,[17,3]],
[TENSOR,[17,2]],[8,-4,2,-1,-4,8,2,-1,0,0,2,-1,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,
-1,-1,2,-4,2,0,0],
[TENSOR,[21,3]],[8,-4,2,-1,4,-8,-2,1,0,0,2,-1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
-3,3,0,0,0,0,0],
[TENSOR,[23,3]],[12,6,0,-6,6,12,0,-6,2,-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],[12,0,-3,3,0,12,-3,3,0,0,0,0,0,0,0,0,-1,2,-4,0,0,-1,2,0,0,0,0,1,
1,-2,-2,1,0,0],
[TENSOR,[26,4]],
[TENSOR,[26,3]],
[TENSOR,[26,2]],[12,6,0,-6,-6,-12,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-2*E(8)-2*E(8)^3,E(8)+E(8)^3,2*E(8)+2*E(8)^3,-E(8)-E(8)^3,0,0,0,0,0,0,0],
[TENSOR,[30,2]],[16,-8,4,-2,-8,16,4,-2,0,0,-2,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[16,-8,4,-2,8,-16,-4,2,0,0,-2,1,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[24,0,-6,6,0,-24,6,-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]],
[(28,29),(15,16)(20,21)(33,34),(24,26)(25,27)(33,34)]);
ARC("2.(3^3:(S4x2))","tomfusion",rec(name:="2.(3^3:(S4x2))",map:=[1,7,9,8,
18,2,20,19,69,14,10,57,117,34,4,3,60,62,11,41,42,40,6,45,138,45,138,28,27,
26,5,24,49,49],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2.(3^3:(S4x2))","s3wrs3",[1,2,4,3,2,1,4,3,6,5,7,8,8,7,12,12,11,10,9,
13,13,22,21,19,20,19,20,17,17,16,14,15,18,18]);
ALF("2.(3^3:(S4x2))","2.U4(2).2",[1,7,9,5,8,2,10,6,20,4,9,21,22,10,26,26,
31,30,25,32,32,32,26,27,37,28,38,16,17,18,3,19,13,13],[
"fusion map is unique up to table automorphisms"
]);
ALF("2.(3^3:(S4x2))","2.S6(2)",[1,7,11,9,8,2,12,10,25,5,11,34,35,12,6,6,
26,21,3,28,28,28,6,15,38,15,38,23,24,22,4,27,18,18],[
"fusion map is unique up to table aut."
]);

MOT("2.(S3xS6)",
[
"origin: Dixon's Algorithm"
],
[8640,8640,4320,4320,1440,96,288,144,32,96,48,144,288,96,32,32,24,48,36,108,
108,216,216,36,36,36,12,36,36,36,12,36,108,108,216,216,48,24,16,60,60,30,30,20
,20],
[,[1,1,3,3,2,2,2,4,1,2,4,3,1,1,10,10,11,10,22,21,21,23,23,20,20,22,22,34,34,36
,36,35,34,34,36,36,10,11,10,41,41,43,43,40,40],[1,2,1,2,5,6,7,7,9,10,10,13,13,
14,15,16,18,18,5,2,1,2,1,7,7,7,6,13,13,13,14,5,2,1,2,1,37,37,39,40,41,40,41,44
,45],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,15,17,18,19,20,21,22,23,24,25,26,27
,28,29,30,31,32,33,34,35,36,37,38,39,2,1,4,3,5,5]],
[[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],[1,1,1,1,-1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,1,1,-1,
1,1,1,-1,-1,1,1,1,1,1,1,-1,1,1,1,1,-1,-1],[1,1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,
-1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,1,1,1,1,1,-1,-1],
[TENSOR,[2,3]],[2,2,-1,-1,0,0,-2,1,0,2,-1,1,-2,0,0,0,-1,2,0,-1,-1,2,2,1,1,-2,
0,1,1,-2,0,0,-1,-1,2,2,-2,1,0,2,2,-1,-1,0,0],
[TENSOR,[5,3]],[5,5,5,5,-5,-3,3,3,-1,1,1,-1,-1,1,1,1,-1,-1,-2,2,2,2,2,0,0,0,0
,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,0,0,0,0,0,0],[5,5,5,5,-5,-1,1,1,-1,1,1,-3,-3,
3,1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,0,0,0,0,-2,2,2,2,2,-1,-1,1,0,0,0,0,0,0],
[TENSOR,[8,4]],
[TENSOR,[7,4]],
[TENSOR,[7,3]],
[TENSOR,[8,3]],
[TENSOR,[8,2]],
[TENSOR,[7,2]],[8,-8,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,0,0,0,0,0,0
,0,0,0,4,-4,4,-4,0,0,0,2,-2,2,-2,0,0],[8,-8,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,4,-4,4,-4,0,0,0,0,0,0,0,0,0,-2,2,-2,2,0,0,0,2,-2,2,-2,0,0],[8,-8,-4,4,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,-2,2,4,-4,0,0,0,0,-3,3,0,0,0,1,-1,-2,2,0,0,0,2,-2,-1,1,
0,0],
[TENSOR,[17,3]],[8,-8,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-2,2,-3*E(4),
3*E(4),0,0,0,0,0,0,0,-2,2,4,-4,0,0,0,2,-2,-1,1,0,0],
[TENSOR,[19,3]],[9,9,9,9,-9,-3,3,3,-1,1,1,3,3,-3,-1,-1,1,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-1,-1,1,-1,-1,-1,-1,1,1],
[TENSOR,[21,4]],
[TENSOR,[21,3]],
[TENSOR,[21,2]],[10,10,-5,-5,0,0,-6,3,0,2,-1,-1,2,0,0,0,1,-2,0,-2,-2,4,4,0,0,
0,0,-1,-1,2,0,0,1,1,-2,-2,-2,1,0,0,0,0,0,0,0],[10,10,-5,-5,0,0,-2,1,0,2,-1,-3,
6,0,0,0,1,-2,0,1,1,-2,-2,1,1,-2,0,0,0,0,0,0,-2,-2,4,4,2,-1,0,0,0,0,0,0,0],
[TENSOR,[26,3]],
[TENSOR,[25,3]],[10,10,10,10,-10,-2,2,2,2,-2,-2,-2,-2,2,0,0,0,0,-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],
[TENSOR,[29,4]],
[TENSOR,[29,3]],
[TENSOR,[29,2]],[16,16,16,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,-2,-2,0,0,
0,0,0,0,0,0,2,-2,-2,-2,-2,0,0,0,1,1,1,1,-1,-1],
[TENSOR,[33,2]],[16,-16,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,0,0,0,
0,0,0,0,0,0,2,-2,2,-2,0,0,0,-1,1,-1,1,-E(20)-E(20)^9+E(20)^13+E(20)^17,
E(20)+E(20)^9-E(20)^13-E(20)^17],
[TENSOR,[35,2]],[18,18,-9,-9,0,0,-6,3,0,2,-1,3,-6,0,0,0,-1,2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,2,-1,0,-2,-2,1,1,0,0],
[TENSOR,[37,3]],[20,20,-10,-10,0,0,-4,2,0,-4,2,-2,4,0,0,0,0,0,0,-1,-1,2,2,-1,
-1,2,0,1,1,-2,0,0,-1,-1,2,2,0,0,0,0,0,0,0,0,0],
[TENSOR,[39,3]],[20,-20,20,-20,0,0,0,0,0,0,0,0,0,0,-2*E(8)-2*E(8)^3,
2*E(8)+2*E(8)^3,0,0,0,-2,2,-2,2,0,0,0,0,0,0,0,0,0,-2,2,-2,2,0,0,0,0,0,0,0,0,0]
,
[TENSOR,[41,2]],[32,32,-16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-4,-4,0,0,0,
0,0,0,0,0,0,2,2,-4,-4,0,0,0,2,2,-1,-1,0,0],[32,-32,-16,16,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-2,2,4,-4,0,0,0,0,0,0,0,0,0,-2,2,4,-4,0,0,0,-2,2,1,-1,0,0],[40,-40,
-20,20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-4,4,0,0,0,0,0,0,0,0,0,2,-2,-4,4,0,0
,0,0,0,0,0,0,0]],
[(44,45),(28,29),(24,25),(15,16)]);
ARC("2.(S3xS6)","tomfusion",rec(name:="2.(S3xS6)",map:=[1,2,6,20,11,14,12,
73,5,15,79,23,3,4,56,56,186,51,81,25,9,22,7,90,90,86,95,34,33,30,43,87,27,
10,21,8,50,190,59,70,19,214,108,170,170],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2.(S3xS6)","S3xS6",[1,1,12,12,23,29,7,18,24,2,13,19,8,30,27,27,16,5,
25,14,14,3,3,21,21,10,32,22,22,11,33,26,15,15,4,4,9,20,31,6,6,17,17,28,28]);
ALF("2.(S3xS6)","2.S6(2)",[1,2,7,8,3,5,3,21,6,5,25,22,4,6,18,18,38,15,21,
12,11,8,7,26,26,21,25,23,24,27,28,26,10,9,12,11,16,39,18,20,19,43,42,36,
37],[
"fusion map is unique up to table automorphisms"
]);

MOT("2.(S6x2)",
[
"origin: Dixon's Algorithm"
],
[2880,2880,1440,96,96,96,96,32,32,16,32,32,12,12,12,12,72,72,36,72,72,36,16,16
,20,20,20,20],
[,[1,1,2,2,2,1,1,12,12,12,1,2,20,20,18,18,17,17,18,20,20,21,12,12,26,26,25,25]
,[1,2,3,4,5,6,7,8,9,10,11,12,7,6,4,5,1,2,3,1,2,3,23,24,25,26,27,28],,[1,2,3,4,
5,6,7,9,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,2,1,3,3]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,-1,1,1,-1,
-1,-1,1,-1,1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,1,1,-1,-1],[1,1,-1,1,-1,-1,1,-1,-1,1
,-1,1,1,-1,1,-1,1,1,-1,1,1,-1,-1,1,1,1,-1,-1],
[TENSOR,[2,3]],[5,5,-5,-3,3,-1,1,1,1,-1,-1,1,1,-1,0,0,2,2,-2,-1,-1,1,1,-1,0,0
,0,0],[5,5,-5,-1,1,-3,3,1,1,-1,-1,1,0,0,-1,1,-1,-1,1,2,2,-2,-1,1,0,0,0,0],
[TENSOR,[6,4]],
[TENSOR,[5,4]],
[TENSOR,[5,3]],
[TENSOR,[6,3]],
[TENSOR,[6,2]],
[TENSOR,[5,2]],[8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,4,0,2,-2,0,0,0,2,-2,0,0],
[8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,-4,4,0,0,0,2,-2,0,0],[9,9,-9,-3,3,3,
-3,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,1],
[TENSOR,[15,4]],
[TENSOR,[15,3]],
[TENSOR,[15,2]],[10,10,-10,-2,2,-2,2,0,0,0,2,-2,-1,1,1,-1,1,1,-1,1,1,-1,0,0,0
,0,0,0],
[TENSOR,[19,4]],
[TENSOR,[19,3]],
[TENSOR,[19,2]],[16,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,-2,2,0,0,1,1,
-1,-1],
[TENSOR,[23,2]],[16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,-2,2,0,0,0,-1,1,
-E(20)-E(20)^9+E(20)^13+E(20)^17,E(20)+E(20)^9-E(20)^13-E(20)^17],
[TENSOR,[25,2]],[20,-20,0,0,0,0,0,-2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,0,0,0,0,
0,0,2,-2,0,2,-2,0,0,0,0,0,0,0],
[TENSOR,[27,2]]],
[(27,28),(8,9),( 4, 5)( 6, 7)(13,14)(15,16)(23,24)]);
ARC("2.(S6x2)","tomfusion",rec(name:="2.(S6x2)",map:=[1,2,8,11,10,3,4,43,
43,45,5,13,26,25,57,61,7,17,56,6,18,52,34,36,49,16,111,111],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2.(S6x2)","2.U4(2).2",[1,2,25,4,25,26,3,27,28,13,26,4,19,32,20,30,7,
8,30,9,10,31,29,13,15,14,35,36],[
"fusion map is unique up to table automorphisms"
]);

MOT("2.2^6.L3(2)",
[
"origin: Dixon's Algorithm"
],
[21504,21504,1536,1536,384,512,256,256,64,128,64,32,64,64,128,128,32,32,16,16,
16,24,24,12,12,12,14,14,14,14],
[,[1,1,1,2,1,2,3,3,1,3,6,6,6,3,1,2,10,10,7,15,16,22,22,22,22,23,27,27,29,29],[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,2,3,5,4,29,30,27,28],,
,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,2,1,
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],[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,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4],
[GALOIS,[2,3]],[6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,
-1],[7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,0,0,0,
0],[7,7,7,-1,-1,-1,3,3,3,3,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,0,0,0,0],
[7,7,-1,-5,-1,3,3,3,-1,-1,-3,1,1,-1,-1,3,1,1,-1,-1,1,1,1,-1,-1,1,0,0,0,0],[7,7
,-1,-5,-1,3,-1,-1,-1,3,1,1,-3,-1,3,-1,-1,-1,1,1,-1,1,1,-1,-1,1,0,0,0,0],[7,7,7
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,-1,-1,-1,1,1,1,1,1,-1,-1,0,0,0,0],[8,8,8,
8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,1,1,1,1],[8,-8,0,0,0,0,4,-4
,0,0,0,0,0,0,0,0,2,-2,0,0,0,2,-2,0,0,0,1,-1,1,-1],[14,14,14,-2,-2,-2,2,2,2,2,
-2,-2,-2,2,2,2,0,0,0,0,0,-1,-1,-1,1,1,0,0,0,0],[14,14,-2,-10,-2,6,2,2,-2,2,-2,
2,-2,-2,2,2,0,0,0,0,0,-1,-1,1,1,-1,0,0,0,0],[21,21,21,-3,-3,-3,1,1,1,1,1,1,1,
-3,-3,-3,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0],[21,21,-3,-15,-3,9,1,1,1,-3,-1,-1,3,1
,-3,1,-1,-1,1,1,-1,0,0,0,0,0,0,0,0,0],[21,21,-3,9,-3,1,5,5,-3,1,3,-1,-1,1,-3,1
,1,1,-1,1,-1,0,0,0,0,0,0,0,0,0],[21,21,-3,9,-3,1,-3,-3,1,1,-1,-1,3,-3,5,1,1,1,
-1,1,-1,0,0,0,0,0,0,0,0,0],[21,21,-3,-15,-3,9,-3,-3,1,1,3,-1,-1,1,1,-3,1,1,-1,
-1,1,0,0,0,0,0,0,0,0,0],[21,21,-3,9,-3,1,1,1,-3,5,-1,-1,3,1,1,-3,-1,-1,1,-1,1,
0,0,0,0,0,0,0,0,0],[21,21,-3,9,-3,1,1,1,1,-3,3,-1,-1,-3,1,5,-1,-1,1,-1,1,0,0,0
,0,0,0,0,0,0],[21,21,21,-3,-3,-3,-3,-3,-3,-3,1,1,1,1,1,1,1,1,1,-1,-1,0,0,0,0,0
,0,0,0,0],[24,-24,0,0,0,0,-4,4,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,
E(7)^3+E(7)^5+E(7)^6,-E(7)^3-E(7)^5-E(7)^6,E(7)+E(7)^2+E(7)^4,
-E(7)-E(7)^2-E(7)^4],
[GALOIS,[22,3]],[28,28,-4,-4,4,-4,-4,-4,0,4,0,0,0,0,-4,4,0,0,0,0,0,1,1,-1,1,
-1,0,0,0,0],[28,28,-4,-4,4,-4,4,4,0,-4,0,0,0,0,4,-4,0,0,0,0,0,1,1,-1,1,-1,0,0,
0,0],[42,42,-6,18,-6,2,-2,-2,2,-2,-2,2,-2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
,[48,-48,0,0,0,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1],[56,56,-8
,-8,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,-1,1,0,0,0,0],[56,-56,0,0,0,0,
-4,4,0,0,0,0,0,0,0,0,-2,2,0,0,0,2,-2,0,0,0,0,0,0,0],[64,-64,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,1,-1,1,-1]],
[(27,29)(28,30)]);
ARC("2.2^6.L3(2)","tomfusion",rec(name:="2.2^6.L3(2)",map:=[1,2,3,8,4,10,
14,13,6,15,78,119,67,20,5,16,120,105,140,29,136,7,32,37,38,158,39,163,39,
163],text:=[
"fusion map is unique"
]));
ALF("2.2^6.L3(2)","2^6:L3(2)",[1,1,2,4,5,3,7,7,14,6,10,11,9,8,12,13,19,19,
20,21,22,15,15,16,18,17,23,23,24,24]);
ALF("2.2^6.L3(2)","2.S6(2)",[1,2,4,3,6,5,13,14,6,17,16,18,15,17,4,5,32,33,
31,17,18,11,12,27,28,26,29,30,29,30],[
"fusion map is unique"
]);
ALF("2.2^6.L3(2)","Co3",[1,2,2,7,3,8,8,7,3,8,17,19,18,8,2,8,17,18,19,8,19,
5,13,13,14,28,16,29,16,29],[
"fusion map is unique"
]);

MOT("D108",
0,
0,
0,
0,
[(29,30),
( 2, 6,26,18,24, 8,20,14,12)( 3,11, 5,21, 9,15,17,27,23)( 4,16,22)( 7,25,13)],
["ConstructPermuted",["Dihedral",108]]);
ARC("D108","tomfusion",rec(name:="27:2^2",map:=[1,19,15,14,15,19,10,19,15,
9,15,19,10,19,15,14,15,19,5,19,15,14,15,19,10,19,15,4,2,3],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("D108","L2(109)",[1,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,30,30],[
"fusion map is unique up to table automorphisms"
]);
ALN("D108",["27:2^2"]);

MOT("D112",
0,
0,
0,
0,
[(30,31),
( 2, 4,10,28,26,20)( 3, 7,19)( 5,13,21)( 6,16,12,24,14,18)( 8,22)( 9,25,17)
(11,27,23),
( 2, 6,26,14,10,12)( 3,11, 7,27,19,23)( 4,16,20,18,28,24)( 5,21,13)( 8,22)
( 9,17,25)],
["ConstructPermuted",["Dihedral",112]]);
ARC("D112","tomfusion",rec(name:="28.2^2",map:=[1,20,18,20,12,20,18,10,8,
20,18,20,12,20,7,20,8,20,18,20,12,10,18,20,8,20,18,20,2,3,4],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("D112","L2(113)",[1,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,31,31],[
"fusion map is unique up to table automorphisms"
]);
ALN("D112",["28.2^2"]);

MOT("2^(1+4)+.(S3xS3)",
[
"origin: Dixon's Algorithm"
],
[1152,1152,64,96,36,36,16,48,36,36,12,72,72,12,12,16,8,16,12,12,16,48],
[,[1,1,1,2,5,5,3,2,9,9,12,13,13,10,10,1,4,3,5,5,3,1],[1,2,3,4,1,2,7,8,1,2,4,2,
1,8,8,16,17,18,22,22,21,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,1,1,1,1,1,-1
,-1,-1,-1,-1,1,1,1,1],[1,1,1,1,1,1,-1,-1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,-1,-1,0,0,2,2,-1,-1,-1,0,0,0,0,0,1,1,-2,-2],
[TENSOR,[5,3]],[2,2,2,2,2,2,-2,-2,-1,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0],
[TENSOR,[7,2]],[4,4,4,4,-2,-2,0,0,-2,-2,1,1,1,0,0,0,0,0,0,0,0,0],[6,6,-2,2,0,
0,0,0,0,0,-1,3,3,0,0,-2,0,2,0,0,0,0],
[TENSOR,[10,2]],[8,-8,0,0,2,-2,0,0,2,-2,0,4,-4,0,0,0,0,0,0,0,0,0],[8,-8,0,0,
-1,1,0,0,2,-2,0,-2,2,0,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0],
[TENSOR,[13,3]],[8,-8,0,0,2,-2,0,0,-1,1,0,-2,2,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,0,0,0,0,0,0,0],
[TENSOR,[15,2]],[9,9,1,-3,0,0,-1,3,0,0,0,0,0,0,0,-1,1,-1,0,0,1,-3],
[TENSOR,[17,4]],
[TENSOR,[17,3]],
[TENSOR,[17,2]],[12,12,-4,4,0,0,0,0,0,0,1,-3,-3,0,0,0,0,0,0,0,0,0],[16,-16,0,
0,-2,2,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0]],
[(19,20),(14,15)]);
ARC("2^(1+4)+.(S3xS3)","tomfusion",rec(name:="2^(1+4)+.(S3xS3)",map:=[1,2,
3,9,8,25,16,13,7,24,56,23,6,61,61,5,43,17,28,28,18,4],text:=[
"fusion map is unique"
]));
ALF("2^(1+4)+.(S3xS3)","G2(3).2",[1,2,2,7,6,10,19,19,5,9,16,8,3,23,24,2,
12,7,21,22,19,18],[
"compatible with 2^(1+4)+:3^2.2 -> G2(3)"
]);

MOT("2^(1+8)+:L2(8)",
[
"origin: Dixon's Algorithm"
],
[258048,258048,1024,14336,3584,1536,28,56,56,28,28,28,28,56,56,28,28,28,56,56,
28,32,32,128,256,256,64,64,64,12,72,72,18,18,18,18,18,18],
[,[1,1,1,1,2,2,14,14,14,14,15,20,19,19,19,19,9,8,8,8,8,5,6,1,4,4,3,3,3,31,32,
32,36,36,38,38,33,33],[1,2,3,4,5,6,21,19,20,18,17,11,7,8,9,10,12,13,14,15,16,
22,23,24,25,26,27,28,29,6,2,1,32,31,31,32,31,32],,,,[1,2,3,4,5,6,4,1,2,4,5,5,4
,1,2,4,5,4,1,2,4,22,23,24,25,26,27,28,29,30,31,32,36,35,37,38,34,33]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
,[7,7,7,7,7,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-2,-2,-2,1
,1,1,1,1,1],[7,7,7,7,7,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1
,1,1,1,E(9)^2+E(9)^4+E(9)^5+E(9)^7,E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^2-E(9)^7,
-E(9)^2-E(9)^7,-E(9)^4-E(9)^5,-E(9)^4-E(9)^5],
[GALOIS,[3,2]],
[GALOIS,[3,4]],[8,8,8,8,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,-1,
-1,-1,-1,-1,-1,-1,-1,-1],[9,9,1,-7,5,-3,0,2,2,0,-2,-2,0,2,2,0,-2,0,2,2,0,-1,-1
,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0],[9,9,9,9,9,9,E(7)+E(7)^6,E(7)+E(7)^6,
E(7)+E(7)^6,E(7)+E(7)^6,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^2+E(7)^5,E(7)^2+E(7)^5,
E(7)^2+E(7)^5,E(7)^2+E(7)^5,E(7)^3+E(7)^4,E(7)^3+E(7)^4,E(7)^3+E(7)^4,
E(7)^3+E(7)^4,E(7)^3+E(7)^4,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0],
[GALOIS,[8,3]],
[GALOIS,[8,2]],[9,9,1,-7,5,-3,-E(7)+E(7)^6,E(7)+E(7)^6,E(7)+E(7)^6,
E(7)-E(7)^6,-E(7)-E(7)^6,-E(7)^2-E(7)^5,E(7)^2-E(7)^5,E(7)^2+E(7)^5,
E(7)^2+E(7)^5,-E(7)^2+E(7)^5,-E(7)^3-E(7)^4,E(7)^3-E(7)^4,E(7)^3+E(7)^4,
E(7)^3+E(7)^4,-E(7)^3+E(7)^4,-1,-1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,2]],
[GALOIS,[11,3]],
[GALOIS,[11,4]],
[GALOIS,[11,5]],
[GALOIS,[11,6]],[16,-16,0,0,0,0,0,2,-2,0,0,0,0,2,-2,0,0,0,2,-2,0,0,0,0,-4,4,0
,0,0,0,2,-2,1,-1,-1,1,-1,1],[36,36,-4,20,8,0,-1,1,1,-1,1,1,-1,1,1,-1,1,-1,1,1,
-1,-2,2,-4,4,4,0,0,0,0,0,0,0,0,0,0,0,0],[36,36,-4,20,8,0,-1,1,1,-1,1,1,-1,1,1,
-1,1,-1,1,1,-1,2,-2,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0],[63,63,7,-49,35,-21,0,0,0
,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],[72,72,-8,40
,16,0,-E(7)^2-E(7)^5,E(7)^2+E(7)^5,E(7)^2+E(7)^5,-E(7)^2-E(7)^5,E(7)^2+E(7)^5,
E(7)^3+E(7)^4,-E(7)^3-E(7)^4,E(7)^3+E(7)^4,E(7)^3+E(7)^4,-E(7)^3-E(7)^4,
E(7)+E(7)^6,-E(7)-E(7)^6,E(7)+E(7)^6,E(7)+E(7)^6,-E(7)-E(7)^6,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[21,3]],
[GALOIS,[21,2]],[84,84,-4,-28,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-4,4,4,0
,0,0,-1,3,3,0,0,0,0,0,0],[84,84,-4,-28,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,
4,-4,-4,0,0,0,-1,3,3,0,0,0,0,0,0],[112,-112,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,4,-4,0,0,0,0,-4,4,1,-1,-1,1,-1,1],[112,-112,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,4,-4,0,0,0,0,2,-2,E(9)^2+E(9)^4+E(9)^5+E(9)^7,
-E(9)^2-E(9)^4-E(9)^5-E(9)^7,E(9)^2+E(9)^7,-E(9)^2-E(9)^7,E(9)^4+E(9)^5,
-E(9)^4-E(9)^5],
[GALOIS,[27,2]],
[GALOIS,[27,4]],[126,126,6,14,-14,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,6,
-2,-2,-2,0,0,0,0,0,0,0,0,0],[126,126,6,14,-14,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,-2,-2,-2,6,-2,-2,0,0,0,0,0,0,0,0,0],[126,126,6,14,-14,-6,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,6,0,0,0,0,0,0,0,0,0],[126,126,6,14,-14,-6,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,6,-2,0,0,0,0,0,0,0,0,0],[128,-128,0
,0,0,0,0,2,-2,0,0,0,0,2,-2,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,-2,2,-1,1,1,-1,1,-1]
,[144,-144,0,0,0,0,0,2*E(7)^2+2*E(7)^5,-2*E(7)^2-2*E(7)^5,0,0,0,0,
2*E(7)^3+2*E(7)^4,-2*E(7)^3-2*E(7)^4,0,0,0,2*E(7)+2*E(7)^6,-2*E(7)-2*E(7)^6,0,
0,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[35,3]],
[GALOIS,[35,2]],[168,168,-8,-56,0,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,-3,-3,0,0,0,0,0,0]],
[(33,36,38)(34,35,37),(28,29),(27,28),( 7,10)(13,16)(18,21),
( 7,13,18,10,16,21)( 8,14,19)( 9,15,20)(11,12,17)]);
ARC("2^(1+8)+:L2(8)","tomfusion",rec(name:="2^(1+8)+:L2(8)",map:=[1,5,2,4,
37,36,194,40,196,194,873,873,194,40,196,194,873,194,40,196,194,186,178,3,
34,33,20,21,23,193,39,6,188,857,857,188,857,188],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^(1+8)+:L2(8)","3D4(2)",[1,2,3,2,6,7,24,11,24,24,33,34,25,12,25,25,
35,26,13,26,26,15,16,3,7,6,8,8,8,20,9,5,17,27,28,18,29,19],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^(2+4):(3xD10)",
[
"origin: Dixon's Algorithm"
],
[1920,640,32,30,30,60,20,15,15,60,20,15,15,6,24,16,16,6],
[,[1,1,2,5,4,10,10,13,12,6,6,9,8,4,1,3,3,5],[1,2,3,1,1,10,11,10,10,6,7,6,6,15,
15,17,16,15],,[1,2,3,5,4,1,2,5,4,1,2,5,4,18,15,16,17,14]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1],[1,1,1,E(3)^2,E(3),1,1,E(3)^2,E(3),1,1,E(3)^2,E(3),-E(3),-1,-1,-1,-E(3)^2]
,
[GALOIS,[3,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],[2,2,2,2,2,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)^3,0,0,0,0,0],
[GALOIS,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],
[TENSOR,[8,3]],
[TENSOR,[8,4]],[12,-4,0,0,0,-3,1,0,0,-3,1,0,0,0,0,-2*E(4),2*E(4),0],
[TENSOR,[13,2]],[15,15,-1,0,0,0,0,0,0,0,0,0,0,0,-3,1,1,0],
[TENSOR,[15,2]],[24,-8,0,0,0,-3*E(5)-3*E(5)^4,E(5)+E(5)^4,0,0,
-3*E(5)^2-3*E(5)^3,E(5)^2+E(5)^3,0,0,0,0,0,0,0],
[GALOIS,[17,2]]],
[(16,17),( 6,10)( 7,11)( 8,12)( 9,13),( 4, 5)( 8, 9)(12,13)(14,18)]);
ARC("2^(2+4):(3xD10)","tomfusion",rec(name:="2^(2+4):(3xD10)",map:=[1,2,7,
4,4,8,15,19,19,8,15,19,19,9,3,11,11,9],text:=[
"fusion map is unique"
]));
ALF("2^(2+4):(3xD10)","U3(4).2",[1,2,4,3,3,5,9,13,13,6,10,14,14,16,15,17,
18,16],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^(2+4):15",
[
"origin: Dixon's Algorithm"
],
[960,320,16,15,15,60,20,15,15,60,20,15,15,60,20,15,15,60,20,15,15],
[,[1,1,2,5,4,10,10,13,12,14,14,17,16,18,18,21,20,6,6,9,8],[1,2,3,1,1,18,19,18,
18,6,7,6,6,10,11,10,10,14,15,14,14],,[1,2,3,5,4,1,2,5,4,1,2,5,4,1,2,5,4,1,2,5,
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,E(5)^4,E(5)^4,E(5)^4,
E(5)^4,E(5)^3,E(5)^3,E(5)^3,E(5)^3,E(5),E(5),E(5),E(5),E(5)^2,E(5)^2,E(5)^2,
E(5)^2],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],[1,1,1,E(3)^2,E(3),1,1,E(3)^2,E(3),1,1,E(3)^2,E(3),1,1,E(3)^2,
E(3),1,1,E(3)^2,E(3)],
[TENSOR,[6,6]],
[TENSOR,[2,6]],
[TENSOR,[2,8]],
[TENSOR,[2,9]],
[TENSOR,[2,10]],
[TENSOR,[2,7]],
[TENSOR,[2,12]],
[TENSOR,[2,13]],
[TENSOR,[2,14]],[12,-4,0,0,0,-3,1,0,0,-3,1,0,0,-3,1,0,0,-3,1,0,0],
[TENSOR,[16,2]],
[TENSOR,[16,3]],
[TENSOR,[16,4]],
[TENSOR,[16,5]],[15,15,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 6,10,14,18)( 7,11,15,19)( 8,12,16,20)( 9,13,17,21),
( 4, 5)( 8, 9)(12,13)(16,17)(20,21)]);
ARC("2^(2+4):15","tomfusion",rec(name:="2^(2+4):15",map:=[1,2,5,3,3,6,8,
10,10,6,8,10,10,6,8,10,10,6,8,10,10],text:=[
"fusion map is unique"
]));
ALF("2^(2+4):15","U3(4)",[1,2,4,3,3,5,11,19,19,7,13,21,21,6,12,20,20,8,14,
22,22],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^(3+6):21",
[
"origin: Dixon's Algorithm"
],
[10752,1536,64,64,64,21,21,21,21,21,21,24,168,21,21,21,21,21,21,168,24,21,21,
21,21,21,21],
[,[1,1,2,2,2,8,9,10,11,6,7,20,20,24,25,26,27,22,23,13,13,16,17,18,19,14,15],[1
,2,3,4,5,7,8,9,10,11,6,2,1,7,8,9,10,11,6,1,2,7,8,9,10,11,6],,,,[1,2,3,4,5,1,1,
1,1,1,1,12,13,13,13,13,13,13,13,20,21,20,20,20,20,20,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,
1,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3),E(3),E(3),E(3),
E(3),E(3),E(3),E(3)],
[TENSOR,[2,2]],[1,1,1,1,1,E(7)^6,E(7)^4,E(7)^5,E(7),E(7)^3,E(7)^2,1,1,E(7)^6,
E(7)^4,E(7)^5,E(7),E(7)^3,E(7)^2,1,1,E(7)^6,E(7)^4,E(7)^5,E(7),E(7)^3,E(7)^2],
[TENSOR,[4,4]],
[TENSOR,[4,5]],
[TENSOR,[4,6]],
[TENSOR,[4,7]],
[TENSOR,[4,8]],
[TENSOR,[2,4]],
[TENSOR,[2,10]],
[TENSOR,[2,5]],
[TENSOR,[2,12]],
[TENSOR,[2,6]],
[TENSOR,[2,14]],
[TENSOR,[2,7]],
[TENSOR,[2,16]],
[TENSOR,[2,8]],
[TENSOR,[2,18]],
[TENSOR,[2,9]],
[TENSOR,[2,20]],[21,21,5,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
21,21,-3,-3,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[21,21,-3,5,-3,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[56,-8,0,0,0,0,0,0,0,0,0,1,-7,0,0,0,0
,0,0,-7,1,0,0,0,0,0,0],
[TENSOR,[25,2]],
[TENSOR,[25,3]]],
[(4,5),(3,4),(12,21)(13,20)(14,22)(15,23)(16,24)(17,25)(18,26)(19,27),
( 6, 7, 8, 9,10,11)(14,15,16,17,18,19)(22,23,24,25,26,27)]);
ARC("2^(3+6):21","tomfusion",rec(name:="2^(3+6):21",map:=[1,2,5,6,7,9,9,9,
9,9,9,8,3,48,48,48,48,48,48,3,8,48,48,48,48,48,48],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^(3+6):21","U3(8)",[1,2,6,7,8,11,13,12,11,13,12,9,3,23,27,25,23,27,
25,4,10,24,28,26,24,28,26],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^2.(3^2:2A4)",
[
"origin: Dixon's Algorithm"
],
[864,108,32,288,36,96,16,16,16,16,9,18,6,9,18,6],
[,[1,2,1,1,2,1,3,3,3,3,14,15,15,11,12,12],[1,1,3,4,4,6,9,10,7,8,1,1,6,1,1,6]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,E(3)^2,E(3)^2,E(3)^2,
E(3),E(3),E(3)],
[TENSOR,[2,2]],[2,2,-2,2,2,-2,0,0,0,0,-1,-1,1,-1,-1,1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[3,3,3,3,3,3,-1,-1,-1,-1,0,0,0,0,0,0],[3,3,-1,-1,-1,3,
-1+2*E(4),1,-1-2*E(4),1,0,0,0,0,0,0],
[GALOIS,[8,3]],[3,3,-1,-1,-1,3,1,-1-2*E(4),1,-1+2*E(4),0,0,0,0,0,0],
[GALOIS,[10,3]],[6,6,2,-2,-2,-6,0,0,0,0,0,0,0,0,0,0],[8,-1,0,8,-1,0,0,0,0,0,
-1,2,0,-1,2,0],
[TENSOR,[13,3]],
[TENSOR,[13,2]],[24,-3,0,-8,1,0,0,0,0,0,0,0,0,0,0,0]],
[(11,14)(12,15)(13,16),( 8,10),( 7, 8)( 9,10)]);
ARC("2^2.(3^2:2A4)","tomfusion",rec(name:="2^2.(3^2:2A4)",map:=[1,5,4,2,
14,3,12,11,12,11,7,6,16,7,6,16],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^2.(3^2:2A4)","2^2.L3(4).3",[1,5,4,2,6,3,7,8,7,8,19,17,21,20,18,22],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^2.(3^2:Q8)",
[
"origin: Dixon's Algorithm"
],
[288,32,36,32,36,288,16,16,32,36,32,36,16,16,16,16,16,16,16,16,16,16,288,288],
[,[1,1,3,1,3,1,2,2,1,3,1,3,11,11,9,9,11,11,9,9,2,2,1,1],[1,2,1,4,6,6,8,7,9,24,
11,23,17,18,19,20,13,14,15,16,22,21,23,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,1,1,1,1,
-1,-1,1,1,-1,-1,1,1,-1,-1,1,1],[1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,
-1,-1,1,1],
[TENSOR,[2,3]],[1,-1,1,1,-1,-1,-E(4),E(4),-1,1,1,-1,-1,1,E(4),-E(4),-1,1,
-E(4),E(4),E(4),-E(4),-1,1],
[TENSOR,[3,5]],
[TENSOR,[2,6]],
[TENSOR,[2,5]],[1,-1,1,1,-1,-1,-E(4),E(4),1,-1,-1,1,-E(4),E(4),-1,1,E(4),
-E(4),-1,1,-E(4),E(4),1,-1],
[TENSOR,[2,9]],
[TENSOR,[3,10]],
[TENSOR,[2,11]],
[TENSOR,[5,11]],
[TENSOR,[5,9]],
[TENSOR,[2,14]],
[TENSOR,[2,13]],[2,-2,2,-2,2,2,0,0,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,2,2],
[TENSOR,[17,13]],
[TENSOR,[17,9]],
[TENSOR,[17,5]],[8,0,-1,0,-1,8,0,0,0,-1,0,-1,0,0,0,0,0,0,0,0,0,0,8,8],
[TENSOR,[21,13]],
[TENSOR,[21,5]],
[TENSOR,[21,9]]],
[(13,14)(15,16)(17,18)(19,20),(13,17)(14,18)(15,20)(16,19),
( 9,11)(10,12)(13,15,14,16)(17,19,18,20)(21,22)(23,24),
( 7, 8)(15,16)(19,20)(21,22),( 7,21)( 8,22)(15,19)(16,20),
( 2, 9)( 5,12)( 6,23)( 7,15,22,20)( 8,19,21,16)(14,18)]);
ARC("2^2.(3^2:Q8)","tomfusion",rec(name:="2^2.(3^2:Q8)",map:=[1,5,9,3,25,
8,12,12,6,26,7,24,22,13,21,20,22,13,21,20,14,14,2,4],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^2.(3^2:Q8)","2^2.L3(4)",[1,6,9,5,10,2,13,13,7,12,8,11,17,18,15,16,
17,18,15,16,14,14,3,4],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^2.(3^2:Q8.2)",
[
"origin: Dixon's Algorithm"
],
[576,72,64,64,72,576,32,32,16,16,16,16,288,36,32,16,24,12,12,24,16,16,16,16],
[,[1,2,1,1,2,1,3,3,7,7,8,8,1,2,1,3,1,2,5,6,15,15,15,15],[1,1,3,4,6,6,8,7,12,11
,10,9,13,13,15,16,17,17,20,20,24,23,22,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,
-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1],
[TENSOR,[2,3]],[1,1,1,1,1,1,-1,-1,-E(4),-E(4),E(4),E(4),-1,-1,-1,1,-1,-1,1,1,
E(4),E(4),-E(4),-E(4)],
[TENSOR,[3,5]],
[TENSOR,[2,6]],
[TENSOR,[2,5]],[2,2,2,2,2,2,2,2,0,0,0,0,-2,-2,-2,-2,0,0,0,0,0,0,0,0],
[TENSOR,[9,5]],[2,2,-2,-2,2,2,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,2,2,-2,0,0,0,0,0,0,0,0,0],
[TENSOR,[11,2]],
[TENSOR,[11,5]],
[TENSOR,[11,6]],[2,2,-2,2,-2,-2,-2*E(4),2*E(4),0,0,0,0,0,0,0,0,0,0,0,0,
-1+E(4),1-E(4),1+E(4),-1-E(4)],
[TENSOR,[15,5]],
[TENSOR,[15,3]],
[TENSOR,[15,6]],[4,4,4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,-1,0,
0,-1,8,0,0,0,0,0,0,-8,1,0,0,-2,1,-1,2,0,0,0,0],
[TENSOR,[20,2]],
[TENSOR,[20,7]],
[TENSOR,[20,5]],[16,-2,0,0,2,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(21,22)(23,24),( 9,10)(11,12),( 7, 8)( 9,11)(10,12)(21,23)(22,24)]);
ARC("2^2.(3^2:Q8.2)","tomfusion",rec(name:="2^2.(3^2:Q8.2)",map:=[1,8,4,5,
22,2,14,14,41,41,41,41,3,23,6,16,7,27,50,12,20,19,19,20],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^2.(3^2:Q8.2)","2^2.L3(4).2_2",[1,7,5,4,8,2,11,11,30,30,31,31,3,9,6,
10,24,28,29,25,12,13,13,12],[
"fusion map is unique up to table automorphisms"
]);

MOT("7:3xS4",
0,
0,
0,
0,
[(6,11)(7,12)(8,13)(9,14)(10,15),(16,21)(17,22)(18,23)(19,24)(20,25)],
["ConstructDirectProduct",[["7:3"],["s4"]]]);
ARC("7:3xS4","tomfusion",rec(name:="2^2.(7:3xS3)",map:=[1,2,4,3,8,13,21,
25,22,31,13,21,25,22,31,5,11,6,12,19,5,11,6,12,19],text:=[
"fusion map is unique"
]));
ALF("7:3xS4","2^2.psl(3,4).s3",[1,2,16,22,23,11,12,21,30,31,13,14,20,32,
33,5,6,16,26,27,5,6,16,26,27],[
"fusion map is unique up to table automorphisms"
]);

MOT("D8xL3(2)",
0,
0,
0,
0,
[(19,25)(20,26)(21,27)(22,28)(23,29)(24,30),(5,6)(11,12)(17,18)(23,24)(29,
30)],
["ConstructDirectProduct",[["Dihedral",8],["L3(2)"]]]);
ARC("D8xL3(2)","tomfusion",rec(name:="2^2.(L2(7)x2)",map:=[1,6,9,17,45,45,
12,16,104,33,180,180,2,5,38,18,110,110,3,8,41,32,112,112,4,7,44,30,111,
111],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("D8xL3(2)","He",[1,3,4,7,12,13,6,6,19,6,32,33,2,2,10,7,21,22,2,2,10,7,
21,22,2,3,10,8,21,22],[
"fusion map is unique up to table automorphisms"
]);
ALF("D8xL3(2)","2^2.L3(4).2_2",[1,5,7,10,18,21,25,25,29,27,33,35,2,4,8,10,
19,22,3,6,9,11,20,23,24,24,28,26,32,34],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^2.[2^6].(S3xS3)",
[
"origin: Dixon's Algorithm"
],
[9216,4608,9216,128,128,768,768,256,256,1536,1536,72,36,72,24,24,144,144,144,
144,48,48,288,144,288,12,12,384,384,32,128,128,64,64,128,64,128,32,32,64,64,32
,32,16,32,32,192,192,192,192,24,24,24,24],
[,[1,1,1,1,2,2,2,1,3,3,3,12,12,12,19,19,17,17,17,17,25,25,23,23,23,12,14,1,3,9
,3,1,9,9,8,8,8,1,10,9,9,5,5,7,9,8,3,1,10,10,21,21,23,25],[1,2,3,4,5,6,7,8,9,10
,11,1,2,3,7,6,1,2,2,3,10,11,1,2,3,28,29,28,29,30,31,32,33,34,35,36,37,38,39,40
,41,42,43,44,45,46,47,48,49,50,50,49,48,47]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1
,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,1,
1,-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],
[TENSOR,[5,2]],[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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,1,1,1,1],
[TENSOR,[7,3]],[3,3,3,-1,-1,3,3,-1,3,-1,-1,0,0,0,0,0,0,0,0,0,-1,-1,3,3,3,0,0,
-3,-3,1,1,1,-3,1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,1,1,1,1,-1,-1],
[TENSOR,[9,4]],
[TENSOR,[9,3]],
[TENSOR,[9,2]],[4,4,4,4,4,4,4,4,4,4,4,-2,-2,-2,1,1,1,1,1,1,-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],[4,-4,4,0,0,0,0,0,0,4,
-4,1,-1,1,0,0,-2,2,2,-2,1,-1,1,-1,1,1,-1,-2,2,0,-2,2,0,0,-2,2,-2,0,0,-2,2,0,0,
0,0,0,2,-2,-2,2,-1,1,1,-1],
[TENSOR,[14,4]],
[TENSOR,[14,2]],
[TENSOR,[14,3]],[6,6,6,-2,-2,6,6,-2,6,-2,-2,0,0,0,0,0,0,0,0,0,1,1,-3,-3,-3,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,-2,2,2,-1,-1,1,1],
[TENSOR,[18,3]],[6,6,6,-2,2,2,2,-2,-2,6,6,0,0,0,-1,-1,3,3,3,3,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,-2,-2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[20,2]],[8,-8,8,0,0,0,0,0,0,8,-8,2,-2,2,0,0,2,-2,-2,2,-1,1,-1,1,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,-4,4,1,-1,-1,1],
[TENSOR,[22,3]],[8,-8,8,0,0,0,0,0,0,8,-8,-1,1,-1,0,0,2,-2,-2,2,2,-2,2,-2,2,-1
,1,-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],
[TENSOR,[24,2]],[8,0,-8,0,0,-4,4,0,0,0,0,2,0,-2,1,-1,-1,-3,3,1,0,0,-4,0,4,0,0
,0,0,0,0,0,0,0,-4,0,4,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[26,2]],[9,9,9,1,-3,-3,-3,1,1,9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,
-3,1,-3,-3,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,3,3,3,3,0,0,0,0],
[TENSOR,[28,4]],
[TENSOR,[28,3]],
[TENSOR,[28,2]],[9,9,9,-3,1,-3,-3,5,1,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-3,-3,1,1,1,1,-3,-1,-1,-1,1,-1,1,1,1,1,-1,1,-1,-3,-3,3,3,0,0,0,0],
[TENSOR,[32,4]],
[TENSOR,[32,2]],
[TENSOR,[32,3]],[12,-12,12,0,0,0,0,0,0,-4,4,0,0,0,0,0,0,0,0,0,-1,1,3,-3,3,0,0
,-6,6,0,2,-2,0,0,-2,2,-2,0,0,2,-2,0,0,0,0,0,-2,2,-2,2,-1,1,-1,1],
[TENSOR,[36,4]],
[TENSOR,[36,3]],
[TENSOR,[36,2]],[12,12,12,-4,4,4,4,-4,-4,12,12,0,0,0,1,1,-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],[16,-16,16,0,0,0,
0,0,0,16,-16,-2,2,-2,0,0,-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],[16,0,-16,0,0,-8,8,0,0,0,0,-2,0,2,-1,1,-5,-3,3,5,
0,0,4,0,-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],[16,0,
-16,0,0,-8,8,0,0,0,0,-2,0,2,2,-2,4,0,0,-4,0,0,4,0,-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],[16,0,-16,0,0,-8,8,0,0,0,0,-2,0,2,-1,1,1,3,
-3,-1,0,0,-8,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
16,0,-16,0,0,-8,8,0,0,0,0,4,0,-4,-1,1,1,3,-3,-1,0,0,4,0,-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],[18,18,18,2,-2,6,6,2,-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,-2,-2,-2,-2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,
0,0],
[TENSOR,[46,2]],[18,18,18,2,2,-6,-6,-6,2,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-6,-6,-2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[48,2]],[24,-24,24,0,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,1,-1,-3,3,-3,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,4,-4,4,1,-1,1,-1],
[TENSOR,[50,3]],[24,0,-24,0,0,4,-4,0,0,0,0,0,0,0,-1,1,3,-3,3,-3,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,-4,0,4,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[52,2]],[48,0,-48,0,0,8,-8,0,0,0,0,0,0,0,1,-1,-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]],
[(35,37)(42,43)]);
ARC("2^2.[2^6].(S3xS3)","tomfusion",rec(name:="2^2.[2^6].(S3xS3)",map:=[1,
3,2,8,24,17,16,5,20,15,14,12,58,56,236,239,11,54,55,51,227,226,10,53,50,
66,244,4,19,155,26,7,118,138,25,33,30,9,143,120,112,169,162,195,141,40,23,
6,78,80,649,647,61,233],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^2.[2^6].(S3xS3)","2.[2^6]:(S3xS3)",[1,2,1,8,7,9,9,5,6,4,3,10,11,10,
22,22,24,23,23,24,20,21,18,19,18,37,36,30,29,34,32,33,35,31,38,39,38,42,
40,43,44,45,45,41,15,14,12,13,16,17,28,27,25,26]);
ALF("2^2.[2^6].(S3xS3)","2.S6(2)",[1,4,2,6,17,14,13,4,5,5,3,11,27,12,40,
41,9,24,23,10,25,21,7,22,8,28,26,6,3,18,5,6,16,15,13,17,14,6,18,15,16,32,
33,31,18,17,5,4,16,15,38,39,22,25],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^2.S6",
[
"origin: Dixon's Algorithm"
],
[2880,2880,1440,96,96,96,96,16,32,32,64,64,32,12,12,72,72,36,12,12,72,72,36,16
,16,20,20,20,20],
[,[1,1,1,2,1,1,2,11,11,11,1,1,1,21,22,16,16,16,17,16,21,21,21,12,11,26,26,26,
26],[1,2,3,4,5,6,7,8,9,10,11,12,13,6,7,1,2,3,4,5,1,2,3,24,25,26,27,29,28],,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,1,2,3,3]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,-1,1,1,-1
,-1,1,1,1,1,-1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1],[1,1,-1,1,-1,-1,1,-1,1,
1,1,1,-1,-1,1,1,1,-1,1,-1,1,1,-1,1,-1,1,1,-1,-1],
[TENSOR,[2,3]],[2,-2,0,0,0,0,0,0,2,-2,2,-2,0,0,0,2,-2,0,0,0,2,-2,0,0,0,2,-2,0
,0],[5,5,5,-3,-3,1,1,-1,-1,-1,1,1,1,1,1,2,2,2,0,0,-1,-1,-1,-1,-1,0,0,0,0],
[TENSOR,[6,4]],
[TENSOR,[6,2]],
[TENSOR,[6,3]],[5,5,-5,-1,1,-3,3,1,-1,-1,1,1,-1,0,0,-1,-1,1,-1,1,2,2,-2,1,-1,
0,0,0,0],
[TENSOR,[10,4]],
[TENSOR,[10,3]],
[TENSOR,[10,2]],[9,9,9,3,3,3,3,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1
,-1],
[TENSOR,[14,4]],
[TENSOR,[14,2]],
[TENSOR,[14,3]],[10,10,-10,-2,2,-2,2,0,0,0,-2,-2,2,1,-1,1,1,-1,1,-1,1,1,-1,0,
0,0,0,0,0],
[TENSOR,[18,4]],
[TENSOR,[18,3]],
[TENSOR,[18,2]],[10,-10,0,0,0,0,0,0,-2,2,2,-2,0,0,0,4,-4,0,0,0,-2,2,0,0,0,0,0
,0,0],[10,-10,0,0,0,0,0,0,-2,2,2,-2,0,0,0,-2,2,0,0,0,4,-4,0,0,0,0,0,0,0],[16,
16,16,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,0,0,-2,-2,-2,0,0,1,1,1,1],
[TENSOR,[24,2]],[16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,-2,2,0,0,0,1,-1,
-E(5)+E(5)^2+E(5)^3-E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4],
[TENSOR,[26,2]],[18,-18,0,0,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,
0,0],[20,-20,0,0,0,0,0,0,0,0,-4,4,0,0,0,2,-2,0,0,0,2,-2,0,0,0,0,0,0,0]],
[(28,29),( 4, 7)( 5, 6)(14,20)(15,19)(16,21)(17,22)(18,23)]);
ARC("2^2.S6","tomfusion",rec(name:="2^2.S6",map:=[1,2,3,15,4,5,16,35,23,
19,7,6,8,52,122,9,40,43,124,50,10,41,45,34,37,39,107,109,109],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^2.S6","2^2.L3(4).2_2",[1,2,3,25,24,24,25,11,10,10,5,4,6,28,29,7,8,
9,29,28,7,8,9,27,26,14,15,16,17],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^3.L3(2):2",
[
"origin: Dixon's Algorithm"
],
[2688,336,384,32,16,32,12,12,12,12,8,8,14,14,14,14],
[,[1,1,1,3,3,1,7,7,7,7,4,6,13,13,15,15],[1,2,3,4,5,6,1,3,2,2,11,12,15,16,13,14
],,,,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,1,2]],
[[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],[3
,-3,3,-1,1,-1,0,0,0,0,1,-1,E(7)^3+E(7)^5+E(7)^6,-E(7)^3-E(7)^5-E(7)^6,
E(7)+E(7)^2+E(7)^4,-E(7)-E(7)^2-E(7)^4],
[GALOIS,[3,3]],
[TENSOR,[3,2]],
[TENSOR,[4,2]],[6,6,6,2,2,2,0,0,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[7,2]],[7,7,7,-1,-1,-1,1,1,1,1,-1,-1,0,0,0,0],
[TENSOR,[9,2]],[8,8,8,0,0,0,-1,-1,-1,-1,0,0,1,1,1,1],
[TENSOR,[11,2]],[14,0,-2,2,0,-2,2,-2,0,0,0,0,0,0,0,0],[14,0,-2,2,0,-2,-1,1,
-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0],
[TENSOR,[14,2]],[42,0,-6,-2,0,2,0,0,0,0,0,0,0,0,0,0]],
[( 9,10),(13,15)(14,16)]);
ARC("2^3.L3(2):2","tomfusion",rec(name:="2^3.L3(2):2",map:=[1,3,2,9,12,4,
5,14,15,15,31,13,17,38,17,38],text:=[
"fusion map is unique"
]));
ALF("2^3.L3(2):2","G2(3).2",[1,18,2,7,19,2,6,10,21,22,12,19,11,25,11,25],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^6:(3xA5)",
[
"origin: Dixon's Algorithm"
],
[11520,256,3840,768,180,180,192,32,32,64,12,12,15,60,20,15,15,15,60,20,36,12,
36,12,36,12],
[,[1,1,1,1,6,5,1,2,2,1,6,5,17,19,19,18,13,16,14,14,25,25,23,23,21,21],[1,2,3,4
,1,1,7,8,9,10,7,7,19,19,20,19,14,14,14,15,1,4,1,3,1,4],,[1,2,3,4,6,5,7,8,9,10,
12,11,5,1,3,6,6,5,1,3,25,26,23,24,21,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,E(3)^2,E(3),1,
1,1,1,E(3)^2,E(3),E(3),1,1,E(3)^2,E(3)^2,E(3),1,1,E(3),E(3),1,1,E(3)^2,E(3)^2]
,
[TENSOR,[2,2]],[3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-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)^3,0,0,0,0,0,0],
[GALOIS,[4,2]],
[TENSOR,[4,2]],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[4,3]],[4,4,4,4,4,4,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1],
[TENSOR,[10,2]],
[TENSOR,[10,3]],[5,5,5,5,5,5,1,1,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1],
[TENSOR,[13,2]],
[TENSOR,[13,3]],[15,-1,15,-1,0,0,3,-1,-1,3,0,0,0,0,0,0,0,0,0,0,3,-1,0,0,3,-1]
,
[TENSOR,[16,3]],
[TENSOR,[16,2]],[18,2,-6,-6,0,0,6,2,-2,-2,0,0,0,3,-1,0,0,0,3,-1,0,0,0,0,0,0],
[18,2,-6,-6,0,0,-6,-2,2,2,0,0,0,3,-1,0,0,0,3,-1,0,0,0,0,0,0],[30,-2,-10,6,0,0,
-6,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,3,-1,0,0],[30,-2,-10,6,0,0,6,-2,2,-2,0,0,0,0
,0,0,0,0,0,0,0,0,3,-1,0,0],[36,4,-12,-12,0,0,0,0,0,0,0,0,0,3*E(5)^2+3*E(5)^3,
-E(5)^2-E(5)^3,0,0,0,3*E(5)+3*E(5)^4,-E(5)-E(5)^4,0,0,0,0,0,0],
[GALOIS,[23,2]],[45,-3,45,-3,0,0,-3,1,1,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
60,-4,-20,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,1,0,0]],
[( 5, 6)(11,12)(13,16)(17,18)(21,25)(22,26),
( 5, 6)(11,12)(13,17)(14,19)(15,20)(16,18)(21,25)(22,26)]);
ARC("2^6:(3xA5)","tomfusion",rec(name:="2^6:(3xA5)",map:=[1,4,2,3,7,7,5,
41,29,6,51,51,176,46,156,176,176,176,46,156,9,50,8,49,9,50],text:=[
"fusion map is unique"
]));
ALF("2^6:(3xA5)","S4(4)",[1,4,2,3,5,5,2,7,8,4,14,14,20,9,16,20,21,21,10,
17,6,15,5,14,6,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^6:(3xA5)","2^2.L3(4).3",[1,4,2,3,17,18,3,8,7,4,21,22,24,9,10,23,25,
26,11,12,18,22,5,6,17,21],[
"fusion map is unique up to table automorphisms"
]);
#T 2nd fusion?

MOT("S4(4)M2",
[
"2nd maximal subgroup of S4(4)"
],
0,
0,
0,
0,
["ConstructPermuted",["2^6:(3xA5)"]]);
ALF("S4(4)M2","S4(4)",[1,4,3,2,6,6,3,7,8,4,15,15,22,11,18,22,23,23,12,19,
5,14,6,15,5,14],[
"fusion 2^6:(3xA5) -> S4(4) mapped under S4(4).4"
]);

MOT("2^6:(3xA5):2",
[
"origin: Dixon's Algorithm"
],
[23040,512,1536,7680,180,16,16,16,16,384,64,64,128,12,60,20,15,15,96,32,32,96,
72,24,36,12,12,12],
[,[1,1,1,1,5,10,11,11,13,1,2,2,1,5,15,15,17,18,1,2,3,4,23,23,25,25,23,24],[1,2
,3,4,1,6,8,7,9,10,11,12,13,10,15,16,15,15,19,20,21,22,1,4,1,3,19,22],,[1,2,3,4
,5,6,7,8,9,10,11,12,13,14,1,4,5,5,19,20,21,22,23,24,25,26,27,28]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,-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,-1,0,0,0,0,2,2,2,2,
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-2,-2,-2,-2,1,1,1,1,1,1],
[TENSOR,[4,2]],[5,5,5,5,5,-1,-1,-1,-1,1,1,1,1,1,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1
,1],
[TENSOR,[6,2]],[6,6,6,6,6,0,0,0,0,-2,-2,-2,-2,-2,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
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-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[9,7]],[8,8,8,8,-4,0,0,0,0,0,0,0,0,0,-2,-2,1,1,0,0,0,0,2,2,-1,-1,0,0]
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[TENSOR,[13,2]],[18,2,-6,-6,0,-2,0,0,2,6,2,-2,-2,0,3,-1,0,0,0,0,0,0,0,0,0,0,0
,0],
[TENSOR,[15,2]],[18,2,-6,-6,0,0,-2*E(4),2*E(4),0,-6,-2,2,2,0,3,-1,0,0,0,0,0,0
,0,0,0,0,0,0],
[TENSOR,[17,2]],[30,-2,6,-10,0,0,0,0,0,-6,2,-2,2,0,0,0,0,0,-2,2,-2,2,3,-1,0,0
,1,-1],
[TENSOR,[19,2]],[30,-2,6,-10,0,0,0,0,0,6,-2,2,-2,0,0,0,0,0,-4,0,0,4,3,-1,0,0,
-1,1],
[TENSOR,[21,2]],[30,-2,-2,30,0,0,0,0,0,6,-2,-2,6,0,0,0,0,0,0,0,0,0,0,0,-3,1,0
,0],[45,-3,-3,45,0,-1,1,1,-1,-3,1,1,-3,0,0,0,0,0,3,-1,-1,3,0,0,0,0,0,0],
[TENSOR,[24,2]],[60,-4,12,-20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,2,-3,1,0,0,
1,-1],
[TENSOR,[26,2]],[72,8,-24,-24,0,0,0,0,0,0,0,0,0,0,-3,1,0,0,0,0,0,0,0,0,0,0,0,
0]],
[(7,8),(17,18)]);
ARC("2^6:(3xA5):2","tomfusion",rec(name:="2^6:(3xA5):2",map:=[1,4,3,2,8,
51,175,175,48,5,32,29,6,57,52,185,216,216,7,41,44,27,9,55,10,59,58,205],
text:=[
"fusion map is unique"
]));
ALF("2^6:(3xA5):2","S4(4).2",[1,4,3,2,5,21,26,27,23,2,7,8,4,12,9,14,16,16,
20,23,22,21,5,12,6,13,24,29],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^6:(3xA5):2","2^2.psl(3,4).s3",[1,4,3,2,15,24,28,29,25,3,8,7,4,17,9,
10,18,19,22,25,24,23,5,6,15,17,26,27],[
"fusion map is unique up to table automorphisms"
]);

MOT("S4(4).2M3",
[
"3rd maximal subgroup of S4(4).2"
],
0,
0,
0,
0,
["ConstructPermuted",["2^6:(3xA5):2"]]);
ALF("S4(4).2M3","S4(4).2",[1,4,2,3,6,22,26,27,23,3,7,8,4,13,10,15,17,17,20,
23,21,22,6,13,5,12,25,30],[
"fusion 2^6:(3xA5):2 -> S4(4).2 mapped under S4(4).4"
]);

MOT("2^6:(7xL2(8))",
[
"origin: Dixon's Algorithm,\n",
"constructions: AGL(2,8)"
],
[225792,3584,3528,3528,3528,3528,3528,3528,392,56,49,49,49,392,56,49,49,392,56
,49,392,56,49,49,49,49,49,49,49,56,392,49,56,392,49,56,56,56,56,448,64,56,56,
63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,
63,63],
[,[1,1,5,6,7,8,3,4,34,34,32,29,28,31,31,35,27,9,9,13,14,14,16,17,11,12,24,20,
26,21,21,25,18,18,23,5,7,3,6,1,2,4,8,44,47,48,49,50,45,46,70,69,67,66,68,71,65
,57,51,56,54,53,55,52,58,61,62,63,64,59,60],[1,2,4,5,6,7,8,3,21,22,24,26,23,18
,19,20,25,31,30,35,34,33,28,32,27,29,11,16,12,10,9,17,15,14,13,39,43,42,37,40,
41,36,38,1,4,5,6,7,8,3,48,47,45,50,46,49,44,44,46,47,48,49,50,45,44,46,47,48,
49,50,45],,,,[1,2,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,2,1,1,2,1,1,1,1,1,1,1,2,1,1,
2,1,1,40,40,40,40,40,41,40,40,44,44,44,44,44,44,44,65,65,65,65,65,65,65,57,57,
57,57,57,57,57,58,58,58,58,58,58,58]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,E(7)^6
,E(7)^4,E(7)^5,E(7),E(7)^3,E(7)^2,E(7)^3,E(7)^3,E(7)^2,1,E(7),E(7)^4,E(7)^4,
E(7)^6,E(7)^5,E(7)^5,E(7)^5,E(7)^4,E(7)^2,E(7)^2,E(7)^3,E(7)^6,E(7),1,E(7)^3,
E(7)^2,1,E(7),E(7),E(7)^4,E(7)^6,E(7)^6,E(7)^5,E(7)^6,E(7)^5,E(7)^3,E(7)^4,1,1
,E(7)^2,E(7),1,E(7)^6,E(7)^4,E(7)^5,E(7),E(7)^3,E(7)^2,E(7)^5,E(7)^4,E(7)^2,
E(7)^3,E(7)^6,E(7),1,1,E(7)^6,E(7)^4,E(7)^5,E(7),E(7)^3,E(7)^2,1,E(7)^6,E(7)^4
,E(7)^5,E(7),E(7)^3,E(7)^2],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[7,7,7,7,7,7,7,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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[TENSOR,[8,7]],
[TENSOR,[8,2]],
[TENSOR,[8,3]],
[TENSOR,[8,4]],
[TENSOR,[8,5]],
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E(63)^10+E(63)^17+E(63)^31+E(63)^59,E(63)+E(63)^8+E(63)^22+E(63)^50,
E(63)^23+E(63)^37+E(63)^44+E(63)^58,E(63)^5+E(63)^19+E(63)^26+E(63)^40,
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-E(63)^4-E(63)^32,-E(63)^5-E(63)^40,-E(63)^22-E(63)^50,-E(63)^31-E(63)^59],
[GALOIS,[15,29]],
[GALOIS,[15,22]],
[TENSOR,[15,3]],
[TENSOR,[16,3]],
[TENSOR,[17,3]],
[TENSOR,[15,4]],
[TENSOR,[16,4]],
[TENSOR,[17,4]],
[TENSOR,[15,5]],
[TENSOR,[16,5]],
[TENSOR,[17,5]],
[TENSOR,[15,6]],
[TENSOR,[16,6]],
[TENSOR,[17,6]],
[TENSOR,[15,7]],
[TENSOR,[16,7]],
[TENSOR,[17,7]],
[TENSOR,[15,2]],
[TENSOR,[16,2]],
[TENSOR,[17,2]],[8,8,8,8,8,8,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[TENSOR,[36,7]],
[TENSOR,[36,2]],
[TENSOR,[36,3]],
[TENSOR,[36,4]],
[TENSOR,[36,5]],
[TENSOR,[36,6]],[9,9,9*E(7),9*E(7)^3,9*E(7)^2,9*E(7)^6,9*E(7)^4,9*E(7)^5,
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-E(7)-E(7)^2-E(7)^3-E(7)^4-E(7)^5,E(7)^4+E(7)^5,E(7)^5+E(7)^6,
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E(7)+E(7)^5,-E(7)-E(7)^2-E(7)^4-E(7)^5-E(7)^6,
-E(7)-E(7)^2-E(7)^4-E(7)^5-E(7)^6,E(7)^2+E(7)^6,E(7)^3+E(7)^6,E(7)+E(7)^4,
E(7)^2+E(7)^5,E(7)^3+E(7)^5,E(7)^4+E(7)^6,E(7)+E(7)^6,
-E(7)-E(7)^2-E(7)^3-E(7)^4-E(7)^6,-E(7)-E(7)^2-E(7)^3-E(7)^4-E(7)^6,
E(7)^2+E(7)^4,-E(7)-E(7)^3-E(7)^4-E(7)^5-E(7)^6,
-E(7)-E(7)^3-E(7)^4-E(7)^5-E(7)^6,E(7)+E(7)^3,E(7),E(7)^2,E(7)^4,E(7)^3,1,1,
E(7)^5,E(7)^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],
[TENSOR,[43,3]],
[GALOIS,[43,5]],
[GALOIS,[43,4]],
[TENSOR,[46,2]],
[TENSOR,[45,4]],
[TENSOR,[45,5]],
[TENSOR,[45,7]],
[TENSOR,[46,7]],
[TENSOR,[43,5]],
[TENSOR,[43,6]],
[TENSOR,[46,3]],
[TENSOR,[46,4]],
[TENSOR,[46,6]],
[TENSOR,[43,4]],
[TENSOR,[45,2]],
[TENSOR,[45,3]],
[TENSOR,[43,7]],
[TENSOR,[46,5]],
[TENSOR,[43,2]],
[TENSOR,[45,6]],[63,-1,0,0,0,0,0,0,7,-1,0,0,0,7,-1,0,0,7,-1,0,7,-1,0,0,0,0,0,
0,0,-1,7,0,-1,7,0,0,0,0,0,7,-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],
[TENSOR,[64,6]],
[TENSOR,[64,3]],
[TENSOR,[64,5]],
[TENSOR,[64,7]],
[TENSOR,[64,2]],
[TENSOR,[64,4]],[441,-7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,-7,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0]],
[(51,61,68)(52,60,67)(53,64,71)(54,63,70)(55,59,66)(56,62,69)(57,58,65),
( 3, 4, 5, 6, 7, 8)( 9,21,34,14,18,31)(10,22,33,15,19,30)(11,24,32,17,25,27)
(12,26,29)(13,23,28,16,20,35)(36,39,37,43,38,42)(45,46,47,48,49,50)
(51,56,54,53,55,52)(59,60,61,62,63,64)(66,67,68,69,70,71)
]);
ARC("2^6:(7xL2(8))","tomfusion",rec(name:="2^6:(7xL2(8))",map:=[1,2,12,12,
12,12,12,12,13,35,15,14,16,13,35,16,15,13,35,16,13,35,16,15,15,14,15,16,
14,35,13,15,35,13,16,34,34,34,34,3,9,34,34,4,57,57,57,57,57,57,103,103,
103,103,103,103,31,31,103,103,103,103,103,103,31,103,103,103,103,103,103],
text:=[
"fusion map determined by the groups"
]));
ALF("2^6:(7xL2(8))","L3(8)",[1,2,5,10,7,6,9,8,6,20,14,13,12,5,19,11,14,10,
24,12,9,23,11,13,13,15,15,12,14,21,7,15,22,8,11,19,21,23,24,2,4,22,20,3,
25,30,27,26,29,28,33,44,34,43,41,42,17,16,31,40,47,32,39,48,18,45,36,37,
46,35,38],[
"fusion map is unique up to table automorphisms"
]);
ALN("2^6:(7xL2(8))",["AGL(2,8)"]);

MOT("2^6:3^3:S4",
[
"origin: Dixon's Algorithm"
],
[41472,4608,1536,1536,1728,288,192,216,72,162,162,384,192,384,128,64,128,48,24
,48,9,9,12,36,16,16,16,16,72,24,18,18,192,64,576,192,48,144,48,144],
[,[1,1,1,1,5,5,5,8,8,11,10,1,2,3,1,2,3,5,6,7,22,21,24,24,12,15,14,17,8,8,10,11
,3,3,1,1,7,5,7,5],[1,2,3,4,1,2,3,1,2,1,1,12,13,14,15,16,17,12,13,14,11,10,4,1,
25,26,27,28,35,36,35,35,33,34,35,36,33,35,33,35]],
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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],[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],[3,3,3,3,3,3,3,3,3,3,3,-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,-1,-1,-1],
[TENSOR,[4,2]],[4,4,4,4,-2,-2,-2,1,1,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,0,0,0,0,0,0
,0,0,0,E(3)^2,E(3),1,1,0,0,0,0,-1,-1,-E(3)^2,-E(3),2,2,2,2,2*E(3)^2,2*E(3)^2,
2*E(3),2*E(3)],
[GALOIS,[6,2]],
[TENSOR,[6,2]],
[TENSOR,[7,2]],[6,6,6,6,3,3,3,0,0,-3,-3,2,2,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,
-2,-2,1,1,-2,-2,-2,-2,1,1,1,1],
[TENSOR,[10,2]],[6,6,6,6,3,3,3,0,0,-3,-3,-2,-2,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,
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,E(3)-E(3)^2],
[TENSOR,[12,2]],[8,8,8,8,-4,-4,-4,2,2,-2*E(3)+4*E(3)^2,4*E(3)-2*E(3)^2,0,0,0,
0,0,0,0,0,0,-E(3)^2,-E(3),-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[14,2]],[9,5,1,-3,6,2,-2,3,-1,0,0,1,3,5,-3,-1,1,-2,0,2,0,0,0,0,-1,1,
-1,1,3,-1,0,0,3,-1,3,-1,0,0,0,0],
[TENSOR,[16,2]],[9,5,1,-3,6,2,-2,3,-1,0,0,5,3,1,1,-1,-3,2,0,-2,0,0,0,0,-1,1,
-1,1,-3,1,0,0,-3,1,-3,1,0,0,0,0],
[TENSOR,[18,2]],[12,12,12,12,0,0,0,-3,-3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-1,-1,-1,-1,2,2,2,2,2,2,2,2],
[TENSOR,[20,2]],[18,10,2,-6,12,4,-4,6,-2,0,0,-6,-6,-6,2,2,2,0,0,0,0,0,0,0,0,0
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[TENSOR,[23,2]],[27,3,-5,3,9,-3,1,0,0,0,0,-5,-1,7,3,-1,-1,1,-1,1,0,0,0,0,-1,
-1,1,1,0,0,0,0,-1,-1,3,3,-1,3,-1,3],
[TENSOR,[25,2]],[27,3,-5,3,9,-3,1,0,0,0,0,7,-1,-5,-1,-1,3,1,-1,1,0,0,0,0,-1,
-1,1,1,0,0,0,0,1,1,-3,-3,1,-3,1,-3],
[TENSOR,[27,2]],[36,20,4,-12,-12,-4,4,3,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[29,2]],[36,20,4,-12,6,2,-2,-6,2,0,0,-4,0,4,-4,0,4,2,0,-2,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[36,20,4,-12,6,2,-2,-6,2,0,0,4,0,-4,4,0,-4,-2,0,
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[54,6,-10,6,-9,3,-1,0,0,0,0,2,-2,2,
2,-2,2,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-6,-6,-1,3,-1,3],
[TENSOR,[33,2]],[54,6,-10,6,18,-6,2,0,0,0,0,-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],[54,-18,6,-2,0,0,0,0,0,0,0,6,-6,6,-2,2,-2,0,0,
0,0,0,1,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[54,6,-10,6,-9,3,-1,0,0,0,0,-2,2,
-2,-2,2,-2,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(3)+E(3)^2,3*E(3)-3*E(3)^2
,E(3)-E(3)^2,-3*E(3)+3*E(3)^2],
[TENSOR,[37,2]],[81,-27,9,-3,0,0,0,0,0,0,0,-3,3,-3,1,-1,1,0,0,0,0,0,0,0,1,-1,
-1,1,0,0,0,0,3,-1,-9,3,0,0,0,0],
[TENSOR,[39,2]]],
[(10,11)(21,22)(31,32)(37,39)(38,40)]);
ARC("2^6:3^3:S4","tomfusion",rec(name:="2^6:3^3:S4",map:=[1,2,4,8,9,59,64,
10,57,11,11,6,35,29,7,27,30,69,238,232,229,229,66,12,51,49,117,119,67,61,
58,58,23,43,5,3,243,63,243,63],text:=[
"fusion map is unique"
]));
ALF("2^6:3^3:S4","A12",[1,2,4,3,5,15,16,6,17,8,8,2,9,10,4,11,12,15,32,34,
26,27,20,7,11,12,23,24,19,18,21,21,10,12,4,3,34,16,34,16],[
"fusion map is unique up to table automorphisms"
]);

MOT("2S5.2",
[
"origin: Dixon's Algorithm"
],
[480,24,24,16,12,24,12,20,8,8,12,20,20,20,16,24,240,480],
[,[1,1,1,1,6,6,6,13,15,15,16,8,13,8,18,6,18,1],[1,2,3,4,3,1,2,8,9,10,17,12,13,
14,15,18,17,18],,[1,2,3,4,5,6,7,18,9,10,11,17,1,17,15,16,17,18]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,1,1,1,
1,1],[1,-1,1,-1,1,1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1],
[TENSOR,[2,3]],[4,-2,-2,0,1,1,1,-1,0,0,1,-1,-1,-1,0,1,4,4],
[TENSOR,[5,4]],
[TENSOR,[5,3]],
[TENSOR,[5,2]],[4,0,0,0,0,-2,0,1,0,0,0,-E(20)-E(20)^9+E(20)^13+E(20)^17,-1,
E(20)+E(20)^9-E(20)^13-E(20)^17,0,2,0,-4],
[TENSOR,[9,3]],[5,-1,-1,1,-1,-1,-1,0,1,1,-1,0,0,0,1,-1,5,5],
[TENSOR,[11,4]],
[TENSOR,[11,3]],
[TENSOR,[11,2]],[6,0,0,2,0,0,0,1,0,0,0,-1,1,-1,-2,0,-6,6],
[TENSOR,[15,3]],[8,0,0,0,0,2,0,2,0,0,0,0,-2,0,0,-2,0,-8],[12,0,0,0,0,0,0,-2,0
,0,0,0,2,0,0,0,0,-12]],
[(12,14),( 2, 3)( 5, 7)( 9,10)]);
ARC("2S5.2","tomfusion",rec(name:="2S5.2",map:=[1,4,3,5,21,6,18,31,25,28,
38,53,14,53,11,17,7,2],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2S5.2","U3(5).2",[1,2,12,12,14,3,8,11,10,15,17,18,5,19,4,8,13,2],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^(1+2)+.2S4",
[
"origin: Dixon's Algorithm"
],
[1296,648,54,144,72,24,12,54,54,54,9,18,18,18,8,8,12,6],
[,[1,2,3,1,2,4,5,10,8,9,11,8,9,10,6,6,1,3],[1,1,1,4,4,6,6,2,2,2,1,5,5,5,15,16,
17,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[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,-1,-1,-1,-1,-1,-1,-1,0,0,0,0],[2,2,2,-2,-2,0,0,-1,-1,-1,-1,
1,1,1,-E(8)-E(8)^3,E(8)+E(8)^3,0,0],
[TENSOR,[4,2]],[3,3,3,3,3,-1,-1,0,0,0,0,0,0,0,-1,-1,1,1],
[TENSOR,[6,2]],[4,4,4,-4,-4,0,0,1,1,1,1,-1,-1,-1,0,0,0,0],[6,-3,0,-2,1,2,-1,
-E(9)^2-2*E(9)^4-2*E(9)^5-E(9)^7,-E(9)^2+E(9)^4+E(9)^5-E(9)^7,
2*E(9)^2+E(9)^4+E(9)^5+2*E(9)^7,0,E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^4-E(9)^5,
-E(9)^2-E(9)^7,0,0,0,0],
[GALOIS,[9,2]],
[GALOIS,[9,4]],[8,8,-1,0,0,0,0,2,2,2,-1,0,0,0,0,0,-2,1],
[TENSOR,[12,2]],[12,-6,0,4,-2,0,0,-2*E(9)^2-E(9)^4-E(9)^5-2*E(9)^7,
E(9)^2+2*E(9)^4+2*E(9)^5+E(9)^7,E(9)^2-E(9)^4-E(9)^5+E(9)^7,0,-E(9)^2-E(9)^7,
E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^4-E(9)^5,0,0,0,0],
[GALOIS,[14,2]],
[GALOIS,[14,4]],[16,16,-2,0,0,0,0,-2,-2,-2,1,0,0,0,0,0,0,0],[18,-9,0,-6,3,-2,
1,0,0,0,0,0,0,0,0,0,0,0]],
[(15,16),( 8, 9,10)(12,13,14)]);
ARC("3^(1+2)+.2S4","tomfusion",rec(name:="3^(1+2)+.2S4",map:=[1,4,6,2,9,7,
21,19,19,19,5,29,29,29,17,17,3,11],text:=[
"fusion map is unique"
]));
ALF("3^(1+2)+.2S4","3D4(2)",[1,5,4,2,9,7,20,17,19,18,5,29,28,27,16,16,3,
10],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^(1+2)+:2S4",
[
"origin: Dixon's Algorithm"
],
[1296,648,54,144,72,24,12,54,54,54,9,18,18,18,8,8,12,6],
[,[1,2,3,1,2,4,5,8,9,10,11,8,9,10,6,6,1,3],[1,1,1,4,4,6,6,1,1,1,2,4,4,4,15,16,
17,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[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,-1,-1,-1,-1,-1,-1,-1,0,0,0,0],[2,2,2,-2,-2,0,0,-1,-1,-1,-1,
1,1,1,-E(8)-E(8)^3,E(8)+E(8)^3,0,0],
[TENSOR,[4,2]],[3,3,3,3,3,-1,-1,0,0,0,0,0,0,0,-1,-1,1,1],
[TENSOR,[6,2]],[4,4,4,-4,-4,0,0,1,1,1,1,-1,-1,-1,0,0,0,0],[6,-3,0,-2,1,2,-1,0
,3,-3,0,-2,1,1,0,0,0,0],[6,-3,0,-2,1,2,-1,-3,0,3,0,1,-2,1,0,0,0,0],[6,-3,0,-2,
1,2,-1,3,-3,0,0,1,1,-2,0,0,0,0],[8,8,-1,0,0,0,0,2,2,2,-1,0,0,0,0,0,-2,1],
[TENSOR,[12,2]],[12,-6,0,4,-2,0,0,-3,3,0,0,1,1,-2,0,0,0,0],[12,-6,0,4,-2,0,0,
3,0,-3,0,1,-2,1,0,0,0,0],[12,-6,0,4,-2,0,0,0,-3,3,0,-2,1,1,0,0,0,0],[16,16,-2,
0,0,0,0,-2,-2,-2,1,0,0,0,0,0,0,0],[18,-9,0,-6,3,-2,1,0,0,0,0,0,0,0,0,0,0,0]],
[(15,16),( 8, 9,10)(12,13,14)]);
ARC("3^(1+2)+:2S4","tomfusion",rec(name:="3^(1+2)+:2S4",map:=[1,4,7,2,16,
10,38,5,8,6,29,12,18,13,27,27,3,19],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^(1+2)+:2S4","S6(2)",[1,7,8,3,17,9,29,6,7,8,25,16,17,20,23,23,5,21],[
"fusion map is unique up to table aut."
]);
ALF("3^(1+2)+:2S4","U4(2).2",[1,4,6,2,10,7,15,4,6,5,14,10,12,11,23,23,17,
22],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^(1+4)+.2^(1+4)-.S3",
[
"origin: Dixon's Algorithm"
],
[46656,23328,324,486,576,288,96,48,324,648,27,72,36,48,24,24,48,36,36,36,288,
144,36,432,864,48,24,24,48,144,18,32,32,12,96,288,36,16,16,96,36,288,12],
[,[1,2,3,4,1,2,5,6,9,10,11,10,9,5,6,8,7,12,13,13,5,6,3,2,1,5,6,8,7,1,4,7,7,12,
5,1,3,5,7,5,3,1,12],[1,1,1,1,5,5,7,7,1,1,2,5,5,14,14,17,17,21,21,21,21,21,25,
25,25,26,26,29,29,30,30,32,33,35,35,36,36,38,39,40,42,42,40]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,
1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1],[1,1,1,1
,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1
,-1,-1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,-2,-2,-2,-2,-2,0
,0,0,0,0,0,0,0,1,-2,-2,-2,0,0,2,2,2,-1],
[TENSOR,[9,5]],
[TENSOR,[9,2]],
[TENSOR,[9,3]],[3,3,3,3,3,3,-1,-1,0,0,0,0,0,-1,-1,1,1,0,0,0,-3,-3,1,1,1,1,1,
-1,-1,-1,-1,1,1,0,3,-1,-1,1,-1,-3,1,1,0],
[TENSOR,[13,8]],
[TENSOR,[13,7]],
[TENSOR,[13,6]],
[TENSOR,[13,5]],
[TENSOR,[13,4]],
[TENSOR,[13,3]],
[TENSOR,[13,2]],[4,4,4,4,-4,-4,0,0,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,-2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[21,2]],[8,8,8,8,-8,-8,0,0,2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[18,-9,0,0,2,-1,2,-1,3,-6,0,2,-1,-2,1,-1,2,-2,1
,1,-2,1,0,-3,6,2,-1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[24,6]],
[TENSOR,[24,4]],
[TENSOR,[24,2]],[32,32,-4,5,0,0,0,0,8,8,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-8,1,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[28,2]],[36,-18,0,0,4,-2,4,-2,-3,6,0,-2,1,0,0,0,0,-2,1,1,4,-2,0,6,-12
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[30,2]],[48,48,3,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,8,8,0,0,0,
0,0,0,0,0,0,0,-8,1,0,0,0,1,-8,0],
[TENSOR,[32,5]],
[TENSOR,[32,2]],
[TENSOR,[32,3]],[54,-27,0,0,6,-3,-2,1,0,0,0,0,0,-2,1,1,-2,0,0,0,-6,3,0,3,-6,2
,-1,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[36,6]],
[TENSOR,[36,4]],
[TENSOR,[36,2]],[64,64,-8,10,0,0,0,0,-8,-8,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[72,-36,0,0,-8,4,0,0,-6,12,0,4,-2,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[72,-36,0,0,-8,4,0,0,3,-6,0,
-2,1,0,0,0,0,0,-3*E(4),3*E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[42,2]]],
[(32,33),(19,20),(14,26)(15,27)(16,28)(17,29)(34,43)(35,40)(36,42)(37,41)]);
ARC("3^(1+4)+.2^(1+4)-.S3","tomfusion",rec(name:="3^(1+4)+.2^(1+4)-.S3",map:=[
1,11,10,7,3,31,22,103,8,9,87,30,28,18,101,229,76,92,91,91,14,93,36,41,5,
15,94,228,75,2,24,73,73,99,17,6,38,13,72,16,40,4,95],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^(1+4)+.2^(1+4)-.S3","U4(3).(2^2)_{133}",[1,3,5,4,2,9,6,14,4,3,13,9,
10,28,34,35,30,24,25,25,17,24,21,19,15,37,43,44,39,16,20,22,22,43,37,36,
38,7,12,28,29,27,34],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^(1+4)+.4S4",
[
"origin: Dixon's Algorithm"
],
[23328,11664,486,162,486,288,144,48,24,324,324,324,27,27,36,36,36,72,18,18,16,
16,36,36,36,36,36,36,288,144,288,144,18,216,432,8,16,16],
[,[1,2,3,4,5,1,2,6,7,10,11,12,13,14,12,10,11,1,3,5,8,8,15,16,17,15,16,17,6,7,6
,7,4,2,1,6,8,8],[1,1,1,1,1,6,6,8,8,1,1,1,2,2,6,6,6,18,18,18,21,22,31,31,31,29,
29,29,31,31,29,29,35,35,35,36,38,37]],
[[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,-1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1
,1,1,1,1,1,1,1,1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,1,1,1,1,1
,1,-2,-2,-2,-2,-2,-2,-2,0,0,0],
[TENSOR,[5,2]],[2,2,2,2,2,-2,-2,0,0,-1,-1,-1,-1,-1,1,1,1,0,0,0,-E(8)-E(8)^3,
E(8)+E(8)^3,-E(4),-E(4),-E(4),E(4),E(4),E(4),2*E(4),2*E(4),-2*E(4),-2*E(4),0,0
,0,0,E(8)-E(8)^3,-E(8)+E(8)^3],
[TENSOR,[7,4]],
[TENSOR,[7,3]],
[TENSOR,[7,2]],[3,3,3,3,3,3,3,-1,-1,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,0,0,0,0,0,0,
-3,-3,-3,-3,1,1,1,1,-1,-1],
[TENSOR,[11,4]],
[TENSOR,[11,3]],
[TENSOR,[11,2]],[4,4,4,4,4,-4,-4,0,0,1,1,1,1,1,-1,-1,-1,0,0,0,0,0,-E(4),-E(4)
,-E(4),E(4),E(4),E(4),-4*E(4),-4*E(4),4*E(4),4*E(4),0,0,0,0,0,0],
[TENSOR,[15,2]],[16,16,-2,-2,7,0,0,0,0,4,4,4,-2,1,0,0,0,-4,2,-1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[17,2]],[16,16,7,-2,-2,0,0,0,0,4,4,4,1,-2,0,0,0,-4,-1,2,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[19,2]],[18,-9,0,0,0,2,-1,2,-1,3,3,-6,0,0,2,-1,-1,0,0,0,0,0,2,-1,-1,2
,-1,-1,2,-1,2,-1,0,3,-6,0,0,0],
[TENSOR,[21,2]],[18,-9,0,0,0,2,-1,2,-1,-6,3,3,0,0,-1,2,-1,0,0,0,0,0,-1,2,-1,
-1,2,-1,2,-1,2,-1,0,3,-6,0,0,0],
[TENSOR,[23,2]],[18,-9,0,0,0,2,-1,2,-1,3,-6,3,0,0,-1,-1,2,0,0,0,0,0,-1,-1,2,
-1,-1,2,2,-1,2,-1,0,3,-6,0,0,0],
[TENSOR,[25,2]],[32,32,-4,-4,14,0,0,0,0,-4,-4,-4,2,-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],[32,32,14,-4,-4,0,0,0,0,-4,-4,-4,-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],[36,-18,0,0,0,-4,2,0,0,-3,-3,6,0,0,2,-1,-1,
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[TENSOR,[37,2]]],
[(21,22)(37,38),( 3, 5)(13,14)(19,20),
(23,26)(24,27)(25,28)(29,31)(30,32)(37,38),(11,12)(15,17)(23,25)(26,28),
(10,11)(16,17)(24,25)(27,28)]);
ARC("3^(1+4)+.4S4","tomfusion",rec(name:="3^(1+4)+.4S4",map:=[1,5,7,11,6,
3,19,14,65,10,8,9,63,62,26,28,27,4,30,33,42,42,67,68,69,67,68,69,12,64,12,
64,32,17,2,15,44,44],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^(1+4)+.4S4","U4(3).2_1",[1,3,4,6,5,2,10,7,18,3,4,5,16,17,12,10,11,
20,24,25,27,27,32,29,31,32,30,31,21,30,21,29,26,23,19,8,15,15],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^(2+4):80",
[
"origin: Dixon's Algorithm"
],
[58320,7290,81,720,90,720,90,720,90,720,90,720,90,90,720,90,720,90,720,90,720,
80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,
80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,
80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80],
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58,60,57,59,56,53,55,52,54,66,63,65,62,64,71,68,70,67,69],,[1,2,3,1,2,1,2,1,2,
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,79,79,79]],
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[
(52,57)(53,58)(54,59)(55,60)(56,61)(62,67)(63,68)(64,69)(65,70)(66,71)(72,77)
(73,78)(74,79)(75,80)(76,81)(82,87)(83,88)(84,89)(85,90)(86,91)
,
(32,37)(33,38)(34,39)(35,40)(36,41)(42,47)(43,48)(44,49)(45,50)(46,51)
(52,62,57,67)(53,63,58,68)(54,64,59,69)(55,65,60,70)(56,66,61,71)(72,87,77,82)
(73,88,78,83)(74,89,79,84)(75,90,80,85)(76,91,81,86)
,
(22,27)(23,28)(24,29)(25,30)(26,31)(32,42)(33,43)(34,44)(35,45)(36,46)(37,47)
(38,48)(39,49)(40,50)(41,51)(52,76,57,81)(53,75,58,80)(54,72,59,77)
(55,74,60,79)(56,73,61,78)(62,91,67,86)(63,90,68,85)(64,87,69,82)(65,89,70,84)
(66,88,71,83)
,
( 4, 6, 8,10)( 5, 7, 9,11)(14,16,18,20)(15,17,19,21)(23,24,25,26)(28,29,30,31)
(32,34,33,35)(37,39,38,40)(42,44,43,45)(47,49,48,50)(52,53,56,54)(57,58,61,59)
(62,63,66,64)(67,68,71,69)(72,76,75,73)(77,81,80,78)(82,86,85,83)(87,91,90,88)
]);
ARC("3^(2+4):80","tomfusion",rec(name:="3^(2+4):80",map:=[1,3,4,6,19,6,19,
6,19,6,19,2,7,34,17,34,17,34,17,34,17,5,27,27,27,27,5,27,27,27,27,37,37,
37,37,9,37,37,37,37,9,37,37,37,37,9,37,37,37,37,9,48,48,48,20,48,48,48,48,
20,48,48,48,48,20,48,48,48,48,20,48,48,48,20,48,48,48,48,20,48,48,48,48,
20,48,48,48,48,20,48,48],text:=[
"fusion map is unique"
]));
ALF("3^(2+4):80","U3(9)",[1,3,4,6,29,8,31,7,30,9,32,2,12,41,15,43,17,42,
16,44,18,5,37,39,38,40,5,37,39,38,40,47,48,50,49,14,51,52,46,45,13,51,52,
46,45,13,47,48,50,49,14,81,79,88,35,90,89,87,80,36,82,77,91,84,33,86,85,
83,92,34,78,84,86,33,91,77,92,78,34,83,85,88,90,35,79,81,80,82,36,87,89],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^2.(3x3^(1+2)+):D8",
[
"origin: Dixon's Algorithm"
],
[5832,486,324,324,1458,243,1458,81,162,81,162,162,81,54,54,54,36,18,18,18,18,
36,36,18,72,18,18,18,36,36,54,108,12,12,12],
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,25,22,22],[1,1,1,1,1,1,1,1,1,1,1,1,1,7,7,7,17,17,17,17,17,25,25,25,25,31,31,
31,32,32,32,32,33,33,33]],
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[(34,35),(14,15)(26,28)(29,30),( 8,10,13)( 9,11,12)(19,20,21)]);
ARC("3^2.(3x3^(1+2)+):D8","tomfusion",rec(name:="3^2.(3x3^(1+2)+):D8",map:=[
1,7,8,9,5,10,6,15,11,16,12,13,14,80,80,69,4,33,30,34,35,28,27,32,3,135,
113,135,31,31,26,2,18,90,90],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^2.(3x3^(1+2)+):D8","G2(3).2",[1,3,6,5,3,4,4,5,3,6,5,6,4,14,15,13,2,
8,8,9,10,9,10,8,2,28,26,27,22,21,20,18,19,23,24],[
"compatible with 3^2.(3x3^(1+2)+):2^2 -> G2(3)"
]);

MOT("3^3:S4`",
[
"origin: Dixon's Algorithm"
],
[648,162,162,108,54,24,12,9,9,9,4,18,18,18,36,36,36],
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15]],
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],
[TENSOR,[4,2]],[4,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,-2,1,0,0,E(3),1,E(3)^2,0,1,
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[GALOIS,[6,2]],
[TENSOR,[6,2]],
[TENSOR,[7,2]],[6,-3,-3,3,0,2,-1,0,0,0,0,2,-1,-1,2,-1,-1],
[TENSOR,[10,2]],[6,-3,-3,3,0,-2,1,0,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,
-E(3)+E(3)^2,E(3)-E(3)^2],
[TENSOR,[12,2]],[8,-2*E(3)+4*E(3)^2,4*E(3)-2*E(3)^2,-4,2,0,0,-E(3),-1,-E(3)^2
,0,0,0,0,0,0,0],
[GALOIS,[14,2]],[12,3,3,0,-3,0,0,0,0,0,0,-1,-1,-1,2,2,2],
[TENSOR,[16,2]]],
[( 2, 3)( 8,10)(13,14)(16,17)]);
ARC("3^3:S4`","tomfusion",rec(name:="3^3:S4`",map:=[1,5,5,7,4,2,12,21,6,
21,9,15,17,17,3,18,18],text:=[
"fusion map is unique"
]));
ALF("3^3:S4`","s3wrs3",[1,3,3,2,4,5,6,8,7,8,18,15,17,17,14,16,16],[
"fusion map is unique"
]);
ALF("3^3:S4`","U4(2)",[1,4,5,6,7,3,16,17,7,18,9,15,12,11,2,14,13],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^4:(2xA6)",
[
"origin: Dixon's Algorithm"
],
[58320,1944,1944,2916,720,72,36,36,36,36,8,144,36,72,72,36,36,144,18,162,81,27
,18,81,162,27,10,10,10,10],
[,[1,2,3,4,1,12,13,14,15,13,12,1,4,2,3,2,3,1,20,20,21,22,25,24,25,26,30,30,28,
28],[1,1,1,1,5,6,6,6,6,6,11,12,12,12,12,18,18,18,5,1,1,4,5,1,1,4,29,30,27,28],
,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,5,1,5,1
]],
[[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,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,-1,1],[5,5,5,5,-5,1,1,1,
1,1,-1,1,1,1,1,-1,-1,-1,-2,2,2,2,1,-1,-1,-1,0,0,0,0],[5,5,5,5,-5,1,1,1,1,1,-1,
1,1,1,1,-1,-1,-1,1,-1,-1,-1,-2,2,2,2,0,0,0,0],
[TENSOR,[4,2]],
[TENSOR,[3,2]],[8,8,8,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,-1,1,-1,-1,-1,
E(5)^2+E(5)^3,-E(5)^2-E(5)^3,E(5)+E(5)^4,-E(5)-E(5)^4],
[GALOIS,[7,2]],
[TENSOR,[8,2]],
[TENSOR,[7,2]],[9,9,9,9,-9,-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],
[TENSOR,[11,2]],[10,10,10,10,-10,0,0,0,0,0,0,-2,-2,-2,-2,2,2,2,-1,1,1,1,-1,1,
1,1,0,0,0,0],
[TENSOR,[13,2]],[20,2,2,-7,0,-4,-1,2,2,-1,0,4,1,-2,-2,0,0,0,0,2,2,-1,0,2,2,-1
,0,0,0,0],
[TENSOR,[15,2]],[20,2,2,-7,0,0,-3*E(4),0,0,3*E(4),0,-4,-1,2,2,0,0,0,0,2,2,-1,
0,2,2,-1,0,0,0,0],
[TENSOR,[17,2]],[30,-6,3,3,0,2,-1,2,-1,-1,0,2,-1,2,-1,-2,1,4,0,6,-3,0,0,0,0,0
,0,0,0,0],
[TENSOR,[19,2]],[30,3,-6,3,0,2,-1,-1,2,-1,0,2,-1,-1,2,1,-2,4,0,0,0,0,0,-3,6,0
,0,0,0,0],
[TENSOR,[21,2]],[60,-12,6,6,0,0,0,0,0,0,0,4,-2,4,-2,0,0,0,0,-6,3,0,0,0,0,0,0,
0,0,0],[60,6,-12,6,0,0,0,0,0,0,0,4,-2,-2,4,0,0,0,0,0,0,0,0,3,-6,0,0,0,0,0],[80
,8,8,-28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,2,0,2,2,-1,0,0,0,0],[80,8,8,-28,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-1,0,-4,-4,2,0,0,0,0],[90,-18,9,9,0,-2,1,-2,1
,1,0,-2,1,-2,1,-2,1,4,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,2]],[90,9,-18,9,0,-2,1,1,-2,1,0,-2,1,1,-2,1,-2,4,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[29,2]]],
[( 7,10),( 2, 3)( 8, 9)(14,15)(16,17)(19,23)(20,25)(21,24)(22,26),
(27,29)(28,30)]);
ARC("3^4:(2xA6)","tomfusion",rec(name:="3^4:(2xA6)",map:=[1,6,7,5,2,13,78,
70,73,78,18,3,30,26,27,32,31,4,37,9,11,58,34,10,8,57,66,19,66,19],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^4:(2xA6)","2xA6",[1,1,1,1,2,10,10,10,10,10,9,3,3,3,3,4,4,4,6,5,5,5,
8,7,7,7,12,11,14,13]);
ALF("3^4:(2xA6)","2x3^4:(2xA6)",[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,
31,33,35,37,39,41,43,45,47,49,51,53,55,57,59],[
"embedding into the direct product"
]);
ALF("3^4:(2xA6)","U4(3).2_1",[1,4,5,3,20,21,29,31,32,30,8,2,10,11,12,24,
25,20,25,5,6,17,24,6,4,16,28,9,28,9],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^4:2^3.S4",
[
"origin: Dixon's Algorithm"
],
[15552,1944,648,486,972,288,72,72,192,32,144,36,36,32,6,54,27,27,27,27,16,144,
36,36,36,18,72,36,8,8],
[,[1,2,3,4,5,1,2,3,1,9,1,3,5,9,16,16,17,18,20,19,6,6,7,8,3,4,1,2,14,10],[1,1,1
,1,1,6,6,6,9,10,11,11,11,14,9,1,1,4,4,4,21,22,22,22,27,27,27,27,29,30]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,
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,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,
-1,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,1,1],
[TENSOR,[4,2]],[3,3,3,3,3,-1,-1,-1,3,-1,-1,-1,-1,3,0,0,0,0,0,0,-1,-1,-1,-1,1,
1,1,1,1,-1],
[TENSOR,[6,2]],[3,3,3,3,3,-1,-1,-1,3,3,-1,-1,-1,-1,0,0,0,0,0,0,-1,-1,-1,-1,1,
1,1,1,-1,1],
[TENSOR,[8,2]],[4,4,4,4,4,0,0,0,-4,0,0,0,0,0,-1,1,1,1,1,1,2,-2,-2,-2,0,0,0,0,
0,0],
[TENSOR,[10,2]],[6,6,6,6,6,-2,-2,-2,6,-2,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0],[8,5,2,-1,-4,4,1,-2,0,0,0,0,0,0,0,2,-1,2,-1,-1,0,-4,-1,2,-2,1,-2,1,0,0],
[TENSOR,[13,2]],[8,8,8,8,8,0,0,0,-8,0,0,0,0,0,1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,
0,0,0],[16,10,4,-2,-8,8,2,-4,0,0,0,0,0,0,0,-2,1,-2,1,1,0,0,0,0,0,0,0,0,0,0],[
16,-8,4,-2,1,0,0,0,0,0,4,-2,1,0,0,4,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0],[16,-8,4,-2
,1,0,0,0,0,0,4,-2,1,0,0,-2,1,1,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,
0],
[GALOIS,[18,2]],[24,15,6,-3,-12,-4,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-1,2,2,
-1,2,-1,0,0],
[TENSOR,[20,2]],[24,6,-3,-3,6,4,-2,1,0,0,-4,-1,2,0,0,0,0,0,0,0,0,-4,2,-1,-1,
-1,2,2,0,0],
[TENSOR,[22,2]],[24,6,-3,-3,6,4,-2,1,0,0,4,1,-2,0,0,0,0,0,0,0,0,-4,2,-1,1,1,
-2,-2,0,0],
[TENSOR,[24,2]],[32,-4,-4,5,-4,0,0,0,0,0,0,0,0,0,0,2,2,-1,-1,-1,0,0,0,0,-2,1,
4,-2,0,0],
[TENSOR,[26,2]],[48,12,-6,-6,12,-8,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0],[48,-24,12,-6,3,0,0,0,0,0,-4,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
64,-8,-8,10,-8,0,0,0,0,0,0,0,0,0,0,-2,-2,1,1,1,0,0,0,0,0,0,0,0,0,0]],
[(19,20),(10,14)(29,30)]);
ARC("3^4:2^3.S4","tomfusion",rec(name:="3^4:2^3.S4",map:=[1,9,8,10,6,3,25,
28,2,22,5,43,24,21,31,11,7,72,67,67,12,20,99,93,45,26,4,40,46,56],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^4:2^3.S4","A12",[1,5,6,8,7,2,15,17,4,12,3,18,20,12,21,8,7,25,26,27,
11,9,32,33,19,21,4,16,24,24],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^4:GL2(9)",
[
"origin: Dixon's Algorithm,\n",
"constructions: AGL(2,9)"
],
[466560,5832,5760,5760,5760,5760,5760,5760,5760,64,72,576,64,72,576,64,64,64,
64,64,64,64,576,72,64,64,64,576,72,72,576,64,64,64,64,64,64,72,576,64,72,576,
64,64,72,72,72,72,72,72,72,81,648,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80
,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80],
[,[1,2,1,3,3,5,5,4,4,31,30,31,31,30,31,32,32,32,32,13,13,15,15,14,10,10,12,12,
11,2,1,3,5,4,10,10,12,11,12,15,14,15,13,13,50,50,49,49,51,51,53,52,53,9,8,7,6,
77,77,76,76,75,75,74,74,87,87,86,86,88,88,89,89,84,84,85,85,82,82,83,83,79,79,
78,78,80,80,81,81],[1,1,3,5,4,9,8,7,6,13,15,15,10,12,12,16,17,19,18,36,35,37,
39,39,43,44,40,42,42,31,31,32,34,33,21,20,22,23,23,27,28,28,25,26,8,9,6,7,5,4,
3,1,1,57,56,55,54,70,71,73,72,67,66,68,69,63,62,64,65,58,59,61,60,86,87,89,88,
83,82,84,85,79,78,80,81,74,75,77,76],,[1,2,3,4,5,7,6,9,8,10,11,12,13,14,15,17,
16,19,18,44,43,40,42,41,35,36,37,39,38,30,31,32,33,34,25,26,27,29,28,22,24,23,
21,20,46,45,48,47,49,50,51,52,53,55,54,57,56,57,57,56,56,54,54,55,55,57,57,56,
56,54,54,55,55,8,9,7,6,3,1,5,4,1,3,4,5,7,6,9,8]],
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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
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-E(8)^3,-1,-1,1,E(4),-E(4),-E(8)^3,-E(8)^3,E(8)^3,E(8)^3,E(8)^3,-E(8),-E(8),
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-E(4),E(4),E(4)],
[TENSOR,[2,3]],
[GALOIS,[3,3]],
[TENSOR,[2,5]],
[TENSOR,[3,4]],
[TENSOR,[2,7]],[8,8,-8,-8*E(4),8*E(4),8*E(8),-8*E(8),-8*E(8)^3,8*E(8)^3,0,0,0
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-E(8)^3,E(8)^3,E(4),-E(4),1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-2*E(8)^3,2*E(8)^3,-2*E(8),2*E(8),2,-2,-2*E(4),2*E(4),-2,2,2*E(4),-2*E(4),
-2*E(8),2*E(8),2*E(8)^3,-2*E(8)^3],
[TENSOR,[9,7]],
[TENSOR,[9,3]],
[TENSOR,[9,5]],[8,8,-8,-8*E(4),8*E(4),-8*E(8),8*E(8),8*E(8)^3,-8*E(8)^3,0,0,0
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E(40)^7+E(40)^23],
[GALOIS,[13,17]],
[TENSOR,[14,2]],
[TENSOR,[13,2]],
[TENSOR,[13,8]],
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[GALOIS,[29,17]],
[TENSOR,[30,2]],
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[(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73),
(58,66,59,67)(60,68,61,69)(62,70,63,71)(64,72,65,73)(74,89)(75,88)(76,86)
(77,87)(78,83)(79,82)(80,85)(81,84)
,
( 6, 7)( 8, 9)(16,17)(18,19)(20,44)(21,43)(22,40)(23,42)(24,41)(25,35)(26,36)
(27,37)(28,39)(29,38)(45,46)(47,48)(54,55)(56,57)(58,60,59,61)(62,65,63,64)
(66,68,67,69)(70,73,71,72)(74,75)(76,77)(86,87)(88,89)
,
( 4, 5)( 6, 8)( 7, 9)(10,13)(11,14)(12,15)(16,17)(20,26)(21,25)(22,27)(23,28)
(24,29)(33,34)(35,43)(36,44)(37,40)(38,41)(39,42)(45,47)(46,48)(49,50)(54,56)
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(80,81)(84,85)(86,88)(87,89)
]);
ARC("3^4:GL2(9)","tomfusion",rec(name:="3^4:GL2(9)",map:=[1,4,2,7,7,20,20,
20,20,10,45,9,10,45,9,22,22,23,23,25,26,27,24,83,26,25,27,24,83,19,3,8,21,
21,26,25,27,83,24,27,83,24,26,25,84,84,84,84,46,46,18,5,6,52,52,52,52,193,
193,193,193,193,193,193,193,193,193,193,193,193,193,193,193,127,127,127,
127,43,12,81,81,12,43,81,81,127,127,127,127],text:=[
"fusion map determined by the groups"
]));
ALF("3^4:GL2(9)","L3(9)",[1,3,2,5,6,14,15,13,16,7,25,5,7,26,6,22,21,19,20,
21,20,18,14,40,20,22,17,13,39,10,2,7,18,17,19,21,17,42,16,18,41,15,19,22,
41,40,42,39,25,26,10,4,3,34,31,33,32,53,61,65,57,66,58,54,62,56,64,52,60,
51,59,55,63,47,43,44,48,23,8,36,35,9,24,38,37,49,45,50,46],[
"fusion map is unique up to table automorphisms"
]);
ALN("3^4:GL2(9)",["AGL(2,9)"]);

MOT("4(A4xA4).4",
[
"origin: Dixon's Algorithm"
],
[2304,2304,128,192,72,72,96,32,72,72,24,144,144,12,32,16,64,64,96,32,12,96,32,
12,32,16,32,32,96,192,128,1152,36,12,36,144,144,24],
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12,12,13],[1,2,3,4,1,2,7,8,1,2,4,2,1,7,15,16,17,18,19,20,19,22,23,22,25,26,27,
28,29,30,31,32,32,29,32,32,32,30]],
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[TENSOR,[37,2]]],
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( 5, 9)( 6,10)( 7,19)( 8,20)(14,21)(22,29)(23,28)(24,34)(33,35)]);
ARC("4(A4xA4).4","tomfusion",rec(name:="4(A4xA4).4",map:=[1,2,4,15,12,49,
5,36,11,50,159,48,10,63,9,111,24,25,7,27,61,8,35,64,34,121,43,28,6,3,17,
13,155,62,157,149,149,59],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("4(A4xA4).4","U4(3).2_1",[1,2,2,7,4,11,2,8,5,12,18,10,3,12,20,27,21,
22,20,22,24,2,8,11,7,15,8,22,20,19,22,21,31,25,32,29,30,23],[
"fusion map is unique up to table automorphisms"
]);

MOT("5^(1+2)+:24",
[
"origin: Dixon's Algorithm"
],
[3000,750,25,120,30,24,24,120,30,120,30,24,24,120,30,120,30,24,24,24,24,24,24,
24,24,24,24,24,24,24,24],
[,[1,2,3,1,2,4,4,14,15,14,15,16,16,8,9,8,9,10,10,13,13,12,12,7,7,6,6,19,19,18,
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],,[1,1,1,4,4,6,7,14,14,16,16,18,19,8,8,10,10,12,13,29,28,31,30,25,24,27,26,21
,20,23,22]],
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[TENSOR,[2,7]],
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[TENSOR,[2,11]],
[GALOIS,[7,11]],
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[TENSOR,[3,8]],
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[TENSOR,[3,11]],
[TENSOR,[3,13]],
[TENSOR,[2,21]],
[TENSOR,[2,22]],[20,-5,0,-4,1,0,0,-4,1,-4,1,0,0,-4,1,-4,1,0,0,0,0,0,0,0,0,0,0
,0,0,0,0],
[TENSOR,[25,3]],
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[TENSOR,[25,19]],
[TENSOR,[25,7]],
[TENSOR,[25,9]],[24,24,-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]],
[(20,21)(22,23)(24,25)(26,27)(28,29)(30,31),
( 8,14)( 9,15)(10,16)(11,17)(12,18)(13,19)(20,28)(21,29)(22,30)(23,31),
( 6, 7)(12,13)(18,19)(20,22)(21,23)(24,26)(25,27)(28,30)(29,31)]);
ARC("5^(1+2)+:24","tomfusion",rec(name:="5^(1+2)+:24",map:=[1,5,6,2,9,4,4,
3,12,7,17,11,11,3,12,7,17,11,11,15,15,15,15,8,8,8,8,15,15,15,15],text:=[
"fusion map is unique"
]));
ALF("5^(1+2)+:24","U3(5).3",[1,5,6,2,12,4,4,13,23,17,33,21,21,14,24,18,34,
22,22,30,32,32,30,10,11,11,10,29,31,31,29],[
"fusion map is unique up to table automorphisms"
]);

MOT("5^(1+2)+:4A5",
[
"origin: Dixon's Algorithm"
],
[30000,15000,15000,250,1200,600,600,240,240,40,10,40,20,20,500,250,250,25,100,
50,50,20,20,500,250,250,25,100,50,50,20,20,12,12,30,30,60,30,30,60],
[,[1,3,2,4,1,3,2,5,5,1,4,5,7,6,24,26,25,27,24,26,25,28,28,15,17,16,18,15,17,16
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28,30,29,32,31,15,17,16,18,19,21,20,23,22,8,9,3,2,1,6,7,5],,[1,1,1,1,5,5,5,8,9
,10,10,12,12,12,1,1,1,1,5,5,5,8,9,1,1,1,1,5,5,5,8,9,33,34,37,37,37,40,40,40]],
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[GALOIS,[3,13]],
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-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,0,0,0,0,0,0,0,
6*E(5)+4*E(5)^2+4*E(5)^3+6*E(5)^4,-4*E(5)-E(5)^2-E(5)^3-4*E(5)^4,
E(5)-E(5)^2-E(5)^3+E(5)^4,0,-2*E(5)-2*E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,1,0
,0,4*E(5)+6*E(5)^2+6*E(5)^3+4*E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,
-E(5)-4*E(5)^2-4*E(5)^3-E(5)^4,0,-2*E(5)^2-2*E(5)^3,1,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,2,
E(5)^2+E(5)^3,E(5)+E(5)^4,2],
[GALOIS,[21,2]],[20,10*E(5)+10*E(5)^4,10*E(5)^2+10*E(5)^3,0,-4,
-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,0,0,0,0,0,0,0,
-4*E(5)-6*E(5)^2-6*E(5)^3-4*E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,
E(5)+4*E(5)^2+4*E(5)^3+E(5)^4,0,-2*E(5)^2-2*E(5)^3,1,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,0,0,-6*E(5)-4*E(5)^2-4*E(5)^3-6*E(5)^4,
4*E(5)+E(5)^2+E(5)^3+4*E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,0,-2*E(5)-2*E(5)^4,
2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,1,0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,2,
E(5)^2+E(5)^3,E(5)+E(5)^4,2],
[GALOIS,[23,2]],[24,24,24,-1,0,0,0,0,0,-4,1,0,0,0,4,4,4,-1,0,0,0,0,0,4,4,4,-1
,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[25,2]],[30,15*E(5)+15*E(5)^4,15*E(5)^2+15*E(5)^3,0,6,3*E(5)+3*E(5)^4
,3*E(5)^2+3*E(5)^3,0,0,0,0,2,E(5)+E(5)^4,E(5)^2+E(5)^3,
-6*E(5)-4*E(5)^2-4*E(5)^3-6*E(5)^4,4*E(5)+E(5)^2+E(5)^3+4*E(5)^4,
-E(5)+E(5)^2+E(5)^3-E(5)^4,0,-2*E(5)-2*E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,1,
0,0,-4*E(5)-6*E(5)^2-6*E(5)^3-4*E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,
E(5)+4*E(5)^2+4*E(5)^3+E(5)^4,0,-2*E(5)^2-2*E(5)^3,1,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[27,2]],[30,15*E(5)+15*E(5)^4,15*E(5)^2+15*E(5)^3,0,6,3*E(5)+3*E(5)^4
,3*E(5)^2+3*E(5)^3,0,0,0,0,2,E(5)+E(5)^4,E(5)^2+E(5)^3,
4*E(5)+6*E(5)^2+6*E(5)^3+4*E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,
-E(5)-4*E(5)^2-4*E(5)^3-E(5)^4,0,-2*E(5)^2-2*E(5)^3,1,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,0,0,6*E(5)+4*E(5)^2+4*E(5)^3+6*E(5)^4,
-4*E(5)-E(5)^2-E(5)^3-4*E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,0,-2*E(5)-2*E(5)^4,
2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,1,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[29,2]],[40,20*E(5)+20*E(5)^4,20*E(5)^2+20*E(5)^3,0,-8,
-4*E(5)-4*E(5)^4,-4*E(5)^2-4*E(5)^3,0,0,0,0,0,0,0,
2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,-3*E(5)-2*E(5)^2-2*E(5)^3-3*E(5)^4,
2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,0,2,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,
-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,
-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,0,2,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,-2,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-2],
[GALOIS,[31,2]],[40,20*E(5)+20*E(5)^4,20*E(5)^2+20*E(5)^3,0,8,4*E(5)+4*E(5)^4
,4*E(5)^2+4*E(5)^3,0,0,0,0,0,0,0,2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,
-3*E(5)-2*E(5)^2-2*E(5)^3-3*E(5)^4,2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,0,-2,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,
3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,0,-2,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-2,
E(5)^2+E(5)^3,E(5)+E(5)^4,2],
[GALOIS,[33,2]],[48,48,48,-2,0,0,0,0,0,0,0,0,0,0,4*E(5)+4*E(5)^4,
4*E(5)+4*E(5)^4,4*E(5)+4*E(5)^4,-E(5)-E(5)^4,0,0,0,0,0,4*E(5)^2+4*E(5)^3,
4*E(5)^2+4*E(5)^3,4*E(5)^2+4*E(5)^3,-E(5)^2-E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[35,2]],[50,25*E(5)+25*E(5)^4,25*E(5)^2+25*E(5)^3,0,10,
5*E(5)+5*E(5)^4,5*E(5)^2+5*E(5)^3,0,0,0,0,-2,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,2,-E(5)^2-E(5)^3,
-E(5)-E(5)^4,-2],
[GALOIS,[37,2]],[60,30*E(5)+30*E(5)^4,30*E(5)^2+30*E(5)^3,0,-12,
-6*E(5)-6*E(5)^4,-6*E(5)^2-6*E(5)^3,0,0,0,0,0,0,0,
-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,
-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,0,-2,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,
2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,-3*E(5)-2*E(5)^2-2*E(5)^3-3*E(5)^4,
2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,0,-2,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0
,0,0,0,0],
[GALOIS,[39,2]]],
[
( 2, 3)( 6, 7)(13,14)(15,24)(16,26)(17,25)(18,27)(19,28)(20,30)(21,29)(22,31)
(23,32)(35,36)(38,39)
,( 8, 9)(22,23)(31,32)(33,34)]);
ARC("5^(1+2)+:4A5","tomfusion",rec(name:="5^(1+2)+:4A5",map:=[1,8,8,9,2,
20,20,5,5,3,30,6,45,45,10,11,12,13,23,27,25,48,48,10,12,11,13,23,25,27,48,
48,36,36,38,38,4,60,60,14],text:=[
"fusion map is unique"
]));
ALF("5^(1+2)+:4A5","S4(5)",[1,8,9,11,2,17,18,6,6,3,22,6,31,32,9,10,11,12,
18,21,20,32,32,8,11,10,13,17,19,21,31,31,24,24,28,29,5,34,33,14],[
"fusion map is unique up to table automorphisms"
]);

MOT("5^(1+2)+:8",
[
"origin: Dixon's Algorithm"
],
[1000,250,25,25,25,40,10,8,8,8,8,8,8],
[,[1,2,3,4,5,1,2,6,6,8,8,9,9],,,[1,1,1,1,1,6,6,8,9,11,10,13,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1],[1,1,1,1,1,-1,-1,
-E(4),E(4),-E(8)^3,E(8)^3,-E(8),E(8)],
[TENSOR,[2,3]],
[GALOIS,[3,3]],
[TENSOR,[2,5]],
[TENSOR,[3,3]],
[TENSOR,[2,7]],[8,8,3,-2,-2,0,0,0,0,0,0,0,0],[8,8,-2,-2,3,0,0,0,0,0,0,0,0],[8
,8,-2,3,-2,0,0,0,0,0,0,0,0],[20,-5,0,0,0,-4,1,0,0,0,0,0,0],
[TENSOR,[12,3]]],
[(4,5),(3,4),(10,11)(12,13),( 8, 9)(10,12)(11,13)]);
ARC("5^(1+2)+:8","tomfusion",rec(name:="5^(1+2)+:8",map:=[1,4,7,6,5,2,9,3,
3,8,8,8,8],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("5^(1+2)+:8","U3(5)",[1,5,6,7,8,2,14,4,4,12,13,12,13],[
"fusion map is unique up to table automorphisms"
]);

MOT("5^2:S3",
[
"origin: Dixon's Algorithm"
],
[150,50,50,50,50,10,10,10,10,10,25,25,3],
[,[1,4,2,5,3,3,5,4,1,2,12,11,13],[1,3,5,2,4,7,8,10,9,6,12,11,1],,[1,1,1,1,1,9,
9,9,9,9,1,1,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1],[2,2,2,2,2,0,0,0
,0,0,2,2,-1],[3,2*E(5)^3+E(5)^4,E(5)^2+2*E(5)^4,2*E(5)+E(5)^3,E(5)+2*E(5)^2,
-E(5),-E(5)^3,-E(5)^4,-1,-E(5)^2,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0],
[GALOIS,[4,3]],
[GALOIS,[4,4]],
[GALOIS,[4,2]],
[TENSOR,[4,2]],
[TENSOR,[5,2]],
[TENSOR,[6,2]],
[TENSOR,[7,2]],[6,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)^2-2*E(5)^3,
-2*E(5)-2*E(5)^4,0,0,0,0,0,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,
2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,0],
[GALOIS,[12,2]]],
[( 2, 3, 5, 4)( 6, 7, 8,10)(11,12)]);
ARC("5^2:S3","tomfusion",rec(name:="5^2:S3",map:=[1,4,4,4,4,7,7,7,2,7,5,5,
3],text:=[
"fusion map is unique"
]));
ALF("5^2:S3","U3(4)",[1,5,8,7,6,12,13,11,2,14,10,9,3],[
"fusion map is unique up to table automorphisms"
]);

MOT("5^3:(2xA5).2",
[
"origin: Dixon's Algorithm"
],
[30000,2500,2500,750,500,240,400,100,100,50,100,100,20,80,40,20,20,20,40,20,50
,25,25,10,24,24,15,60,12,12,12],
[,[1,3,2,4,5,1,1,3,2,4,5,5,5,1,7,8,9,9,7,8,21,23,22,21,6,6,27,28,28,29,29],[1,
3,2,4,5,6,7,9,8,10,12,11,13,14,19,18,20,16,15,17,21,23,22,24,26,25,4,1,6,26,25
],,[1,1,1,1,1,6,7,7,7,7,7,7,14,14,15,15,15,19,19,19,1,1,1,6,25,26,28,28,29,30,
31]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,-1,-1],[1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,1,1,-E(4),-E(4),-E(4),E(4),E(4),E(4),1,1,1,-1,E(4),-E(4),1,1,-1
,E(4),-E(4)],
[TENSOR,[2,3]],[4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-2,-2,1,1
,1,1,1],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[5,5,5,5,5,5,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,-1,
-1,-1,1,1],
[TENSOR,[9,2]],
[TENSOR,[9,4]],
[TENSOR,[9,3]],[6,6,6,6,6,-6,2,2,2,2,2,2,-2,-2,0,0,0,0,0,0,1,1,1,-1,0,0,0,0,0
,0,0],
[TENSOR,[13,3]],[12,-2*E(5)+3*E(5)^2+3*E(5)^3-2*E(5)^4,
3*E(5)-2*E(5)^2-2*E(5)^3+3*E(5)^4,-3,2,0,-4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,1,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,0,0,
-2*E(4),-E(20)-E(20)^9,-E(20)^13-E(20)^17,E(20)^13+E(20)^17,2*E(4),
E(20)+E(20)^9,2,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,0,0,0,0],
[TENSOR,[15,2]],
[GALOIS,[15,13]],
[TENSOR,[17,2]],
[TENSOR,[15,3]],
[TENSOR,[17,3]],
[TENSOR,[15,4]],
[TENSOR,[17,4]],[40,-10,-10,5,0,0,-8,2,2,-3,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-1,4,0,0,0],
[TENSOR,[23,3]],[48,12*E(5)-8*E(5)^2-8*E(5)^3+12*E(5)^4,
-8*E(5)+12*E(5)^2+12*E(5)^3-8*E(5)^4,-12,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,0,0,0,0,0],
[GALOIS,[25,2]],[60,10,10,0,-5,0,8,-2,-2,-2,3,3,-1,4,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[27,3]],[60,10,10,0,-5,0,0,-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,
2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,0,-E(5)+E(5)^2+E(5)^3-E(5)^4,
E(5)-E(5)^2-E(5)^3+E(5)^4,1,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,3]],[80,-20,-20,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
-4,0,0,0]],
[(15,19)(16,20)(17,18)(25,26)(30,31),
( 2, 3)( 8, 9)(11,12)(16,17)(18,20)(22,23)]);
ARC("5^3:(2xA5).2","tomfusion",rec(name:="5^3:(2xA5).2",map:=[1,11,11,12,
13,3,2,27,27,28,25,25,32,4,8,53,53,53,8,53,14,15,15,34,9,9,41,5,17,38,38],
text:=[
"fusion map is unique"
]));
ALF("5^3:(2xA5).2","S4(5)",[1,8,9,10,11,3,2,17,18,21,20,19,22,3,6,32,31,
31,6,32,11,12,13,22,7,7,30,4,16,23,23],[
"fusion map is unique up to table automorphisms"
]);

MOT("5^3:62",
[
"origin: Dixon's Algorithm"
],
[7750,125,125,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,
62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,
62,62,62,62,62,62,62,62,62,62,62,62,62,62],
[,[1,3,2,1,53,53,55,55,57,57,59,59,61,61,63,63,5,5,7,7,9,9,11,11,13,13,15,15,
17,17,19,19,21,21,23,23,25,25,27,27,29,29,31,31,33,33,35,35,37,37,39,39,41,41,
43,43,45,45,47,47,49,49,51,51],,,[1,1,1,4,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24
,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],,,,,,,,,,,,,,,,,
,,,,,,,,,[1,2,3,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,
1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4]],
[[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,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,-1,1,-1,1,-1,1,-1,
1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,
-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1],[1,1,1,-1,E(31)^30,
-E(31)^30,E(31)^28,-E(31)^28,E(31)^22,-E(31)^22,E(31)^4,-E(31)^4,E(31)^12,
-E(31)^12,E(31)^5,-E(31)^5,E(31)^15,-E(31)^15,E(31)^14,-E(31)^14,E(31)^11,
-E(31)^11,E(31)^2,-E(31)^2,E(31)^6,-E(31)^6,E(31)^18,-E(31)^18,E(31)^23,
-E(31)^23,E(31)^7,-E(31)^7,E(31)^21,-E(31)^21,E(31),-E(31),E(31)^3,-E(31)^3,
E(31)^9,-E(31)^9,E(31)^27,-E(31)^27,E(31)^19,-E(31)^19,E(31)^26,-E(31)^26,
E(31)^16,-E(31)^16,E(31)^17,-E(31)^17,E(31)^20,-E(31)^20,E(31)^29,-E(31)^29,
E(31)^25,-E(31)^25,E(31)^13,-E(31)^13,E(31)^8,-E(31)^8,E(31)^24,-E(31)^24,
E(31)^10,-E(31)^10],
[GALOIS,[3,2]],
[GALOIS,[3,3]],
[GALOIS,[3,4]],
[GALOIS,[3,5]],
[GALOIS,[3,6]],
[GALOIS,[3,7]],
[GALOIS,[3,8]],
[GALOIS,[3,9]],
[GALOIS,[3,10]],
[GALOIS,[3,11]],
[GALOIS,[3,12]],
[GALOIS,[3,13]],
[GALOIS,[3,14]],
[GALOIS,[3,15]],
[GALOIS,[3,16]],
[GALOIS,[3,17]],
[GALOIS,[3,18]],
[GALOIS,[3,19]],
[GALOIS,[3,20]],
[GALOIS,[3,21]],
[GALOIS,[3,22]],
[GALOIS,[3,23]],
[GALOIS,[3,24]],
[GALOIS,[3,25]],
[GALOIS,[3,26]],
[GALOIS,[3,27]],
[GALOIS,[3,28]],
[GALOIS,[3,29]],
[GALOIS,[3,30]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],
[TENSOR,[2,7]],
[TENSOR,[2,8]],
[TENSOR,[2,9]],
[TENSOR,[2,10]],
[TENSOR,[2,11]],
[TENSOR,[2,12]],
[TENSOR,[2,13]],
[TENSOR,[2,14]],
[TENSOR,[2,15]],
[TENSOR,[2,16]],
[TENSOR,[2,17]],
[TENSOR,[2,18]],
[TENSOR,[2,19]],
[TENSOR,[2,20]],
[TENSOR,[2,21]],
[TENSOR,[2,22]],
[TENSOR,[2,23]],
[TENSOR,[2,24]],
[TENSOR,[2,25]],
[TENSOR,[2,26]],
[TENSOR,[2,27]],
[TENSOR,[2,28]],
[TENSOR,[2,29]],
[TENSOR,[2,30]],
[TENSOR,[2,31]],
[TENSOR,[2,32]],[62,3*E(5)-2*E(5)^2-2*E(5)^3+3*E(5)^4,
-2*E(5)+3*E(5)^2+3*E(5)^3-2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
],
[GALOIS,[63,2]]],
[(2,3),
( 5, 7, 9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,
 55,57,59,61,63)( 6, 8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,
 46,48,50,52,54,56,58,60,62,64)
]);
ARC("5^3:62","tomfusion",rec(name:="5^3:62",map:=[1,3,3,2,6,8,6,8,6,8,6,8,
6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,8,6,
8,6,8,6,8,6,8,6,8,6,8,6,8,6,8],text:=[
"fusion map is unique"
]));
ALF("5^3:62","L2(125)",[1,2,3,34,5,32,9,28,21,16,11,26,27,10,13,24,33,4,
31,6,25,12,7,30,15,22,29,8,19,18,17,20,23,14,5,32,9,28,21,16,11,26,27,10,
13,24,33,4,31,6,25,12,7,30,15,22,29,8,19,18,17,20,23,14],[
"fusion map is unique up to table automorphisms"
]);

MOT("6^2:D12",
[
"origin: Dixon's Algorithm"
],
[432,72,144,72,24,48,16,24,12,36,72,12,216,6,12,24,18,9,12,24],
[,[1,2,1,2,1,1,1,1,2,2,13,13,13,17,4,3,17,18,11,3],[1,1,3,3,5,6,7,8,8,3,3,5,1,
6,16,16,1,1,20,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,-1,-1,-1,1,1,1,1,-1,1,-1,1
,1,1,1,-1,-1],[1,1,1,1,-1,1,1,-1,-1,1,1,-1,1,1,-1,-1,1,1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,0,-2,-2,0,0,2,2,0,2,1,0,0,-1,-1,0,0],
[TENSOR,[5,2]],[2,-1,2,-1,0,0,0,-2,1,-1,2,0,2,0,1,-2,2,-1,0,0],
[TENSOR,[7,3]],[3,3,-1,-1,-1,-3,1,1,1,-1,-1,-1,3,0,-1,-1,0,0,1,1],
[TENSOR,[9,4]],
[TENSOR,[9,3]],
[TENSOR,[9,2]],[4,-2,4,-2,0,0,0,0,0,-2,4,0,4,0,0,0,-2,1,0,0],[6,0,6,0,-2,0,0,
0,0,0,-3,1,-3,0,0,0,0,0,1,-2],
[TENSOR,[14,2]],[6,-3,-2,1,0,0,0,-2,1,1,-2,0,6,0,-1,2,0,0,0,0],
[TENSOR,[16,3]],[6,0,-2,4,-2,0,0,0,0,-2,1,1,-3,0,0,0,0,0,-1,2],
[TENSOR,[18,2]],[12,0,-4,-4,0,0,0,0,0,2,2,0,-6,0,0,0,0,0,0,0]],
[]);
ARC("6^2:D12","tomfusion",rec(name:="6^2:D12",map:=[1,7,2,29,5,6,3,4,31,
34,23,28,9,27,60,16,10,8,48,17],text:=[
"fusion map is unique"
]));
ALF("6^2:D12","U3(5).3.2",[1,11,2,13,22,22,22,2,14,14,7,24,3,24,15,4,3,12,
27,23],[
"fusion map is unique"
]);
ALF("6^2:D12","3.A7.2",[1,5,3,11,3,16,17,16,19,12,4,4,2,19,22,18,5,6,8,7],[
"fusion map is unique"
]);
ALF("6^2:D12","3.M22.2",[1,5,3,12,3,23,24,23,27,13,4,4,2,27,30,25,5,5,9,8],[
"fusion map is unique"
]);

MOT("6^2:S3",
[
"origin: Dixon's Algorithm"
],
[216,12,12,72,72,12,72,72,72,9,9,12,9,12,12,36,36,36,108],
[,[1,1,5,9,9,9,5,1,5,10,13,4,11,7,8,19,5,9,19],[1,2,2,8,1,2,8,8,1,1,1,15,1,15,
15,8,8,8,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[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)^2,E(3)^2,-E(3)^2,E(3),1,E(3),1,E(3)^2,-E(3),E(3),
-E(3)^2,-1,1,E(3),E(3)^2,1],
[GALOIS,[3,2]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,0,0,2,2,0,2,2,2,-1,-1,0,-1,0,0,2,2,2,2],
[TENSOR,[7,4]],
[TENSOR,[7,3]],[3,-1,-1,-1,3,-1,-1,-1,3,0,0,1,0,1,1,-1,-1,-1,3],
[TENSOR,[10,2]],
[TENSOR,[10,6]],
[TENSOR,[10,5]],
[TENSOR,[10,4]],
[TENSOR,[10,3]],[6,0,0,0,0,0,0,6,0,0,0,0,0,0,0,-3,0,0,-3],[6,0,0,4,0,0,4,-2,0
,0,0,0,0,0,0,1,-2,-2,-3],
[TENSOR,[17,3]],
[TENSOR,[17,4]]],
[( 3, 6)( 4, 7)( 5, 9)(11,13)(12,14)(17,18)]);
ARC("6^2:S3","tomfusion",rec(name:="6^2:S3",map:=[1,3,11,14,5,11,14,2,5,6,
7,25,7,25,9,12,16,16,4],text:=[
"fusion map is unique"
]));
ALF("6^2:S3","U3(5).3",[1,2,19,18,14,20,17,2,13,3,16,21,15,22,4,7,19,20,3],[
"fusion map is unique up to table automorphisms"
]);

MOT("7^(1+2):48",
[
"origin: Dixon's Algorithm"
],
[16464,2744,49,48,48,336,56,48,48,336,56,48,48,336,56,48,48,336,56,48,48,336,
56,48,48,336,56,48,48,336,56,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,
48,48,48,48,48,48,48,48,48,48],
[,[1,2,3,5,4,1,2,5,4,6,7,9,8,6,7,9,8,10,11,13,12,10,11,13,12,14,15,17,16,14,15
,17,16,21,20,18,21,20,18,25,24,22,25,24,22,29,28,26,29,28,26,33,32,30,33,32,30
],[1,2,3,1,1,6,7,6,6,14,15,14,14,10,11,10,10,26,27,26,26,30,31,30,30,18,19,18,
18,22,23,22,22,48,48,48,51,51,51,57,57,57,54,54,54,39,39,39,36,36,36,42,42,42,
45,45,45],,,,[1,1,1,4,5,6,6,8,9,14,14,16,17,10,10,12,13,30,30,32,33,26,26,28,
29,22,22,24,25,18,18,20,21,52,53,54,55,56,57,46,47,48,49,50,51,40,41,42,43,44,
45,34,35,36,37,38,39]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-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(4),-E(4),-E(4),-E(4),E(4),
E(4),E(4),E(4),-E(8)^3,-E(8)^3,-E(8)^3,-E(8)^3,E(8)^3,E(8)^3,E(8)^3,E(8)^3,
-E(8),-E(8),-E(8),-E(8),E(8),E(8),E(8),E(8),-E(16)^7,-E(16)^7,-E(16)^7,E(16)^7
,E(16)^7,E(16)^7,-E(16)^3,-E(16)^3,-E(16)^3,E(16)^3,E(16)^3,E(16)^3,-E(16)^5,
-E(16)^5,-E(16)^5,E(16)^5,E(16)^5,E(16)^5,-E(16),-E(16),-E(16),E(16),E(16),
E(16)],
[TENSOR,[2,3]],
[GALOIS,[3,5]],
[TENSOR,[2,5]],
[GALOIS,[3,3]],
[TENSOR,[2,7]],
[GALOIS,[3,7]],
[TENSOR,[2,9]],
[TENSOR,[3,3]],
[TENSOR,[2,11]],
[TENSOR,[3,5]],
[TENSOR,[2,13]],
[TENSOR,[3,7]],
[TENSOR,[2,15]],[1,1,1,E(3)^2,E(3),-1,-1,-E(3)^2,-E(3),-E(4),-E(4),-E(12)^11,
-E(12)^7,E(4),E(4),E(12)^11,E(12)^7,-E(8)^3,-E(8)^3,-E(24),-E(24)^17,E(8)^3,
E(8)^3,E(24),E(24)^17,-E(8),-E(8),-E(24)^19,-E(24)^11,E(8),E(8),E(24)^19,
E(24)^11,-E(48)^5,-E(48)^37,-E(16)^7,E(48)^5,E(48)^37,E(16)^7,-E(48)^41,
-E(48)^25,-E(16)^3,E(48)^41,E(48)^25,E(16)^3,-E(48)^47,-E(48)^31,-E(16)^5,
E(48)^47,E(48)^31,E(16)^5,-E(48)^35,-E(48)^19,-E(16),E(48)^35,E(48)^19,E(16)],
[TENSOR,[2,17]],
[TENSOR,[17,15]],
[TENSOR,[2,19]],
[TENSOR,[17,11]],
[TENSOR,[2,21]],
[TENSOR,[17,13]],
[TENSOR,[2,23]],
[GALOIS,[17,17]],
[TENSOR,[2,25]],
[TENSOR,[25,15]],
[TENSOR,[2,27]],
[TENSOR,[25,11]],
[TENSOR,[2,29]],
[TENSOR,[25,13]],
[TENSOR,[2,31]],
[TENSOR,[3,17]],
[TENSOR,[2,33]],
[TENSOR,[3,19]],
[TENSOR,[2,35]],
[TENSOR,[3,25]],
[TENSOR,[2,37]],
[TENSOR,[3,27]],
[TENSOR,[2,39]],
[TENSOR,[3,21]],
[TENSOR,[2,41]],
[TENSOR,[3,29]],
[TENSOR,[2,43]],
[TENSOR,[3,23]],
[TENSOR,[3,31]],
[TENSOR,[2,45]],
[TENSOR,[2,46]],[42,-7,0,0,0,-6,1,0,0,-6,1,0,0,-6,1,0,0,-6,1,0,0,-6,1,0,0,-6,
1,0,0,-6,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[49,15]],
[TENSOR,[49,13]],
[TENSOR,[49,11]],
[TENSOR,[49,9]],
[TENSOR,[49,7]],
[TENSOR,[49,5]],
[TENSOR,[49,3]],[48,48,-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]],
[
(34,37)(35,38)(36,39)(40,43)(41,44)(42,45)(46,49)(47,50)(48,51)(52,55)(53,56)
(54,57)
,
(18,22)(19,23)(20,24)(21,25)(26,30)(27,31)(28,32)(29,33)(34,40,37,43)
(35,41,38,44)(36,42,39,45)(46,55,49,52)(47,56,50,53)(48,57,51,54)
,
(10,14)(11,15)(12,16)(13,17)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)
(25,33)(34,46,37,49)(35,47,38,50)(36,48,39,51)(40,55,43,52)(41,56,44,53)
(42,57,45,54)
,
( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29)(32,33)(34,35)(37,38)(40,41)
(43,44)(46,47)(49,50)(52,53)(55,56)
]);
ARC("7^(1+2):48","tomfusion",rec(name:="7^(1+2):48",map:=[1,6,7,3,3,2,10,
5,5,4,16,9,9,4,16,9,9,8,21,15,15,8,21,15,15,8,21,15,15,8,21,15,15,19,19,
12,19,19,12,19,19,12,19,19,12,19,19,12,19,19,12,19,19,12,19,19,12],text:=[
"fusion map is unique"
]));
ALF("7^(1+2):48","U3(7)",[1,8,9,3,3,2,22,7,7,4,31,20,20,5,32,21,21,10,55,
27,27,12,57,29,29,13,58,30,30,11,56,28,28,47,51,23,51,47,23,53,49,25,49,
53,25,54,50,26,50,54,26,48,52,24,52,48,24],[
"fusion map is unique up to table automorphisms"
]);

MOT("7^2:2A4",
[
"origin: Dixon's Algorithm"
],
[1176,147,147,147,49,24,4,42,21,21,21,6,42,21,21,21,6],
[,[1,4,2,3,5,1,6,13,16,14,15,13,8,11,9,10,8],[1,3,4,2,5,6,7,1,4,2,3,6,1,4,2,3,
6],,,,[1,1,1,1,1,6,7,8,8,8,8,12,13,13,13,13,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,E(3)^2,E(3)^2,E(3)^2,
E(3)^2,E(3)^2,E(3),E(3),E(3),E(3),E(3)],
[TENSOR,[2,2]],[2,2,2,2,2,-2,0,-1,-1,-1,-1,1,-1,-1,-1,-1,1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[3,3,3,3,3,3,-1,0,0,0,0,0,0,0,0,0,0],[8,
3*E(7)+E(7)^2+E(7)^5+3*E(7)^6,E(7)+3*E(7)^3+3*E(7)^4+E(7)^6,
3*E(7)^2+E(7)^3+E(7)^4+3*E(7)^5,1,0,0,2*E(3)^2,E(21)^11+E(21)^17,
E(21)^2+E(21)^5,E(21)^8+E(21)^20,0,2*E(3),E(21)^4+E(21)^10,E(21)^16+E(21)^19,
E(21)+E(21)^13,0],
[TENSOR,[8,2]],
[GALOIS,[8,4]],
[TENSOR,[10,2]],
[GALOIS,[8,16]],
[TENSOR,[12,2]],
[TENSOR,[8,3]],
[TENSOR,[10,3]],
[TENSOR,[12,3]],[24,3,3,3,-4,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 8,13)( 9,14)(10,15)(11,16)(12,17),( 2, 3, 4)( 9,10,11)(14,15,16)]);
ARC("7^2:2A4","tomfusion",rec(name:="7^2:2A4",map:=[1,7,7,7,6,2,4,3,11,11,
11,5,3,11,11,11,5],text:=[
"fusion map is unique"
]));
ALF("7^2:2A4","3D4(2)",[1,11,13,12,14,3,8,4,32,31,30,10,4,32,31,30,10],[
"fusion map is unique up to table automorphisms"
]);
ALN("7^2:2A4",["3D4(2)N7"]);

MOT("7^2:S3",
[
"origin: Dixon's Algorithm"
],
[294,14,3,98,14,14,98,14,14,98,14,14,98,49,49,49,49,49,98,98],
[,[1,1,3,7,19,7,10,20,10,4,4,13,19,18,15,16,14,17,20,13],[1,2,1,13,9,5,19,11,8
,20,12,6,7,17,16,15,18,14,10,4],,,,[1,2,3,1,2,2,1,2,2,1,2,2,1,1,1,1,1,1,1,1]],
[[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],[2,0,-1,2,0,0,2,0,0,2,0,0,2,2,2,2,2,2,2,2],[3,-1,0,
E(7)^4+2*E(7)^5,-E(7)^5,-E(7)^4,E(7)+2*E(7)^3,-E(7)^3,-E(7),E(7)^2+2*E(7)^6,
-E(7)^2,-E(7)^6,2*E(7)+E(7)^5,-E(7)^2-E(7)^3-E(7)^4-E(7)^5,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,-E(7)-E(7)^2-E(7)^5-E(7)^6,
-E(7)-E(7)^3-E(7)^4-E(7)^6,2*E(7)^2+E(7)^3,2*E(7)^4+E(7)^6],
[GALOIS,[4,5]],
[GALOIS,[4,4]],
[GALOIS,[4,6]],
[GALOIS,[4,2]],
[GALOIS,[4,3]],
[TENSOR,[4,2]],
[TENSOR,[5,2]],
[TENSOR,[6,2]],
[TENSOR,[7,2]],
[TENSOR,[8,2]],
[TENSOR,[9,2]],[6,0,0,-2*E(7)-2*E(7)^2-2*E(7)^5-2*E(7)^6,0,0,
-2*E(7)^2-2*E(7)^3-2*E(7)^4-2*E(7)^5,0,0,-2*E(7)-2*E(7)^3-2*E(7)^4-2*E(7)^6,0,
0,-2*E(7)-2*E(7)^3-2*E(7)^4-2*E(7)^6,E(7)+2*E(7)^3+2*E(7)^4+E(7)^6,-1,-1,
2*E(7)^2+E(7)^3+E(7)^4+2*E(7)^5,2*E(7)+E(7)^2+E(7)^5+2*E(7)^6,
-2*E(7)-2*E(7)^2-2*E(7)^5-2*E(7)^6,-2*E(7)^2-2*E(7)^3-2*E(7)^4-2*E(7)^5],
[GALOIS,[16,2]],
[GALOIS,[16,3]],[6,0,0,2*E(7)^3+2*E(7)^5+2*E(7)^6,0,0,
2*E(7)^3+2*E(7)^5+2*E(7)^6,0,0,2*E(7)^3+2*E(7)^5+2*E(7)^6,0,0,
2*E(7)+2*E(7)^2+2*E(7)^4,-1,
-2*E(7)-2*E(7)^2-3*E(7)^3-2*E(7)^4-3*E(7)^5-3*E(7)^6,
-3*E(7)-3*E(7)^2-2*E(7)^3-3*E(7)^4-2*E(7)^5-2*E(7)^6,-1,-1,
2*E(7)+2*E(7)^2+2*E(7)^4,2*E(7)+2*E(7)^2+2*E(7)^4],
[GALOIS,[19,3]]],
[( 4, 7,10)( 5, 8,12)( 6, 9,11)(13,19,20)(14,18,17),
( 4,13, 7,19,10,20)( 5, 9, 8,11,12, 6)(14,17,18)(15,16)]);
ARC("7^2:S3","tomfusion",rec(name:="7^2:S3",map:=[1,2,3,7,9,9,7,9,9,7,9,9,
7,6,5,5,6,6,7,7],text:=[
"fusion map is unique"
]));
ALF("7^2:S3","L3(8)",[1,2,3,5,24,19,7,20,21,9,23,22,10,14,12,11,13,15,6,8],[
"fusion map is unique up to table automorphisms"
]);

MOT("8^2:S3",
[
"origin: Dixon's Algorithm"
],
[384,16,128,16,16,128,16,128,128,128,128,128,16,3,16,16,16,64,64,64,64,64,64,
64],
[,[1,10,9,3,6,9,11,1,8,12,12,8,1,14,9,12,8,24,24,12,24,9,24,8],[1,4,10,2,7,11,
5,8,12,3,6,9,13,1,16,15,17,23,19,22,21,20,18,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,1,-1,-1,1,-1,1,1,1,1,
1,-1,1,-1,-1,-1,1,1,1,1,1,1,1],[2,0,2,0,0,2,0,2,2,2,2,2,0,-1,0,0,0,2,2,2,2,2,2
,2],[3,-1,-1,-1,-1,-1,-1,3,3,-1,-1,3,1,0,1,1,1,-1,-1,-1,-1,-1,-1,3],
[TENSOR,[4,2]],[3,-E(4),-1-2*E(4),E(4),E(4),-1-2*E(4),-E(4),3,-1,-1+2*E(4),
-1+2*E(4),-1,1,0,-1,-1,1,1,1,-1+2*E(4),1,-1-2*E(4),1,-1],
[GALOIS,[6,3]],
[TENSOR,[7,2]],
[TENSOR,[6,2]],[3,-E(8),-2*E(8)-E(8)^2,-E(8)^3,E(8)^3,2*E(8)-E(8)^2,E(8),-1,
-1+2*E(4),E(8)^2-2*E(8)^3,E(8)^2+2*E(8)^3,-1-2*E(4),-1,0,E(4),-E(4),1,
1+E(8)-E(8)^3,-1+E(8)+E(8)^3,-E(4),-1-E(8)-E(8)^3,E(4),1-E(8)+E(8)^3,1],
[GALOIS,[10,3]],
[GALOIS,[10,7]],
[GALOIS,[10,5]],
[TENSOR,[13,2]],
[TENSOR,[12,2]],
[TENSOR,[11,2]],
[TENSOR,[10,2]],[6,0,2,0,0,2,0,6,-2,2,2,-2,0,0,0,0,0,-2,-2,2,-2,2,-2,-2],[6,0
,-2-2*E(8)-2*E(8)^3,0,0,-2+2*E(8)+2*E(8)^3,0,-2,2,-2-2*E(8)-2*E(8)^3,
-2+2*E(8)+2*E(8)^3,2,0,0,0,0,0,0,-2*E(8)-2*E(8)^3,2,2*E(8)+2*E(8)^3,2,0,-2],
[GALOIS,[19,5]],[6,0,2+2*E(8)-2*E(8)^3,0,0,2-2*E(8)+2*E(8)^3,0,-2,2,
2-2*E(8)+2*E(8)^3,2+2*E(8)-2*E(8)^3,2,0,0,0,0,0,2*E(8)-2*E(8)^3,0,-2,0,-2,
-2*E(8)+2*E(8)^3,-2],
[GALOIS,[21,3]],[6,0,-2*E(4),0,0,-2*E(4),0,-2,-2-4*E(4),2*E(4),2*E(4),
-2+4*E(4),0,0,0,0,0,-2,2,-2*E(4),2,2*E(4),-2,2],
[GALOIS,[23,3]]],
[( 2, 7)( 3, 6)( 4, 5)(10,11)(18,23)(19,21),
( 2, 4)( 3,10)( 5, 7)( 6,11)( 9,12)(15,16)(18,23)(20,22)]);
ARC("8^2:S3","tomfusion",rec(name:="8^2:S3",map:=[1,32,13,32,32,13,32,2,6,
13,13,6,3,4,18,18,8,12,15,14,15,14,12,7],text:=[
"fusion map is unique"
]));
ALF("8^2:S3","L3(9)",[1,31,15,33,32,14,34,2,6,13,16,5,2,4,18,17,7,19,22,
17,21,18,20,7],[
"fusion map is unique up to table automorphisms"
]);
ALF("8^2:S3","U3(7)",[1,23,13,26,24,11,25,2,5,10,12,4,2,3,15,14,6,16,19,
14,18,15,17,6],[
"fusion map is unique up to table automorphisms"
]);

LIBTABLE.LOADSTATUS.ctomax19:="userloaded";

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