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,
--> --------------------

--> maximum size reached

--> --------------------