#############################################################################
##
#W ctomaxi6.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables of maximal subgroups
## (which are neither ATLAS tables nor tables of Ostermann) of the
## sporadic Janko groups.
##
#H ctbllib history
#H ---------------
#H $Log: ctomaxi6.tbl,v $
#H Revision 4.40 2012/06/20 14:45:32 gap
#H added tables and fusions, as documented in ctbldiff.dat
#H TB
#H
#H Revision 4.39 2012/01/30 08:31:56 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.38 2012/01/26 11:18:40 gap
#H added missing table automorphisms
#H TB
#H
#H Revision 4.37 2011/09/28 13:19:46 gap
#H - removed revision entry and SET_TABLEFILENAME call,
#H - added table of (2.A5xD10).2,
#H - changed constructions of the tables of F3+M7 (use `ConstructAdjusted'
#H not `ConstructPermuted') and j3m6 (which is a subdirect product)
#H - added fusion (A5xD10).2 -> He
#H TB
#H
#H Revision 4.36 2010/12/01 17:47:57 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 4.35 2010/05/05 13:20:06 gap
#H - added many class fusions,
#H - changed several class fusions according to consistency conditions,
#H after systematic checks of consistency
#H - with Brauer tables w.r.t. the restriction of characters,
#H - of subgroup fusions with the corresponding subgroup fusions between
#H proper factors where the factor fusions are stored,
#H - of subgroup fusions from maximal subgroups with subgroup fusions of
#H extensions inside automorphic extensions
#H
#H TB
#H
#H Revision 4.34 2009/07/29 14:00:14 gap
#H added fusion 13:6 -> A13
#H TB
#H
#H Revision 4.33 2009/04/22 12:39:05 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.32 2007/07/03 08:50:15 gap
#H added fusions,
#H encoded several tables as index two subdirect products
#H TB
#H
#H Revision 4.31 2005/08/10 14:36:00 gap
#H added fusion 2^11.M24 = F3+M7 -> 2^12.M24
#H TB
#H
#H Revision 4.30 2005/04/27 07:46:09 gap
#H added fusion 29:28 -> F3+.2
#H TB
#H
#H Revision 4.29 2004/08/31 12:33:33 gap
#H added tables of 4.L2(25).2_3,
#H L2(49).2^2,
#H L2(81).2^2,
#H L2(81).(2x4),
#H 3.L3(4).3.2_2,
#H L3(9).2^2,
#H L4(4).2^2,
#H 2x2^3:L3(2)x2,
#H (2xA6).2^2,
#H 2xL2(11).2,
#H S3xTh,
#H 41:40,
#H 7^(1+4):(3x2.S7),
#H 7xL2(8),
#H (7xL2(8)).3,
#H O7(3)N3A,
#H O8+(3).2_1',
#H O8+(3).2_1'',
#H O8+(3).2_2',
#H O8+(3).(2^2)_{122},
#H S4(9),
#H S4(9).2_i,
#H 2.U4(3).2_2',
#H 2.U4(3).(2^2)_{133},
#H 2.U4(3).D8,
#H 3.U6(2).S3,
#H added fusions 3.A6.2_i -> 3.A6.2^2,
#H L2(49).2_i -> L2(49).2^2,
#H L3(9).2_i -> L3(9).2^2,
#H L4(4).2_i -> L4(4).2^2,
#H G2(3) -> O7(3),
#H L2(17) -> S8(2),
#H 2.L3(4).2_2 -> 2.M22.2
#H 3.L3(4).2_2 -> 3.L3(4).3.2_2
#H 3.L3(4).3 -> 3.L3(4).3.2_2
#H 2^5:S6 -> 2.M22.2
#H O8+(3) -> O8+(3).2_1',
#H O8+(3) -> O8+(3).2_1'',
#H O8+(3) -> O8+(3).2_2',
#H O8+(3) -> O8+(3).(2^2)_{122},
#H O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H 2.U4(3) -> 2.U4(3).2_2',
#H 2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).2_2 -> O7(3),
#H 2.U4(3).2_2' -> U4(3).2_2,
#H 2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).4 -> 2.U4(3).D8,
#H 3.U6(2).2 -> 3.U6(2).S3,
#H 3.U6(2).3 -> 3.U6(2).S3,
#H replaced table of psl(3,4):d12 by L3(4).D12,
#H changed table of O8+(3).S4 to a construction table,
#H changed encoding of the table of 12.A6.2_3,
#H added maxes of Sz(8), Sz(8).3,
#H TB
#H
#H Revision 4.28 2004/01/20 10:26:13 gap
#H added several names of the forms `<name>C<class>', `<name>N<class>'
#H TB
#H
#H Revision 4.27 2003/06/20 15:03:03 gap
#H added several fusions
#H TB
#H
#H Revision 4.26 2003/05/15 17:38:14 gap
#H next step towards the closer connection to the library of tables of marks:
#H added fusions tbl -> tom, adjusted fusions between character tables
#H in order to make the diagrams commute, adjusted orderings of maxes
#H TB
#H
#H Revision 4.25 2003/05/05 14:24:03 gap
#H adjusted fusion texts (no longer ambiguous when s.c. are used)
#H TB
#H
#H Revision 4.24 2003/03/07 15:53:39 gap
#H added tables of `Isoclinic(2.A5.2)' and `L2(125)',
#H and many `tomidentifier' components (still several are missing)
#H TB
#H
#H Revision 4.23 2003/01/21 16:25:32 gap
#H further standardizations of `InfoText' strings,
#H added and corrected `Maxes' infos,
#H added some fusions
#H TB
#H
#H Revision 4.22 2003/01/14 17:28:50 gap
#H changed `InfoText' values (for a better programmatic access)
#H and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H there is only one factor (again better programmatic handling)
#H TB
#H
#H Revision 4.21 2002/10/22 12:44:10 gap
#H added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H (they make it possible to construct <p>-modular Brauer tables
#H for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H of <fact> is in the library)
#H TB
#H
#H Revision 4.20 2002/09/23 14:56:43 gap
#H removed trailing blanks,
#H replaced 2xA5, D6xD10, A5xD10 by ``constructoin'' tables,
#H TB
#H
#H Revision 4.19 2002/09/18 15:22:01 gap
#H changed the `text' components of many fusions,
#H in order to use them as a status information (for evaluation)
#H TB
#H
#H Revision 4.18 2002/09/05 15:03:11 gap
#H fixed a fusion comment (will be used programmatically in the future)
#H TB
#H
#H Revision 4.17 2002/08/21 14:50:48 gap
#H added fusion D6xD10 -> L2(16).2
#H TB
#H
#H Revision 4.16 2002/08/01 13:18:58 gap
#H added fusion 2^(1+4).S5 -> J2.2
#H TB
#H
#H Revision 4.15 2002/07/17 15:25:32 gap
#H added missing table automorphisms
#H TB
#H
#H Revision 4.14 2002/07/12 06:45:55 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.13 2002/07/08 16:06:56 gap
#H changed `construction' component from function (call) to list of function
#H name and arguments
#H TB
#H
#H Revision 4.12 2002/03/25 18:11:45 gap
#H added fusion D6xD10 -> J3, and some names for D6xD10
#H TB
#H
#H Revision 4.11 2002/03/04 17:08:48 gap
#H added some fusions and admissible names
#H TB
#H
#H Revision 4.10 2001/05/04 16:48:30 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.10 of ctbllib coincides with Rev. 4.9 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctomaxi6.tbl,v
#H Working file: ctomaxi6.tbl
#H head: 4.9
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.9.0.6
#H GAP4R2PRE2: 4.9.0.4
#H GAP4R2PRE1: 4.9.0.2
#H GAP4R1: 4.6.0.2
#H keyword substitution: kv
#H total revisions: 11; selected revisions: 11
#H description:
#H ----------------------------
#H revision 4.9
#H date: 1999/10/22 13:24:48; author: gap; state: Exp; lines: +72 -3
#H added maxes of J2.2
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 1999/10/21 14:15:47; author: gap; state: Exp; lines: +19 -36
#H added many `tomidentifer' and `tomfusion' values, which yields a better
#H interface between `tom' and `tbl';
#H
#H added maxes of McL.2,
#H
#H unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1999/10/04 15:57:15; author: gap; state: Exp; lines: +5 -2
#H added and corrected several fusions from character tables
#H to their tables of marks,
#H unified two instances of the table of (A6xA6):2^2,
#H corrected the name of the table of marks of 2F4(2).
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 1999/07/14 11:39:40; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1999/03/25 12:32:29; author: gap; state: Exp; lines: +36 -4
#H added fusions and tables for completing maxes of M12.2
#H
#H TB
#H ----------------------------
#H revision 4.4
#H date: 1998/04/03 09:44:48; author: gap; state: Exp; lines: +265 -253
#H renamed table `l52m10' to `2^10:L5(2)',
#H reordered classes and characters,
#H added fusion into O10+(2)
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1998/03/11 08:05:46; author: gap; state: Exp; lines: +12 -2
#H mainly new fusions to tables of marks added
#H
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/11/25 15:45:17; author: gap; state: Exp; lines: +22 -6
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:43:17; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.2
#H date: 1997/04/04 12:20:11; author: sam; state: Exp; lines: +23 -21
#H added 'ConstructPermuted', 'ConstructSubdirect',
#H changed table constructions involving 'CharTable', 'RecFields'
#H 'Sort...' up to now
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 16:00:15; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("(2x3.A6).2",
[
"2nd maximal subgroup of 2.J2,\n",
"isoclinic table of 2x3.A6_2_2"
],
0,
0,
0,
[(25,27)(26,28),(23,24)(25,26)(27,28)(29,30)(31,32),(15,19)(16,20)(17,21)(18,
22)(29,31)(30,32)],
["ConstructIsoclinic",[["3.A6.2_2"],["Cyclic",2]],[1..22]]);
ALF("(2x3.A6).2","2.J2",[1,2,6,7,3,4,20,21,8,9,10,11,33,34,12,13,35,36,14,
15,37,38,5,5,25,26,25,26,27,27,28,28],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(2x3.A6).2","3.A6.2_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]);
ALF("(2x3.A6).2","C4",[1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,2,4,2,
4,2,4,2,4,2,4]);
MOT("(2xL3(2)).2",
[
"7th maximal subgroup of 2.J2,\n",
"isoclinic table of 2xL3(2).2"
],
0,
0,
0,
[(11,12)(13,14)(15,16)(17,18),(15,17)(16,18)],
["ConstructIsoclinic",[["L3(2).2"],["Cyclic",2]],[1..10]]);
ALF("(2xL3(2)).2","2.J2",[1,2,3,4,8,9,10,11,23,24,5,5,22,22,25,26,25,26],[
"fusion map is unique up to table automorphisms"
]);
ALF("(2xL3(2)).2","L3(2).2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9]);
ALF("(2xL3(2)).2","C4",[1,3,1,3,1,3,1,3,1,3,2,4,2,4,2,4,2,4]);
MOT("(3xM10):2",
[
"source: H. Pahlings,\n",
"6th maximal subgroup of J3.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[4320,2160,96,48,54,27,48,24,30,15,48,16,6,40,8,10,24,12,24,24,24],
[,[1,2,1,2,5,6,3,4,9,10,1,3,5,1,7,9,3,4,7,8,8],[1,1,3,3,1,1,7,7,9,9,11,12,11,
14,15,16,17,17,19,19,19],,[1,2,3,4,5,6,7,8,1,2,11,12,13,14,15,14,17,18,19,20,
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],
[TENSOR,[2,3]],[10,10,2,2,1,1,-2,-2,0,0,2,2,-1,0,0,0,0,0,0,0,0],
[TENSOR,[5,3]],[16,16,0,0,-2,-2,0,0,1,1,0,0,0,4,0,-1,0,0,0,0,0],
[TENSOR,[7,2]],[9,9,1,1,0,0,1,1,-1,-1,3,-1,0,-1,1,-1,1,1,-1,-1,-1],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[20,20,-4,-4,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,-1,2,-1,2,
-1,2,-1,2,-1,0,0,0,0,0,0,2,-1,2,-1,-1],
[TENSOR,[14,2]],[18,-9,2,-1,0,0,2,-1,-2,1,0,0,0,0,0,0,2,-1,-2,1,1],
[TENSOR,[16,2]],[20,-10,4,-2,2,-1,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,-10,-4,
2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(24)+E(24)^11+E(24)^17-E(24)^19,
E(24)-E(24)^11-E(24)^17+E(24)^19],
[TENSOR,[19,2]],[32,-16,0,0,-4,2,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0]],
[(20,21)]);
ARC("(3xM10):2","tomfusion",rec(name:="(3xM10):2",map:=[1,5,2,18,6,7,9,42,
15,50,3,12,22,4,29,39,10,47,24,69,69],text:=[
"fusion map is unique"
]));
ALF("(3xM10):2","J3.2",[1,3,2,7,4,3,5,13,6,14,18,19,20,2,8,12,19,23,21,27,
28],[
"fusion map is unique up to table automorphisms"
]);
ALF("(3xM10):2","A6.2^2",[1,1,2,2,3,3,4,4,5,5,6,7,8,9,10,11,12,12,13,13,13]);
ALF("(3xM10):2","S3",[1,2,1,2,1,2,1,2,1,2,3,3,3,3,3,3,1,2,1,2,2]);
MOT("11:10",
[
"origin: CAS library,\n",
"maximal subgroup of J1,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly\n",
"constructions: AGL(1,11),\n",
"tests: 1.o.r., pow[2,5,11]"
],
0,
0,
0,
[( 3, 9,11, 5)( 4, 6,10, 8)],
["ConstructPermuted",["P:Q",[11,10]]]);
ARC("11:10","tomfusion",rec(name:="11:10",map:=[1,5,4,3,4,3,2,3,4,3,4],text:=[
"fusion map is unique"
]));
ALF("11:10","A11.2",[1,21,46,11,46,11,32,11,46,11,46],[
"fusion map is unique"
]);
ALF("11:10","J1",[1,10,9,4,8,5,2,5,8,4,9],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("11:10","L2(11).2",[1,7,10,5,11,4,8,4,11,5,10],[
"fusion is unique up to table automorphisms"
]);
ALF("11:10","M12.2",[1,12,17,7,18,7,13,7,18,7,17],[
"fusion is unique up to table automorphisms"
]);
ALF("11:10","M24",[1,16,15,9,15,9,3,9,15,9,15],[
"fusion map is unique"
]);
ALF("11:10","Suz",[1,26,25,12,25,12,3,12,25,12,25],[
"fusion map is unique"
]);
ALF("11:10","ON",[1,13,12,6,12,6,2,6,12,6,12],[
"fusion map is unique"
]);
ALF("11:10","Co2",[1,33,32,15,32,15,4,15,32,15,32],[
"fusion map is unique"
]);
ALF("11:10","HS.2",[1,18,33,10,33,10,23,10,33,10,33],[
"fusion map is unique"
]);
ALF("11:10","M22.2",[1,11,18,6,18,6,13,6,18,6,18],[
"fusion map is unique"
]);
ALN("11:10",["AGL(1,11)","J1N11","L2(11).2N11","M12.2N11","M24N11","SuzN11",
"ONN11","Co2N11"]);
MOT("13:6",
0,
0,
0,
0,
[(2,3),(4,8)(5,7)],
["ConstructPermuted",["P:Q",[13,6]]]);
ARC("13:6","tomfusion",rec(name:="13:6",map:=[1,5,5,4,3,2,3,4],text:=[
"fusion map is unique"
]));
ALF("13:6","L2(13)",[1,8,9,4,3,2,3,4],[
"fusion map is unique up to table autom."
]);
ALF("13:6","L3(3).2",[1,8,9,12,4,10,4,12],[
"fusion map is unique up to table autom."
]);
ALF("13:6","Suz",[1,32,33,17,6,3,6,17],[
"fusion is unique up to table automorphisms"
]);
ALF("13:6","U3(4).2",[1,11,12,16,3,15,3,16],[
"fusion map is unique up to table autom."
]);
ALF("13:6","13:12",[1,2,2,4,6,8,10,12],[
"fusion map is unique up to table autom."
]);
ALF("13:6","2x13:6",[1,3,5,7,9,11,13,15]);
ALF("13:6","A13",[1,39,40,22,8,4,8,22],[
"fusion map is unique up to table automorphisms"
]);
ALF("13:6","2F4(2)'",[1,17,18,9,4,3,4,9],[
"fusion map is unique up to table autom."
]);
ALF("13:6","G2(3)",[1,22,23,12,6,2,6,12],[
"fusion map determined using that 13:6 contains 3D elements"
]);
ALF("13:6","G2(4)",[1,25,26,14,5,3,5,14],[
"fusion map is unique up to table autom."
]);
ALF("13:6","Fi22",[1,49,50,25,8,4,8,25],[
"fusion map determined by factorization through 2F4(2)'"
]);
ALF("13:6","O7(3)",[1,51,50,32,11,4,11,32],[
"fusion map determined by factorization through G2(3)"
]);
ALN("13:6",["Fi22N13","G2(3)N13","G2(4)N13","O7(3)N13","SuzN13",
"2F4(2)'N13"]);
MOT("19:18",
[
"3rd maximal subgroup of J3.2,\n",
"constructions: AGL(1,19)"
],
0,
0,
0,
[( 3, 7, 9,19,15,13)( 4,12,16,18,10, 6)( 5,17)( 8,14)],
["ConstructPermuted",["P:Q",[19,18]]]);
ARC("19:18","tomfusion",rec(name:="19:18",map:=[1,7,6,5,4,5,6,3,6,5,2,5,6,
3,6,5,4,5,6],text:=[
"fusion map is unique"
]));
ALF("19:18","L2(19).2",[1,11,15,7,14,8,17,3,16,6,12,6,16,3,17,8,14,7,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("19:18","J3.2",[1,17,26,9,20,10,25,4,24,11,18,11,24,4,25,10,20,9,26],[
"compatible with 19:9 -> J3"
]);
ALF("19:18","Th",[1,29,28,17,11,17,28,4,28,17,2,17,28,4,28,17,11,17,28],[
"fusion determined by the fact that L2(19).2 contains 9C elements of Th"
]);
ALF("19:18","HN.2",[1,33,61,19,51,19,61,5,61,19,45,19,61,5,61,19,51,19,61],[
"fusion map is unique"
]);
ALN("19:18",["AGL(1,19)","ThN19","L2(19).2M2","R(27).3N19","R(27).3M7"]);
MOT("19:6",
[
"origin: CAS library,\n",
"maximal subgroup of J1,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly,\n",
"tests: 1.o.r., pow[2,3,19]"
],
[114,19,19,19,6,6,6,6,6],
[,[1,3,4,2,6,8,1,6,8],[1,3,4,2,7,1,7,1,7],,,,,,,,,,,,,,,,[1,1,1,1,5,6,7,8,9]],
[[1,1,1,1,1,1,1,1,1],[1,1,1,1,-E(3)^2,E(3),-1,E(3)^2,-E(3)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],[6,E(19)+E(19)^7+E(19)^8+E(19)^11+E(19)^12+E(19)^18,
E(19)^2+E(19)^3+E(19)^5+E(19)^14+E(19)^16+E(19)^17,E(19)^4+E(19)^6+E(19)^9
+E(19)^10+E(19)^13+E(19)^15,0,0,0,0,0],
[GALOIS,[7,2]],
[GALOIS,[7,4]]],
[(5,9)(6,8),(2,3,4)]);
ARC("19:6","tomfusion",rec(name:="19:6",map:=[1,5,5,5,4,3,2,3,4],text:=[
"fusion map is unique"
]));
ALF("19:6","19:18",[1,2,2,2,17,14,11,8,5],[
"fusion map is unique up to table autom."
]);
ALF("19:6","J1",[1,13,14,15,6,3,2,3,6],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("19:6","ON",[1,22,23,24,7,3,2,3,7],[
"fusion is unique up to table automorphisms"
]);
ALF("19:6","R(27)",[1,21,22,23,6,5,2,4,7],[
"fusion map is unique up to table aut."
]);
ALN("19:6",["J1N19","ONN19","R(27)M6","R(27)N19"]);
MOT("2.J2M8",
[
"8th maximal subgroup of 2.J2,\n",
"isoclinic table of 2x5^2:D12"
],
0,
0,
0,
[(17,18)(19,20)(21,22)(23,24)(25,26)(27,28),(11,12)(15,16)(23,24)(25,26)(27,
28),( 3, 5)( 4, 6)( 7, 9)( 8,10)(19,21)(20,22)(25,27)(26,28)],
["ConstructIsoclinic",[["5^2:D12"],["Cyclic",2]],[1,2,3,4,5,6,7,8,9,10,13,14,
17,18,19,20,21,22]]);
ALF("2.J2M8","2.J2",[1,2,12,13,14,15,18,19,16,17,5,5,8,9,22,22,3,4,29,30,
31,32,5,5,28,28,27,27],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.J2M8","C4",[1,3,1,3,1,3,1,3,1,3,2,4,1,3,2,4,1,3,1,3,1,3,2,4,2,4,2,
4]);
ALF("2.J2M8","5^2:D12",[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]);
ALF("2.J2M8","2.J2.2N5",[1,2,21,22,21,22,19,20,19,20,7,8,9,10,23,24,3,4,
25,26,25,26,5,6,27,28,27,28],[
"fusion map is unique up to table automorphisms"
]);
ALF("2.J2M8","2.G2(4)",[1,2,14,15,16,17,20,21,18,19,5,5,8,9,24,24,3,4,30,
31,32,33,5,5,35,35,34,34],[
"fusion map is unique up to table automorphisms"
]);
ALN("2.J2M8",["2.G2(4)N5","2.J2N5"]);
MOT("2A4xA5",
[
"5th maximal subgroup of 2.J2"
],
0,
0,
0,
[(16,26)(17,27)(18,28)(19,29)(20,30)(21,31)(22,32)(23,33)(24,34)(25,35),
( 4, 5)( 9,10)(14,15)(19,20)(24,25)(29,30)(34,35)],
["ConstructDirectProduct",[["2.L2(3)"],["A5"]]]);
ALF("2A4xA5","a4xa5",[1,3,7,10,11,1,3,7,10,11,2,4,12,15,16,5,13,8,17,18,5,
13,8,17,18,6,14,9,19,20,6,14,9,19,20]);
ALF("2A4xA5","2.J2",[1,3,8,14,12,2,4,9,15,13,5,5,22,28,27,6,20,8,37,35,7,
21,9,38,36,6,20,8,37,35,7,21,9,38,36],[
"fusion map is unique up to table automorphisms,\n",
"compatible with a4xa5 -> J2"
]);
ALN("2A4xA5",["2.L2(3)xA5"]);
MOT("2A5xD10",
[
"6th maximal subgroup of 2.J2"
],
0,
0,
0,
[( 4, 8)(16,20)(24,28)(32,36),(21,29)(22,30)(23,31)(24,32)(25,33)(26,34)
(27,35)(28,36),( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)
(34,35)],
["ConstructDirectProduct",[["2.A5"],["Dihedral",10]]]);
ALF("2A5xD10","2.J2",[1,12,14,3,2,13,15,4,5,27,28,5,6,35,37,20,7,36,38,21,
18,16,12,31,19,17,13,32,16,14,18,29,17,15,19,30],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2A5xD10","a5xd10",[1,2,3,4,1,2,3,4,5,6,7,8,9,10,11,12,9,10,11,12,13,
14,15,16,13,14,15,16,17,18,19,20,17,18,19,20]);
ALF("2A5xD10","2.G2(4)",[1,14,16,3,2,15,17,4,5,34,35,5,6,44,46,22,7,45,47,
23,18,16,20,30,19,17,21,31,20,18,14,32,21,19,15,33],[
"fusion map is unique up to table automorphisms"
]);
ALF("2A5xD10","(2.A5xD10).2",[1,8,8,17,2,9,9,18,3,10,10,19,4,11,11,20,5,
12,12,21,6,13,14,22,7,15,16,23,6,14,13,22,7,16,15,23],[
"fusion map is unique up to table automorphisms"
]);
MOT("(2.A5xD10).2",
[
"7th maximal subgroup of 2.J2.2"
],
[2400,2400,80,120,120,100,100,600,600,20,30,30,50,50,50,50,480,480,16,24,24,
20,20,24,16,16,24,24,24,16,16,24,24],
[,[1,1,2,4,4,6,6,8,8,9,11,11,13,14,13,14,1,1,2,4,4,6,6,17,19,19,20,20,17,19,
19,20,20],[1,2,3,1,2,6,7,8,9,10,8,9,13,14,15,16,17,18,19,17,18,22,23,29,30,31,
29,29,24,25,26,24,24],,[1,2,3,4,5,1,2,1,2,3,4,5,1,1,2,2,17,18,19,20,21,17,18,
24,26,25,28,27,29,31,30,33,32]],
0,
[(27,28)(32,33),(25,26)(30,31),(13,14)(15,16),
(24,29)(25,30)(26,31)(27,32)(28,33)],
["ConstructIndexTwoSubdirectProduct","D10","5:4","2.A5","2.A5.2",[32,33,34,35,
36,56,57,58,59,60],(),()]);
ALF("(2.A5xD10).2","5:4",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,3,
3,3,3,3,5,5,5,5,5]);
ALF("(2.A5xD10).2","2.A5.2",[1,2,3,4,5,6,7,1,2,3,4,5,6,6,7,7,1,2,3,4,5,6,
7,8,9,10,11,12,8,9,10,11,12]);
ALF("(2.A5xD10).2","(A5xD10).2",[1,1,2,3,3,5,5,4,4,8,9,9,6,7,6,7,10,10,11,
12,12,13,13,14,16,16,18,18,15,17,17,19,19]);
ALF("(2.A5xD10).2","2.J2.2",[1,2,5,6,7,14,15,12,13,22,27,28,12,14,13,15,4,
3,5,17,16,24,23,30,31,32,37,38,30,32,31,38,37],[
"fusion is unique up to table automorphisms",
]);
ALF("(2.A5xD10).2","2.G2(4).2",[1,2,5,6,7,16,17,14,15,28,35,36,14,16,15,
17,3,4,5,18,19,26,27,42,43,44,51,51,42,43,44,51,51],[
"fusion map is unique up to table aut."
]);
ALF("(2.A5xD10).2","2.Suz",[1,2,5,6,7,17,18,19,20,42,63,64,17,19,18,20,4,
3,5,22,21,41,40,15,16,16,49,49,15,16,16,49,49],[
"fusion map is unique up to table aut."
]);
ALN("(2.A5xD10).2",["2.J2.2M7"]);
MOT("2^(1+4).S5",
[
"source: H. Pahlings,\n",
"4th maximal subgroup of J2.2,\n",
"8th maximal subgroup of J3.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[3840,3840,384,192,32,32,16,48,48,12,24,10,10,32,96,96,32,8,16,16,12,24,24],
[,[1,1,1,2,1,3,4,8,8,8,9,12,12,1,2,4,4,5,6,6,9,11,11],[1,2,3,4,5,6,7,1,2,3,4,
12,13,14,15,16,17,18,19,20,15,16,16],,[1,2,3,4,5,6,7,8,9,10,11,1,2,14,15,16,
17,18,19,20,21,22,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[6,6,6,6,-2,-2,-2,0,0,0,0,1,1,0,0,0,0,0,0,0,0,
0,0],[4,4,4,4,0,0,0,1,1,1,1,-1,-1,2,2,2,2,0,0,0,-1,-1,-1],
[TENSOR,[4,2]],[5,5,5,5,1,1,1,-1,-1,-1,-1,0,0,1,1,1,1,-1,-1,-1,1,1,1],
[TENSOR,[6,2]],[5,5,-3,1,1,1,-1,2,2,0,-2,0,0,-1,3,-3,1,1,-1,-1,0,0,0],
[TENSOR,[8,2]],[10,10,-6,2,2,2,-2,-2,-2,0,2,0,0,0,0,0,0,0,0,0,0,0,0],[10,10,2,
-2,-2,2,0,1,1,-1,1,0,0,-2,2,4,0,0,0,0,-1,1,1],
[TENSOR,[11,2]],[10,10,2,-2,2,-2,0,1,1,-1,1,0,0,0,4,2,-2,0,0,0,1,-1,-1],
[TENSOR,[13,2]],[15,15,-9,3,-1,-1,1,0,0,0,0,0,0,1,-3,3,-1,1,-1,-1,0,0,0],
[TENSOR,[15,2]],[16,-16,0,0,0,0,0,4,-4,0,0,1,-1,0,0,0,0,0,0,0,0,0,0],[16,-16,
0,0,0,0,0,-2,2,0,0,1,-1,0,0,0,0,0,0,0,0,-E(24)+E(24)^11+E(24)^17-E(24)^19,
E(24)-E(24)^11-E(24)^17+E(24)^19],
[TENSOR,[18,2]],[20,20,4,-4,0,0,0,-1,-1,1,-1,0,0,-2,-2,2,2,0,0,0,1,-1,-1],
[TENSOR,[20,2]],[24,-24,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,-2,2,0,0,0],
[TENSOR,[22,2]]],
[(19,20),(22,23)]);
ARC("2^(1+4).S5","tomfusion",rec(name:="2^(1+4)-.S5",map:=[1,2,3,8,4,13,41,
6,20,22,59,19,54,5,9,28,32,17,36,44,61,115,115],text:=[
"fusion map is unique up to table autom."
]));
ALF("2^(1+4).S5","J2.2",[1,2,2,6,3,6,12,4,9,9,15,8,14,17,18,21,22,19,21,22,23,
26,27],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(1+4).S5","J3.2",[1,2,2,5,2,5,8,3,7,7,13,6,12,18,19,21,22,19,21,22,
23,27,28],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(1+4).S5","2.A10",[1,2,4,3,4,13,11,7,8,20,19,16,17,4,3,11,12,13,23,
24,19,32,33]);
ALF("2^(1+4).S5","A5.2",[1,1,1,1,2,2,2,3,3,3,3,4,4,5,5,5,5,6,6,6,7,7,7]);
ALF("2^(1+4).S5","mo62",[1,1,3,2,4,5,6,7,7,9,8,10,10,12,11,14,13,17,18,18,
15,16,16]);
ALF("2^(1+4).S5","Ly",[1,2,2,5,2,5,13,4,9,10,20,7,16,2,5,13,12,5,12,13,20,
32,33],[
"fusion map is unique up to table aut."
]);
ALN("2^(1+4).S5",["J2.2C2A","J3.2C2A","J2.2N2A","J3.2N2A"]);
MOT("2^(2+4):(S3xS3)",
[
"source: H. Pahlings,\n",
"5th maximal subgroup of L3(4).D12,\n",
"4th maximal subgroup of J2.2,\n",
"9th maximal subgroup of J3.2,\n",
"8th maximal subgroup of McL.2,\n",
"table is sorted w.r. to normal series 2^2.2^4.3.2.3.2,\n",
"tests: 1.o.r., pow[2,3]"
],
[2304,768,96,64,18,96,96,16,72,36,24,12,12,12,48,32,32,8,6,32,32,16],
[,[1,1,1,2,5,1,2,4,9,10,9,10,9,11,1,1,2,3,5,4,4,4],[1,2,3,4,1,6,7,8,1,1,2,3,6,
7,15,16,17,18,15,20,21,22]],
[[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],[2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0],[
1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,-1,1,1,1,-1],
[TENSOR,[2,4]],
[TENSOR,[3,4]],[2,2,2,2,-1,0,0,0,2,-1,2,-1,0,0,2,0,0,0,-1,2,2,0],
[TENSOR,[7,2]],[4,4,4,4,-2,0,0,0,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0],[6,6,2,-2,0,0,
0,0,0,3,0,-1,0,0,0,-2,-2,0,0,0,0,2],
[TENSOR,[10,2]],[9,9,-3,1,0,3,3,-1,0,0,0,0,0,0,3,1,1,-1,0,-1,-1,1],
[TENSOR,[12,2]],
[TENSOR,[12,4]],
[TENSOR,[12,5]],[12,12,4,-4,0,0,0,0,0,-3,0,1,0,0,0,0,0,0,0,0,0,0],[12,-4,0,0,
0,2,-2,0,3,0,-1,0,-1,1,0,2,-2,0,0,-2,2,0],
[TENSOR,[17,2]],
[TENSOR,[17,4]],
[TENSOR,[17,5]],[24,-8,0,0,0,4,-4,0,-3,0,1,0,1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[21,4]]],
[]);
ARC("2^(2+4):(S3xS3)","tomfusion",rec(name:="2^(2+4):(S3xS3)",map:=[1,2,4,
14,9,3,12,48,7,8,25,28,29,74,5,6,17,20,30,41,39,54],text:=[
"fusion map is unique"
]));
ALF("2^(2+4):(S3xS3)","L3(4).D12",[1,2,2,4,3,7,8,10,11,11,13,13,16,18,24,
19,20,20,25,26,27,22],[
"fusion map is unique"
]);
ALF("2^(2+4):(S3xS3)","McL.2",[1,2,2,5,4,20,21,24,4,4,9,9,22,27,20,2,5,5,
22,24,23,11],[
"fusion map is unique"
]);
ALF("2^(2+4):(S3xS3)","J3.2",[1,2,2,5,4,2,5,8,3,3,7,7,7,13,18,18,19,19,20,
21,22,22],[
"fusion map is unique"
]);
ALF("2^(2+4):(S3xS3)","J2.2",[1,2,3,6,5,2,6,12,4,5,9,10,9,15,17,17,18,19,20,
21,22,22],[
"fusion map is unique"
]);
MOT("2^1+4b:a5",
[
"origin: CAS library,\n",
"8th maximal subgroup of J3,\n",
"3rd maximal subgroup of J2\n",
"tests: 1.o.r., pow[2,3,5]"
],
[1920,1920,192,96,16,16,8,24,24,12,12,12,10,10,10,10],
[,[1,1,1,2,1,3,4,8,8,8,8,9,15,15,13,13],[1,2,3,4,5,6,7,1,2,3,3,4,15,16,13,
14],,[1,2,3,4,5,6,7,8,9,11,10,12,1,2,1,2]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,-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]],[4,4,4,4,0,0,0,1,1,1,1,1,-1,-1,-1,-1],[5,5,5,5,1,1,1,-1,-1,-1,
-1,-1,0,0,0,0],[5,5,-3,1,1,1,-1,2,2,0,0,-2,0,0,0,0],[5,5,-3,1,1,1,-1,-1,-1,
E(3)-E(3)^2,-E(3)+E(3)^2,1,0,0,0,0],
[GALOIS,[7,2]],[10,10,2,-2,2,-2,0,1,1,-1,-1,1,0,0,0,0],[10,10,2,-2,-2,2,0,1,1,
-1,-1,1,0,0,0,0],[15,15,-9,3,-1,-1,1,0,0,0,0,0,0,0,0,0],[20,20,4,-4,0,0,0,-1,
-1,1,1,-1,0,0,0,0],[8,-8,0,0,0,0,0,2,-2,0,0,0,-E(5)-E(5)^4,E(5)+E(5)^4,
-E(5)^2-E(5)^3,E(5)^2+E(5)^3],
[GALOIS,[13,2]],[16,-16,0,0,0,0,0,-2,2,0,0,0,1,-1,1,-1],[24,-24,0,0,0,0,0,0,0,
0,0,0,-1,1,-1,1]],
[(10,11),(13,15)(14,16)]);
ARC("2^1+4b:a5","projectives",["2^{1+4}_-:2A5",[[2,2,2,2,0,0,0,-1,-1,-1,-1,1,
E(5)+E(5)^4,-E(5)-E(5)^4,E(5)^2+E(5)^3,-E(5)^2-E(5)^3],
[GALOIS,[1,2]],[4,4,4,4,0,0,0,1,1,1,1,-1,-1,1,-1,1],[6,6,6,6,0,0,0,0,0,0,0,0,
1,-1,1,-1],[10,10,-6,2,0,0,0,-2,-2,0,0,-2,0,0,0,0],[10,10,2,-2,0,0,2*E(4),1,1,
-1,-1,-1,0,0,0,0],
[GALOIS,[6,3]],[10,10,-6,2,0,0,0,1,1,E(3)-E(3)^2,-E(3)+E(3)^2,1,0,0,0,0],
[GALOIS,[8,2]],[20,20,4,-4,0,0,0,-1,-1,1,1,1,0,0,0,0],[4,-4,0,0,0,2,0,-2,2,0,
0,0,-1,-1,-1,-1],[12,-12,0,0,0,-2,0,0,0,0,0,0,E(5)+E(5)^4,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(5)^2+E(5)^3],
[GALOIS,[12,2]],[16,-16,0,0,0,0,0,-2,2,0,0,0,1,1,1,1],[20,-20,0,0,0,2,0,2,-2,
0,0,0,0,0,0,0]],]);
ARC("2^1+4b:a5","CAS",[rec(name:="2^1+4b:a5",
permchars:=(),
permclasses:=( 4, 5, 8,13, 7, 6)( 9,15,16,12,11,10),
text:=[
"maximal subgroup of sporadic simple Janko group j2\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ARC("2^1+4b:a5","tomfusion",rec(name:="2^(1+4)-:A5",map:=[1,2,3,7,4,10,28,
5,15,17,17,33,14,30,14,30],text:=[
"fusion map is unique"
]));
ALF("2^1+4b:a5","J2",[1,2,2,6,3,6,14,4,11,11,11,19,9,17,10,18],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^1+4b:a5","J3",[1,2,2,5,2,5,9,3,8,8,8,15,6,13,7,14],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^1+4b:a5","2^(1+4).S5",[1,2,3,4,5,6,7,8,9,10,10,11,12,13,12,13],[
"fusion map is unique"
]);
ALF("2^1+4b:a5","A5",[1,1,1,1,2,2,2,3,3,3,3,3,4,4,5,5]);
ALN("2^1+4b:a5",["s2j2","J2C2A","J2N2A","J3C2A","J3N2A"]);
MOT("2^2+4.3xs3",
[
"origin: CAS library,\n",
"9th maximal subgroup of J3,\n",
" test: 1. o.r., sym 2 decompose correctly \n",
"tests: 1.o.r., pow[2,3]"
],
[1152,384,48,32,72,24,72,24,9,36,12,36,12,48,48,8,12,12,12,12],
[,[1,1,1,2,7,7,5,5,9,12,12,10,10,1,2,4,7,8,5,6],[1,2,3,4,1,2,1,2,1,1,3,1,3,14,
15,16,14,15,14,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1],[1,1,1,1,E(3),E(3),E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,E(3)^2,1,
1,1,E(3),E(3),E(3)^2,E(3)^2],
[TENSOR,[3,3]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],[2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,0,0,0,0,0,0,0],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[6,6,2,-2,0,0,0,0,0,3,-1,3,-1,0,0,0,0,0,0,0],
[TENSOR,[10,3]],
[TENSOR,[10,4]],[9,9,-3,1,0,0,0,0,0,0,0,0,0,3,3,-1,0,0,0,0],
[TENSOR,[13,2]],[12,-4,0,0,3,-1,3,-1,0,0,0,0,0,-2,2,0,1,-1,1,-1],
[TENSOR,[15,2]],
[TENSOR,[15,6]],
[TENSOR,[15,5]],
[TENSOR,[15,4]],
[TENSOR,[15,3]]],
[( 5, 7)( 6, 8)(10,12)(11,13)(17,19)(18,20)]);
ARC("2^2+4.3xs3","projectives",["2^{3+4}:(3xS3)",[[4,4,0,0,1,1,1,1,1,-2,0,-2,
0,2,2,0,1,-1,1,-1],[8,8,0,0,2,2,2,2,-1,2,0,2,0,0,0,0,0,0,0,0],[6,-2,0,2,-3,1,
-3,1,0,0,0,0,0,2,-2,0,1,1,1,1],[18,-6,0,-2,0,0,0,0,0,0,0,0,0,0,0,2*E(4),0,0,0,
0]],]);
ARC("2^2+4.3xs3","tomfusion",rec(name:="2^(2+4):(3xS3)",map:=[1,2,4,12,5,
15,5,15,7,6,17,6,17,3,10,27,18,37,18,37],text:=["fusion map is unique"
]));
ALF("2^2+4.3xs3","J2",[1,2,3,6,4,11,4,11,5,5,12,5,12,2,6,14,11,19,11,19],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^2+4.3xs3","J3",[1,2,2,5,3,8,3,8,4,3,8,3,8,2,5,9,8,15,8,15],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^2+4.3xs3","2^(2+4):(S3xS3)",[1,2,3,4,9,11,9,11,5,10,12,10,12,6,7,8,
13,14,13,14],[
"fusion map is unique"
]);
ALF("2^2+4.3xs3","L3(4).6",[1,2,2,4,11,15,12,16,3,11,15,12,16,7,8,10,21,
25,22,26],[
"fusion map is unique up to table aut."
]);
MOT("2^{1+4}_-:2A5",
[
"origin: Dixon's Algorithm,\n",
"3rd maximal subgroup of 2.J2"
],
[3840,3840,3840,3840,384,384,192,192,16,32,32,16,16,48,48,48,48,24,24,24,24,
24,24,20,20,20,20,20,20,20,20],
[,[1,1,1,1,1,1,3,3,2,6,6,8,8,14,14,14,14,14,14,14,14,16,16,28,28,28,28,24,24,
24,24],[1,2,3,4,5,6,7,8,9,10,11,13,12,1,2,3,4,5,6,5,6,8,7,28,29,30,31,24,25,
26,27],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,20,21,18,19,22,23,1,2,4,3,
1,2,4,3]],
0,
[(18,20)(19,21),(12,13),(24,28)(25,29)(26,30)(27,31)],
["ConstructProj",[["2^1+4b:a5",[]],["2^{1+4}_-:2A5",[]]]]);
ALF("2^{1+4}_-:2A5","2^1+4b:a5",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,9,10,10,
11,11,12,12,13,13,14,14,15,15,16,16]);
ALF("2^{1+4}_-:2A5","2.J2",[1,2,3,4,4,3,10,11,5,10,11,25,26,6,7,20,21,21,
20,21,20,34,33,16,17,30,29,18,19,32,31],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^{1+4}_-:2A5","A5",[1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,
4,4,4,5,5,5,5]);
MOT("2^{3+4}:(3xS3)",
[
"origin: Dixon's Algorithm,\n",
"4th maximal subgroup of 2.J2"
],
[2304,2304,768,768,48,64,64,144,144,48,48,144,144,48,48,18,18,72,72,12,72,72,
12,96,96,96,96,16,16,24,24,24,24,24,24,24,24],
[,[1,1,1,1,2,3,3,12,12,12,12,8,8,8,8,16,16,21,21,22,18,18,19,1,1,3,3,7,7,12,
12,14,14,8,8,10,10],[1,2,3,4,5,6,7,1,2,3,4,1,2,3,4,1,2,1,2,5,1,2,5,24,25,26,
27,29,28,25,24,26,27,25,24,26,27]],
0,
[(28,29),(24,25)(26,27)(30,31)(32,33)(34,35)(36,37),( 8,12)( 9,13)(10,14)
(11,15)(18,21)(19,22)(20,23)(30,34)(31,35)(32,36)(33,37)],
["ConstructProj",[["2^2+4.3xs3",[]],["2^{3+4}:(3xS3)",[]]]]);
ALF("2^{3+4}:(3xS3)","2^2+4.3xs3",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
10,11,12,12,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20]);
ALF("2^{3+4}:(3xS3)","2.J2",[1,2,3,4,5,10,11,6,7,20,21,6,7,20,21,8,9,8,9,
22,8,9,22,3,4,10,11,25,26,21,20,33,34,21,20,33,34],[
"fusion is unique up to table automorphisms"
]);
MOT("2xA5",
[
"origin: CAS library, tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
[( 4, 5)( 9,10)],
["ConstructDirectProduct",[["Cyclic",2],["A5"]],(),(2,3)(7,8)]);
ARC("2xA5","CAS",[rec(name:="2xa5",
permchars:=(),
permclasses:=(),
text:=[
"maximal subgroup of sporadic simple Janko Group j1\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly\n",
""])]);
ARC("2xA5","tomfusion",rec(name:="2xA5",map:=[1,3,5,9,9,2,4,10,15,15],text:=[
"fusion map is unique"
]));
ALF("2xA5","J1",[1,2,3,4,5,2,2,6,8,9],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2xA5","L2(16).2",[1,2,3,4,5,12,12,14,15,16],[
"fusion map is unique up to table autom."
]);
ALF("2xA5","L3(4).2_3",[1,2,3,6,7,9,9,10,13,14],[
"fusion map is unique up to table autom."
]);
ALN("2xA5",["J1C2A","J1N2A","L2(16).2C2B","L2(16).2N2B","L3(4).2_3C2B",
"L3(4).2_3N2B"]);
MOT("2xU3(3)",
[
"1st maximal subgroup of 2.J2"
],
0,
0,
0,
[( 9,10)(23,24),( 5, 6)(11,12)(13,14)(19,20)(25,26)(27,28)],
["ConstructDirectProduct",[["Cyclic",2],["U3(3)"]]]);
ARC("2xU3(3)","tomfusion",rec(name:="U3(3)x2",map:=[1,3,5,6,10,10,11,16,20,20,
33,33,36,36,2,4,14,17,9,9,12,15,41,41,34,34,38,38],text:=[
"fusion map is unique"
]));
ALF("2xU3(3)","2.J2",[1,3,6,8,11,11,10,20,23,23,25,26,34,34,2,4,7,9,10,10,
11,21,24,24,26,25,33,33],[
"fusion map is unique up to table automorphisms"
]);
ALF("2xU3(3)","U4(3).2_1",[1,2,3,6,7,7,7,10,13,14,15,15,18,18,19,19,23,26,
21,21,22,23,33,34,27,27,29,30],[
"fusion map is unique up to table autom."
]);
ALN("2xU3(3)",["U4(3).2_1C2B","U4(3).2_1N2B"]);
MOT("37:12",
[
"origin: CAS library,\n",
"maximal subgroup of J4,\n",
"Test: OR1, JAMES,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,37]"
],
[444,37,37,37,12,12,12,12,12,12,12,12,12,12,12],
[,[1,3,4,2,6,8,10,12,14,1,6,8,10,12,14],[1,4,2,3,7,10,13,1,7,10,13,1,7,10,
13],,[1,4,2,3,9,14,7,12,5,10,15,8,13,6,11],,[1,4,2,3,11,6,13,8,15,10,5,12,7,
14,9],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[1,1,1,1,5,6,7,8,9,10,11,12,13,14,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,-E(12)^7,-E(3)^2,E(4),E(3),
-E(12)^11,-1,E(12)^7,E(3)^2,-E(4),-E(3),E(12)^11],
[TENSOR,[2,2]],
[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]],[12,E(37)+E(37)^6+E(37)^8+E(37)^10+E(37)^11+E(37)^14+E(37)^23
+E(37)^26+E(37)^27+E(37)^29+E(37)^31+E(37)^36,E(37)^2+E(37)^9+E(37)^12
+E(37)^15+E(37)^16+E(37)^17+E(37)^20+E(37)^21+E(37)^22+E(37)^25+E(37)^28
+E(37)^35,E(37)^3+E(37)^4+E(37)^5+E(37)^7+E(37)^13+E(37)^18+E(37)^19+E(37)^24
+E(37)^30+E(37)^32+E(37)^33+E(37)^34,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[13,2]],
[GALOIS,[13,3]]],
[( 5, 9)( 6,14)( 8,12)(11,15),( 5,11)( 7,13)( 9,15),(2,3,4),(2,4,3)]);
ALF("37:12","J4",[1,50,51,52,23,11,7,4,23,3,23,4,7,11,23],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("37:12",["J4N37"]);
MOT("3^2.3^(1+2):8.2",
[
"origin: computed using GAP and tables of J3, J3.2, J3M7,\n",
"7th maximal subgroup of J3.2,\n",
"tests: 1.o.r., pow[2,3]"
],
[3888,486,216,54,54,54,48,24,24,12,8,8,36,12,18,12,12,18,18,18],
[,[1,2,3,5,6,4,1,3,7,8,9,9,1,7,2,8,8,5,6,4],[1,1,1,2,2,2,7,7,9,9,11,12,13,14,
13,14,14,15,15,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[1,1]],[2,2,2,2,2,2,-2,-2,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,0,0,0,
0],
[GALOIS,[3,5]],[2,2,2,2,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0],[12,12,-6,0,0,0,4,
-2,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,1,-1,1,1,-1,-1,-1],
[TENSOR,[1,7]],[6,6,-3,0,0,0,-2,1,2,-1,0,0,0,2,0,-1,-1,0,0,0],
[TENSOR,[9,1]],[6,6,-3,0,0,0,-2,1,-2,1,0,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,
0],
[TENSOR,[11,1]],[24,-3,0,E(9)^2+2*E(9)^4+2*E(9)^5+E(9)^7,-2*E(9)^2-E(9)^4
-E(9)^5-2*E(9)^7,E(9)^2-E(9)^4-E(9)^5+E(9)^7,0,0,0,0,0,0,2,0,-1,0,0,
E(9)^2+E(9)^7,E(9)^4+E(9)^5,-E(9)^2-E(9)^4-E(9)^5-E(9)^7],
[TENSOR,[13,1]],
[GALOIS,[13,4]],
[TENSOR,[15,1]],[8,8,8,-1,-1,-1,0,0,0,0,0,0,-2,0,-2,0,0,1,1,1],
[TENSOR,[17,1]],
[GALOIS,[14,2]],
[TENSOR,[19,1]]],
[(16,17),(11,12),( 4, 5, 6)(16,17)(18,19,20)]);
ARC("3^2.3^(1+2):8.2","tomfusion",rec(name:="3^2.3^(1+2):8.2",map:=[1,4,5,
19,19,19,2,10,6,20,16,16,3,7,11,21,21,30,30,30],text:=[
"fusion map is unique"
]));
ALF("3^2.3^(1+2):8.2","J3.2",[1,4,3,9,10,11,2,7,5,13,8,8,18,19,20,23,23,
24,25,26],[
"fusion map is unique up to table automorphisms"
]);
MOT("3x2^4:(3xA5)",
[
"4th maximal subgroup of 3.J3"
],
0,
0,
0,
[(20,39)(21,40)(22,41)(23,42)(24,43)(25,44)(26,45)(27,46)(28,47)(29,48)(30,49)
(31,50)(32,51)(33,52)(34,53)(35,54)(36,55)(37,56)(38,57),(14,17)(15,18)(16,19)
(33,36)(34,37)(35,38)(52,55)(53,56)(54,57),( 3, 4)( 7, 8)( 9,10)(12,13)(15,16)
(18,19)(22,23)(26,27)(28,29)(31,32)(34,35)(37,38)(41,42)(45,46)(47,48)(50,51)
(53,54)(56,57),( 3,22,41)( 4,42,23)( 7,26,45)( 8,46,27)( 9,28,47)(10,48,29)
(12,31,50)(13,51,32)(15,34,53)(16,54,35)(18,37,56)(19,57,38)],
["ConstructDirectProduct",[["Cyclic",3],["J3M4"]]]);
ALF("3x2^4:(3xA5)","3.J3",[1,4,7,7,4,11,20,20,8,9,10,21,22,14,38,38,17,41,
41,2,5,8,8,5,12,21,21,9,7,10,22,20,15,39,39,18,42,42,3,6,9,9,6,13,22,22,7,
8,10,20,21,16,40,40,19,43,43],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("3xL2(16).2",
[
"1st maximal subgroup of 3.J3"
],
0,
0,
0,
[(10,13)(11,14)(12,15)(16,19)(17,20)(18,21)(43,46)(44,47)(45,48),
(22,25)(23,26)(24,27)(28,31)(29,32)(30,33),
(22,28,25,31)(23,29,26,32)(24,30,27,33),
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)
(35,36)(38,39)(41,42)(44,45)(47,48)
],
["ConstructDirectProduct",[["L2(16).2"],["Cyclic",3]]]);
ALF("3xL2(16).2","3.J3",[1,2,3,4,5,6,7,8,9,14,15,16,17,18,19,38,39,40,41,
42,43,47,48,49,47,48,49,44,45,46,44,45,46,4,5,6,11,12,13,20,21,22,29,30,
31,32,33,34],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("3xL2(19)",
[
"2nd maximal subgroup of 3.J3"
],
0,
0,
0,
[(31,34)(32,35)(33,36),(10,13)(11,14)(12,15)(25,28)(26,29)(27,30),
(16,19,22)(17,20,23)(18,21,24),
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)
(35,36)
],
["ConstructDirectProduct",[["L2(19)"],["Cyclic",3]]]);
ALF("3xL2(19)","3.J3",[1,2,3,4,5,6,10,10,10,14,15,16,17,18,19,26,26,26,
27,27,27,28,28,28,29,30,31,32,33,34,50,51,52,53,54,55],[
"fusion map is unique up to table autom.",
]);
MOT("3xL2(17)",
[
"5th maximal subgroup of 3.J3"
],
0,
0,
0,
[(28,31)(29,32)(30,33),(13,16)(14,17)(15,18),(19,22,25)(20,23,26)(21,24,27),
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)]
,
["ConstructDirectProduct",[["L2(17)"],["Cyclic",3]]]);
ALF("3xL2(17)","3.J3",[1,2,3,4,5,6,10,10,10,11,12,13,23,24,25,23,24,25,
26,26,26,27,27,27,28,28,28,44,45,46,47,48,49],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("43:14",
[
"origin: CAS library,\n",
"maximal subgroup of J4,\n",
"Test: 1.OR, JAMES,\n",
"and resticted characters decompose properly.\n",
"tests: 1.o.r., pow[2,7,43]"
],
[602,43,43,43,14,14,14,14,14,14,14,14,14,14,14,14,14],
[,[1,2,3,4,6,8,10,12,14,16,1,6,8,10,12,14,16],,,,,[1,4,2,3,11,1,11,1,11,1,11,
1,11,1,11,1,11],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[1,1,1,1,5,6,7,8,9,10,11,
12,13,14,15,16,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,-E(7)^4,E(7),-E(7)^5,E(7)^2,
-E(7)^6,E(7)^3,-1,E(7)^4,-E(7),E(7)^5,-E(7)^2,E(7)^6,-E(7)^3],
[TENSOR,[2,2]],
[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]],[14,E(43)+E(43)^2+E(43)^4+E(43)^8+E(43)^11+E(43)^16+E(43)^21
+E(43)^22+E(43)^27+E(43)^32+E(43)^35+E(43)^39+E(43)^41+E(43)^42,
E(43)^3+E(43)^5+E(43)^6+E(43)^10+E(43)^12+E(43)^19+E(43)^20+E(43)^23+E(43)^24
+E(43)^31+E(43)^33+E(43)^37+E(43)^38+E(43)^40,E(43)^7+E(43)^9+E(43)^13
+E(43)^14+E(43)^15+E(43)^17+E(43)^18+E(43)^25+E(43)^26+E(43)^28+E(43)^29
+E(43)^30+E(43)^34+E(43)^36,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[15,3]],
[GALOIS,[15,7]]],
[( 5, 7,13,17,15, 9)( 6,10, 8,16,12,14),(2,3,4),(2,4,3)]);
ALF("43:14","J4",[1,57,58,59,27,13,26,13,26,12,3,13,27,12,27,12,26],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("43:14",["J4N43"]);
MOT("5^2:D12",
[
"origin: CAS library,\n",
"Sylow 5 normalizer in sporadic Janko group J2,\n",
" test:= 1. o.r., sym 2 decompose correctly \n",
"tests: 1.o.r., pow[2,3,5]"
],
[300,50,50,50,50,12,6,6,20,10,10,20,10,10],
[,[1,3,2,5,4,1,7,7,1,4,5,1,2,3],[1,3,2,5,4,6,1,6,9,11,10,12,14,13],,[1,1,1,1,
1,6,7,8,9,9,9,12,12,12]],
[[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,-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,-1,-1,0,0,0,0,0,0],
[TENSOR,[5,3]],[6,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,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)^4,0,0,0,-2,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,
0,0],
[GALOIS,[7,2]],
[TENSOR,[7,2]],
[TENSOR,[8,2]],[6,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*E(5)^4,-2*E(5)^2-2*E(5)^3,0,0,0,0,0,0,-2,-E(5)^2-E(5)^3,
-E(5)-E(5)^4],
[GALOIS,[11,2]],
[TENSOR,[12,2]],
[TENSOR,[11,2]]],
[( 2, 3)( 4, 5)(10,11)(13,14),( 2, 5, 3, 4)( 9,12)(10,13,11,14)]);
ARC("5^2:D12","CAS",[rec(name:="j2n5",
permchars:=( 1, 4, 2)( 5, 6)( 7,11, 9,12)( 8,13)(10,14),
permclasses:=( 2, 6, 4, 8,10,12, 3, 7, 5, 9)(11,14),
text:="")]);
ARC("5^2:D12","tomfusion",rec(name:="5^2:D12",map:=[1,7,7,8,8,4,5,9,3,16,16,2,
14,14],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("5^2:D12","J2",[1,7,8,10,9,3,5,12,2,17,18,3,16,15],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("5^2:D12","U3(4).2",[1,5,6,7,8,15,3,16,15,20,19,2,10,9],[
"fusion map is unique up to table autom."
]);
ALF("5^2:D12","G2(4)",[1,9,10,12,11,3,5,14,2,18,19,3,21,20],[
"fusion map is unique up to table autom."
]);
ALF("5^2:D12","5^2:(4xS3)",[1,10,10,11,11,4,5,12,3,14,14,2,13,13],[
"fusion map is unique up to table aut."
]);
ALN("5^2:D12",["G2(4)N5","J2N5"]);
MOT("7:6",
[
"origin: CAS library,\n",
"maximal subgroup of J1,\n",
"test: 1.OR, JAMES, JAMES, n=3,\n",
"and restricted characters decompose properly,\n",
"constructions: AGL(1,7),\n",
"tests: 1.o.r., pow[2,3,7]"
],
0,
0,
0,
[(3,7)(4,6)],
["ConstructPermuted",["P:Q",[7,6]]]);
ARC("7:6","tomfusion",rec(name:="7:6",map:=[1,5,4,3,2,3,4],text:=[
"fusion map is unique"
]));
ALF("7:6","A7.2",[1,8,13,4,10,4,13],[
"fusion map is unique"
]);
ALF("7:6","A8.2",[1,11,19,5,14,5,19],[
"fusion map is unique"
]);
ALF("7:6","J1",[1,7,6,3,2,3,6],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("7:6","J2",[1,13,12,5,3,5,12],[
"fusion map is unique"
]);
ALF("7:6","HS",[1,13,11,4,3,4,11],[
"fusion map is unique"
]);
ALF("7:6","L2(8).3",[1,4,8,7,2,6,9],[
"fusion map is unique up to table autom."
]);
ALF("7:6","L3(2).2",[1,5,7,3,6,3,7],[
"fusion map is unique"
]);
ALF("7:6","S6(2)",[1,22,21,8,5,8,21],[
"fusion map is unique"
]);
ALF("7:6","Sz(8).3",[1,6,10,9,2,8,11],[
"fusion map is unique up to table automorphisms"
]);
ALF("7:6","U3(3).2",[1,8,13,4,11,4,13],[
"fusion map is unique"
]);
ALF("7:6","G2(3)",[1,14,13,7,2,7,13],[
"fusion map determined by the fact that 7:6 contains 3E elements"
]);
ALF("7:6","U6(2)",[1,24,23,7,4,7,23],[
"fusion map is unique"
]);
ALF("7:6","L3(4).2_1",[1,8,11,3,9,3,11],[
"fusion map is unique"
]);
ALF("7:6","L3(4).2_3",[1,8,10,3,9,3,10],[
"fusion map is unique"
]);
ALF("7:6","U4(3).2_2",[1,13,28,6,20,6,28],[
"fusion map is unique"
]);
ALF("7:6","U4(3).2_3",[1,11,18,5,16,5,18],[
"fusion map is unique"
]);
ALF("7:6","O8+(2)",[1,35,34,11,6,11,34],[
"fusion map is unique"
]);
ALN("7:6",["A8.2N7","AGL(1,7)","HSN7","J1N7","J2N7","G2(3)N7","L3(4).2_1N7",
"L3(4).2_3N7","O8+(2)N7","S6(2)N7","U4(3).2_2N7","U4(3).2_3N7","U6(2)N7"]);
MOT("D6xD10",
[
"origin: CAS library,\n",
" test:= 1. o.r.,sym 2, 3 and restricted characters of j1 decompose \n",
" correctly \n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
[( 2, 3)( 6, 7)(10,11)],
["ConstructDirectProduct",[["Dihedral",6],["Dihedral",10]]]);
ARC("D6xD10","tomfusion",rec(name:="D6xD10",map:=[1,7,7,3,5,15,15,9,2,13,
13,4],text:=[
"fusion map is unique"
]));
ALF("D6xD10","J1",[1,5,4,2,3,12,11,6,2,9,8,2],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("D6xD10","J3",[1,6,7,2,3,16,17,8,2,13,14,2],[
"fusion is unique up to table automorphisms"
]);
ALF("D6xD10","L2(16).2",[1,4,5,12,3,6,7,14,12,15,16,2],[
"fusion map is unique up to table autom."
]);
ALN("D6xD10",["J1N3","J1N5","J3N5","L2(16).2M5","L2(16).2N5","s3xd10"]);
MOT("(2^2xA5):2",
[
"origin: Dixon's Algorithm,\n",
"6th maximal subgroup of M12.2,\n",
"table is sorted w.r.t. normal series 2 < 2xA5 < 2^2xA5 < (2^2xA5):2"
],
[480,480,32,32,24,20,24,20,24,8,12,240,16,24,8,12,20,20,12],
[,[1,1,1,1,5,6,5,6,1,3,5,1,1,2,4,5,6,6,7],[1,2,3,4,1,6,2,8,9,10,9,12,13,14,15,
12,18,17,14],,[1,2,3,4,5,1,7,2,9,10,11,12,13,14,15,16,12,12,19],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,18,17,19],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19]],
0,
[(17,18)],
["ConstructIndexTwoSubdirectProduct","V4","D8","A5","A5.2",[19,20,21,33,34,
35],(2,3,5)(4,6)(9,12,17)(10,13,18)(11,16,19),(2,4,7,11,6,9)(3,13,12,8)(10,14)
(16,17)]);
ARC("(2^2xA5):2","tomfusion",rec(name:="(2^2xA5):2",map:=[1,2,4,5,8,25,28,
49,6,23,32,3,7,12,21,30,51,51,60],text:=[
"fusion map is unique"
]));
ALF("(2^2xA5):2","A5.2",[1,1,2,2,3,4,3,4,5,6,7,1,2,5,6,3,4,4,7]);
ALF("(2^2xA5):2","D8",[1,2,1,2,1,1,2,2,4,4,4,5,5,3,3,5,5,5,3]);
ALF("(2^2xA5):2","M12.2",[1,2,3,2,5,7,8,11,2,6,8,13,13,15,15,16,17,18,19],[
"fusion is unique up to table automorphisms"
]);
ALF("(2^2xA5):2","S4(5)",[1,3,3,2,4,11,16,22,3,7,16,2,3,7,6,15,19,20,23],[
"fusion map is unique up to table autom."
]);
ALN("(2^2xA5):2",["M12.2C2A","M12.2N2A","S4(5)C2B","S4(5)N2B"]);
MOT("2^3.(S4x2)",
[
"origin: Dixon's Algorithm,\n",
"7th maximal subgroup of M12.2,\n",
"table is sorted w.r.t. normal series 2<2^3<2^3.2^2<2^3.A4<2^3.S4<2^3.(S4x2)"
],
[384,384,64,32,32,12,12,16,16,8,48,16,12,12,16,16,8],
[,[1,1,1,1,2,6,6,1,3,5,2,3,7,7,1,3,4],[1,2,3,4,5,1,2,8,9,10,11,12,11,11,15,16,
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],[1,1,1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,-1,-1,0,0,0,2,2,-1,-1,0,0,0],
[TENSOR,[5,2]],[3,3,3,-1,-1,0,0,-1,-1,1,3,-1,0,0,-1,-1,1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[6,6,-2,-2,2,0,0,2,-2,0,0,0,0,0,0,0,0],
[TENSOR,[11,3]],[6,6,-2,2,-2,0,0,0,0,0,0,0,0,0,-2,2,0],
[TENSOR,[13,2]],[8,-8,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0],[8,-8,0,0,0,-1,1,0,0,0,
0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,0,0],
[TENSOR,[16,2]]],
[(13,14)]);
ARC("2^3.(S4x2)","tomfusion",rec(name:="M8.S4.2",map:=[1,2,3,4,11,7,28,6,
14,45,10,24,61,61,5,18,26],text:=[
"fusion map is unique"
]));
ALF("2^3.(S4x2)","M12.2",[1,3,3,2,6,4,9,3,6,10,14,14,20,21,13,14,15],[
"fusion is unique up to table automorphisms"
]);
MOT("F3+M7",
[
"7th maximal subgroup of F3+,\n",
"non-split extension 2^11.M_24,\n",
"origin: constructed from table of the split extension (J4M1)\n",
"by changing 2nd power map and representative orders"
],
0,
0,
0,
[(67,68),(65,66),(57,58)(71,72),(57,58)(67,68)(71,72),(57,58)(60,61)(71,72),
(32,33)(53,54)(55,56)(62,63)(69,70),
( 5, 6)(15,16)(21,22)(30,31)(42,43)(49,50)(51,52)],
["ConstructAdjusted",["J4M1"],[["ComputedPowerMaps",
[,[1,1,1,1,3,3,1,8,9,1,3,3,2,3,4,4,7,7,4,7,6,5,23,8,8,8,9,8,8,27,27,32,33,12,
12,11,14,18,17,23,23,40,40,44,26,26,25,9,28,28,31,30,32,33,33,32,57,58,35,23,
23,62,63,44,65,66,46,46,54,53,57,58],[1,2,3,4,5,6,7,1,1,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,3,2,3,3,4,7,5,6,33,32,34,35,36,37,38,39,40,41,42,43,44,
11,12,13,10,16,15,21,22,54,53,56,55,23,23,59,61,60,33,32,64,65,66,34,34,70,69,
40,40],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,24,25,26,
27,28,29,30,31,33,32,34,35,36,37,38,39,3,2,5,6,44,45,46,47,48,49,50,51,52,54,
53,56,55,8,8,59,10,10,63,62,64,66,65,68,67,70,69,24,24],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,1,1,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,2,2,4,4,58,57,59,61,60,9,9,
64,66,65,68,67,13,13,72,71],,,,[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,
45,46,47,48,49,50,51,52,53,54,55,56,58,57,59,60,61,62,63,2,66,65,67,68,69,70,
72,71],,,,,,,,,,,,[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,
49,50,51,52,53,54,55,56,57,58,59,61,60,62,63,64,1,1,67,68,69,70,71,72]]]]]);
ALF("F3+M7","F3+",[1,2,3,2,9,9,3,6,8,3,9,11,10,11,10,10,9,11,10,11,26,26,12,
14,18,21,23,18,21,46,47,24,24,28,27,26,28,27,26,36,35,68,68,37,42,48,49,23,
49,49,79,78,52,52,52,52,56,56,57,36,36,70,70,73,74,75,81,82,87,87,91,91],[
"fusion map is unique up to table automorphisms"
]);
ALF("F3+M7","M24",[1,1,1,2,3,3,2,4,5,3,2,2,2,3,6,6,7,7,7,6,8,8,9,4,4,4,5,
10,10,11,11,12,13,6,7,7,8,14,14,9,9,15,15,16,10,10,10,11,17,17,18,18,12,
13,20,19,21,22,14,15,15,23,24,16,25,26,17,17,20,19,21,22]);
ALF("F3+M7","2^12.M24",[1,2,3,6,16,16,7,20,27,15,10,11,14,19,30,30,36,37,
40,33,47,47,50,21,24,25,28,55,56,65,65,67,71,35,44,45,48,77,78,51,54,82,
82,84,58,59,63,64,89,89,93,93,69,73,99,95,102,106,80,81,81,110,112,85,114,
116,91,91,101,97,103,107],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
MOT("J4M4",
[
"origin: CAS library,",
"2nd power map determined by fusion into J4,\n",
"maximal subgroup of J4,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[660602880,94371840,1572864,1572864,393216,196608,98304,32768,840,840,11520,
11520,768,768,81920,81920,98304,98304,49152,8192,8192,4096,2048,1536,1280,
1536,688128,98304,6144,24576,24576,2048,56,56,192,192,48,192,192,128,512,512,
256,128,128,512,256,512,256,2048,2048,8192,8192,8192,8192,2048,2048,2048,1024,
8064,1152,42,42,192,192,96,48,48,576,576,48,48,96,6720,960,35,35,30,30,80,160,
160,40,40,1032192,147456,12288,12288,3072,84,84,288,288,96,96,24576,24576,256,
12288,4096,4096,2048,2048,1024,512,512,1536,1536,512,512,128,128,8064,1152,42,
42,144,144,24,192,192,96,48,48,5376,768,28,28,48,48,48,48,256,128,64,256,32,
64,128,128],
[,[1,1,1,1,1,1,2,2,9,10,11,11,11,11,1,2,1,1,2,4,4,4,3,17,16,18,1,1,3,4,4,5,9,
10,11,11,13,14,14,22,17,18,16,21,20,6,8,8,7,4,5,4,4,1,2,3,5,5,3,60,60,62,63,
60,60,61,64,65,69,69,69,70,69,74,74,76,77,78,78,74,75,75,82,81,1,1,4,4,6,10,9,
11,11,14,14,1,1,8,2,4,4,4,4,6,6,5,17,18,17,18,21,22,60,60,63,62,69,69,73,60,
60,61,64,65,27,31,34,33,39,39,35,35,31,30,32,28,48,51,54,53],[1,2,3,4,5,6,7,8,
10,9,1,2,3,4,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,33,27,
28,29,30,31,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,1,2,
10,9,17,18,19,24,26,1,2,5,7,6,74,75,77,76,74,75,80,82,81,84,83,85,86,87,88,89,
91,90,85,86,87,88,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,85,86,91,90,85,86,89,96,97,99,107,108,125,126,128,127,126,126,125,125,133,
134,135,136,137,138,139,140],,[1,2,3,4,5,6,7,8,10,9,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,33,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,63,62,64,65,66,67,68,69,70,
71,72,73,1,2,10,9,11,12,15,16,16,25,25,85,86,87,88,89,91,90,92,93,94,95,96,97,
98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,116,115,117,
118,119,120,121,122,123,124,125,126,128,127,130,129,132,131,133,134,135,136,
137,138,139,140],,[1,2,3,4,5,6,7,8,1,1,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,27,27,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,60,60,64,65,66,67,68,69,70,71,72,73,74,75,
74,74,78,79,80,82,81,84,83,85,86,87,88,89,85,85,92,93,94,95,96,97,98,99,100,
101,102,103,104,105,106,107,108,109,110,111,112,113,114,113,113,117,118,119,
120,121,122,123,124,125,126,125,125,130,129,131,132,133,134,135,136,137,138,
139,140]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-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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--> --------------------
--> maximum size reached
--> --------------------
