Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#############################################################################
##
#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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(127,128)]);
ALF("J4M4","J4",[1,2,3,2,2,3,5,6,12,13,4,9,11,10,3,5,2,3,5,5,6,6,7,6,14,7,
3,2,7,5,6,6,26,27,11,10,23,21,22,16,6,7,14,16,14,7,15,16,14,6,6,5,6,3,6,7,
5,6,7,4,10,32,33,10,11,21,22,23,4,10,10,21,11,8,17,48,49,28,42,18,30,31,
53,54,2,3,5,6,7,25,24,10,11,21,22,2,3,16,6,5,6,6,6,7,7,6,5,7,6,7,15,16,9,
11,56,55,10,11,23,10,11,22,21,23,7,15,40,39,37,38,23,23,15,14,16,6,29,16,
7,15],[
"unique up to table automorphisms of J4M4 and Galois automorphisms of J4,\n",
"equal to the fusion map on the CAS table"
]);
ALN("J4M4",["n8j4"]);
MOT("L2(17)x2",
[
"5th maximal subgroup of J3.2"
],
0,
0,
0,
[(19,21)(20,22),( 9,11)(10,12),(13,15,17)(14,16,18)],
["ConstructDirectProduct",[["L2(17)"],["Cyclic",2]]]);
ARC("L2(17)x2","tomfusion",rec(name:="L2(17)x2",map:=[1,2,4,3,5,13,9,10,19,22,
19,22,27,40,27,40,27,40,38,50,38,50],text:=[
"fusion map is unique"
]));
ALF("L2(17)x2","J3.2",[1,18,2,18,4,20,5,19,8,22,8,22,9,24,10,25,11,26,15,
29,16,30],[
"fusion map is unique up to table automorphisms"
]);
MOT("a4xa5",
[
"origin: CAS library,\n",
"maximal subgroup of j2,\n",
"test: 1. o.r., sym 2 decompose correctly \n",
"tests: 1.o.r., pow[2,3,5]"
],
[720,240,48,16,180,180,36,9,9,60,60,12,12,12,20,20,15,15,15,15],
[,[1,1,1,1,6,5,7,9,8,11,10,7,6,5,11,10,20,19,18,17],[1,2,3,4,1,1,1,1,1,11,10,
2,3,3,16,15,11,10,11,10],,[1,2,3,4,6,5,7,9,8,1,1,12,14,13,2,2,6,6,5,5]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,E(3)^2,E(3),1,E(3)^2,E(3),
1,1,1,E(3)^2,E(3),1,1,E(3)^2,E(3)^2,E(3),E(3)],
[TENSOR,[2,2]],[3,3,-1,-1,3,3,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,-1,-1,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,
-E(5)^2-E(5)^3],
[GALOIS,[4,2]],
[TENSOR,[4,2]],
[TENSOR,[5,2]],
[TENSOR,[4,3]],
[TENSOR,[5,3]],[3,-1,3,-1,0,0,3,0,0,3,3,-1,0,0,-1,-1,0,0,0,0],[4,4,0,0,4,4,1,
1,1,-1,-1,1,0,0,-1,-1,-1,-1,-1,-1],
[TENSOR,[11,2]],
[TENSOR,[11,3]],[5,5,1,1,5,5,-1,-1,-1,0,0,-1,1,1,0,0,0,0,0,0],
[TENSOR,[14,2]],
[TENSOR,[14,3]],[9,-3,-3,1,0,0,0,0,0,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3,0,0,
0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0],
[GALOIS,[17,2]],[12,-4,0,0,0,0,3,0,0,-3,-3,-1,0,0,1,1,0,0,0,0],[15,-5,3,-1,0,
0,-3,0,0,0,0,1,0,0,0,0,0,0,0,0]],
[(10,11)(15,16)(17,18)(19,20),( 5, 6)( 8, 9)(13,14)(17,19)(18,20)]);
ARC("a4xa5","tomfusion",rec(name:="A4xA5",map:=[1,2,3,4,5,5,6,7,7,15,15,
17,19,19,25,25,38,38,38,38],text:=[
"fusion map is unique"
]));
ALF("a4xa5","J2",[1,3,2,3,4,4,5,5,5,8,7,12,11,11,16,15,21,20,21,20],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("a4xa5","(A4xA5):2",[1,2,3,4,5,5,6,7,7,8,8,9,10,10,11,11,12,13,13,12],[
"fusion map is unique up to table aut."
]);
MOT("a5xd10",
[
"origin: CAS library,\n",
"maximal subgroup of J2,\n",
"normalizer of a defect 5-subgroup of type 5AB in G2(4),\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly,\n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
[( 2, 3)( 6, 7)(10,11)(13,17)(14,19)(15,18)(16,20),( 2, 3)( 6, 7)(10,11)
(14,15)(18,19)],
["ConstructDirectProduct",[["A5"],["Dihedral",10]],(),(5,9)(6,10)(7,11)(8,
12)]);
ARC("a5xd10","tomfusion",rec(name:="A5xD10",map:=[1,9,9,2,3,19,19,4,5,27,27,
15,10,11,12,21,10,12,11,21],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("a5xd10","J2",[1,7,8,2,3,15,16,3,4,20,21,11,10,9,7,18,9,8,10,17],[
"fusion map is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("a5xd10","2xA5",[1,1,1,6,2,2,2,7,3,3,3,8,4,4,4,9,5,5,5,10]);
ALF("a5xd10","U3(4).2",[1,5,6,15,2,9,10,15,3,13,14,16,7,8,5,19,8,6,7,20],[
"fusion map is unique up to table autom."
]);
ALF("a5xd10","G2(4)",[1,9,10,2,3,20,21,3,4,27,28,13,11,10,12,18,12,11,9,
19],[
"fusion of the 5AB normalizer determined up to table aut."
]);
ALF("a5xd10","(A5xD10).2",[1,4,4,10,2,8,8,11,3,9,9,12,5,6,7,13,5,7,6,13],[
"fusion map is unique up to table aut."
]);
MOT("D10xA5",
[
"normalizer of a defect 5-subgroup of type 5CD in G2(4)"
],
0,
0,
0,
0,
["ConstructPermuted",["a5xd10"]]);
ALF("D10xA5","G2(4)",[1,11,12,3,2,18,19,3,5,29,30,14,9,10,11,20,10,12,9,
21],[
"fusion of the 5CD normalizer determined up to table aut."
]);
ALF("D10xA5","(D10xA5).2",[1,4,4,10,2,8,8,11,3,9,9,12,5,6,7,13,5,7,6,13],[
"fusion map is unique up to table aut."
]);
MOT("c2aj4",
[
"origin: CAS library,\n",
"power maps corrected (using GAP): 93->52, 94->51; T. Breuer, 07.06.90\n",
"tests: 1.o.r., pow[2,3,5,7,11]"
],
[21799895040,21799895040,15728640,7864320,5406720,2661120,2661120,1179648,
1179648,196608,98304,98304,6144,16384,16384,8192,2304,2304,1536,512,256,256,
48,6144,6144,1024,512,512,192,192,192,64,48,48,2304,2304,384,192,192,2304,
2304,384,192,192,288,288,48,960,960,160,160,160,80,30,30,84,84,84,84,42,42,42,
42,264,264,44,66,66,66,66,344064,344064,24576,6144,6144,28,28,28,28,96,96,48,
48,48,40960,40960,4096,2048,1280,80,80,40,40,40,3072,3072,1536,768,256,256,96,
96,48,48,48,1024,1024,512,256,128,64,64,32],
[,[1,1,1,1,2,6,6,1,1,1,2,1,4,3,3,3,6,6,9,10,15,14,18,8,8,10,12,11,17,17,24,26,
29,29,35,35,35,35,36,35,35,35,35,36,35,35,37,48,48,48,49,49,48,54,54,56,56,58,
58,60,60,62,62,64,64,65,67,67,69,69,1,1,3,3,4,56,56,58,58,35,35,38,38,37,3,1,
3,4,5,50,50,48,52,51,10,10,9,11,14,15,42,42,40,44,44,8,10,12,15,16,25,26,28],[
1,2,3,4,5,1,2,8,9,10,11,12,13,14,15,16,8,9,19,20,21,22,19,24,25,26,27,28,24,
25,31,32,31,31,1,2,4,3,5,9,8,10,12,11,8,9,13,48,49,50,52,51,53,48,49,58,59,56,
57,58,59,56,57,64,65,66,64,65,64,65,71,72,73,74,75,78,79,76,77,71,72,73,74,75,
85,86,87,88,89,91,90,92,94,93,95,96,97,98,99,100,95,96,97,98,98,106,107,108,
109,110,111,112,113],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,34,33,35,36,37,38,39,40,41,42,43,44,45,46,47,
1,2,3,5,5,4,6,7,58,59,56,57,62,63,60,61,64,65,66,69,70,67,68,71,72,73,74,75,
78,79,76,77,80,81,82,83,84,85,86,87,88,89,85,85,86,89,89,95,96,97,98,99,100,
101,102,103,105,104,106,107,108,109,110,111,112,113],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,33,35,36,
37,38,39,40,41,42,43,44,45,46,47,48,49,50,52,51,53,54,55,1,2,1,2,6,7,6,7,64,
65,66,69,70,67,68,71,72,73,74,75,71,72,71,72,80,81,82,83,84,85,86,87,88,89,91,
90,92,94,93,95,96,97,98,99,100,101,102,103,105,104,106,107,108,109,110,111,
112,113],,,,[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,
51,52,53,54,55,56,57,58,59,60,61,62,63,1,2,5,6,7,6,7,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
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,
40,41,42,43,44,45,46,47,48,49,50,52,51,53,54,55,58,59,56,57,62,63,60,61,64,65,
66,69,70,67,68,71,72,73,74,75,78,79,76,77,80,81,82,83,84,85,86,87,88,89,91,90,
92,94,93,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113],,,,[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,
27,28,29,30,31,32,34,33,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,52,51,
53,54,55,58,59,56,57,62,63,60,61,64,65,66,67,68,69,70,71,72,73,74,75,78,79,76,
77,80,81,82,83,84,85,86,87,88,89,91,90,92,94,93,95,96,97,98,99,100,101,102,
103,105,104,106,107,108,109,110,111,112,113],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,33,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,58,59,56,57,62,63,60,61,64,65,
66,69,70,67,68,71,72,73,74,75,78,79,76,77,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,105,104,106,107,108,109,110,111,112,
113],,,,[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,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,52,51,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,69,70,67,68,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,85,86,87,88,89,91,90,92,94,93,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,33,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,101,102,103,105,104,106,107,108,109,110,111,
112,113],,[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,
26,27,28,29,30,31,32,34,33,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,54,55,58,59,56,57,62,63,60,61,64,65,66,67,68,69,70,71,72,73,74,75,78,79,
76,77,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,105,104,106,107,108,109,110,111,112,113],,,,,,[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,
39,40,41,42,43,44,45,46,47,48,49,50,52,51,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,91,
90,92,94,93,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,34,33,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,58,59,56,57,62,63,60,61,64,65,66,67,68,69,70,71,72,73,74,75,78,
79,76,77,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,105,104,106,107,108,109,110,111,112,113],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,33,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,52,51,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,69,70,67,68,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,91,
90,92,94,93,95,96,97,98,99,100,101,102,103,105,104,106,107,108,109,110,111,
112,113],,,,[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,
52,51,53,54,55,58,59,56,57,62,63,60,61,64,65,66,69,70,67,68,71,72,73,74,75,78,
79,76,77,80,81,82,83,84,85,86,87,88,89,91,90,92,94,93,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,112,113],,,,,,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,33,35,36,
37,38,39,40,41,42,43,44,45,46,47,48,49,50,52,51,53,54,55,56,57,58,59,60,61,62,
63,64,65,66,69,70,67,68,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
89,91,90,92,94,93,95,96,97,98,99,100,101,102,103,105,104,106,107,108,109,110,
111,112,113],,,,,,[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,
49,50,51,52,53,54,55,58,59,56,57,62,63,60,61,64,65,66,69,70,67,68,71,72,73,74,
75,78,79,76,77,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113],,[1,2,3,4,5,6,7,8,9,
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,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,58,59,56,57,62,63,
60,61,64,65,66,69,70,67,68,71,72,73,74,75,78,79,76,77,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111,112,113]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[21,21,21,21,21,21,21,5,5,5,5,5,5,5,5,5,5,5,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,
1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,7,7,7,7,7,0,0,0,0,1,1,1,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,3,1,1,1],
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( 67, 69)( 68, 70)(104,105),( 71, 72)( 76, 77)( 78, 79)( 80, 81)( 95, 96)
(101,102)]);
ALF("c2aj4","J4",[1,2,2,3,5,4,9,2,3,2,6,3,7,5,6,6,10,11,7,6,15,14,23,6,5,
6,7,16,22,21,15,16,37,38,4,10,11,10,21,11,9,10,11,22,10,11,23,8,17,17,30,
31,18,28,42,13,25,12,24,33,56,32,55,19,34,60,46,61,47,62,2,3,5,6,7,25,27,
24,26,10,11,21,22,23,5,3,6,7,14,30,31,18,53,54,5,6,7,15,14,16,21,22,23,37,
38,6,6,7,15,16,14,16,29],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("c2aj4","3.M22.2",[1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,4,4,8,8,8,8,9,6,6,
6,6,6,7,7,18,18,19,19,5,5,5,5,5,12,12,12,12,12,13,13,13,10,10,10,10,10,10,
11,11,14,14,16,16,15,15,17,17,20,20,20,21,21,22,22,23,23,23,23,23,31,31,
32,32,27,27,27,27,27,24,24,24,24,24,29,29,29,29,29,25,25,25,25,25,25,30,
30,30,30,30,26,26,26,26,26,28,28,28]);
ALN("c2aj4",["J4C2a"]);
MOT("frob",
[
"origin: CAS library,\n",
"constructions: AGL(1,29),\n",
"tests: 1.o.r., pow[2,7,29]"
],
[812,29,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
28,28,28,28],
[,[1,2,4,6,8,3,5,7,1,4,6,8,3,5,7,9,11,13,15,10,12,14,9,11,13,15,10,12,14],[1,
2,5,8,4,7,3,6,9,12,15,11,14,10,13,23,26,29,25,28,24,27,16,19,22,18,21,17,
20],,[1,2,7,5,3,8,6,4,9,14,12,10,15,13,11,16,21,19,17,22,20,18,23,28,26,24,29,
27,25],,[1,2,1,1,1,1,1,1,9,9,9,9,9,9,9,23,23,23,23,23,23,23,16,16,16,16,16,16,
16],,,,[1,2,6,3,7,4,8,5,9,13,10,14,11,15,12,23,27,24,28,25,29,26,16,20,17,21,
18,22,19],,[1,2,8,7,6,5,4,3,9,15,14,13,12,11,10,16,22,21,20,19,18,17,23,29,28,
27,26,25,24],,,,[1,2,5,8,4,7,3,6,9,12,15,11,14,10,13,16,19,22,18,21,17,20,23,
26,29,25,28,24,27],,[1,2,7,5,3,8,6,4,9,14,12,10,15,13,11,23,28,26,24,29,27,25,
16,21,19,17,22,20,18],,,,[1,2,4,6,8,3,5,7,9,11,13,15,10,12,14,23,25,27,29,24,
26,28,16,18,20,22,17,19,21],,,,,,[1,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,E(7),E(7)^2,
E(7)^3,E(7)^4,E(7)^5,E(7)^6,1,E(7),E(7)^2,E(7)^3,E(7)^4,E(7)^5,E(7)^6,1,E(7),
E(7)^2,E(7)^3,E(7)^4,E(7)^5,E(7)^6,1,E(7),E(7)^2,E(7)^3,E(7)^4,E(7)^5,E(7)^6],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1],
[TENSOR,[2,8]],
[TENSOR,[2,9]],
[TENSOR,[2,10]],
[TENSOR,[2,11]],
[TENSOR,[2,12]],
[TENSOR,[2,13]],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,E(4),E(4),E(4),E(4),
E(4),E(4),E(4),-E(4),-E(4),-E(4),-E(4),-E(4),-E(4),-E(4)],
[TENSOR,[2,15]],
[TENSOR,[2,16]],
[TENSOR,[2,17]],
[TENSOR,[2,18]],
[TENSOR,[2,19]],
[TENSOR,[2,20]],
[TENSOR,[8,15]],
[TENSOR,[2,22]],
[TENSOR,[2,23]],
[TENSOR,[2,24]],
[TENSOR,[2,25]],
[TENSOR,[2,26]],
[TENSOR,[2,27]],[28,-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]],
[(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)(22,29),( 3, 5, 4, 8, 6, 7)
(10,12,11,15,13,14)(17,19,18,22,20,21)(24,26,25,29,27,28)]);
ALF("frob","L2(29).2",[1,16,6,7,8,8,7,6,2,9,10,11,11,10,9,18,22,23,27,24,
26,25,18,25,26,24,27,23,22],[
"fusion map is unique up to table automorphisms"
]);
ALF("frob","J4",[1,41,13,13,12,13,12,12,3,27,27,26,27,26,26,7,40,40,39,40,
39,39,7,40,40,39,40,39,39],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("frob","F3+.2",[1,82,25,25,25,25,25,25,3,52,52,52,52,52,52,103,159,
159,160,159,160,160,103,160,160,159,160,159,159],[
"fusion map is unique up to table automorphisms"
]);
ALN("frob",["29:28","AGL(1,29)","L2(29).2M2","F3+.2N29","F3+.2N29A","J4N29",
"J4N29A"]);
MOT("j3m4",
[
"origin: CAS library,\n",
"4th maximal subgroup of J3,\n",
"table is sorted w.r. to normal series 2^4.3.A5,\n",
"constructions: AGL(2,4),\n",
"tests: 1.o.r., pow[2,3,5]"
],
[2880,192,180,180,48,16,12,12,36,36,9,12,12,15,15,15,15,15,15],
[,[1,1,4,3,1,2,4,3,10,9,11,10,9,17,19,18,14,16,15],[1,2,1,1,5,6,5,5,1,1,1,2,2,
17,17,17,14,14,14],,[1,2,4,3,5,6,8,7,10,9,11,13,12,1,4,3,1,4,3]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,-1,-1,-1,-1,0,0,0,0,0,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,
-E(5)^2-E(5)^3],
[GALOIS,[2,2]],[4,4,4,4,0,0,0,0,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[5,5,5,5,1,1,1,1,
-1,-1,-1,-1,-1,0,0,0,0,0,0],[1,1,E(3),E(3)^2,1,1,E(3),E(3)^2,E(3),E(3)^2,1,
E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2],
[TENSOR,[6,6]],
[TENSOR,[3,6]],
[TENSOR,[3,7]],
[TENSOR,[2,6]],
[TENSOR,[2,7]],
[TENSOR,[4,6]],
[TENSOR,[4,7]],
[TENSOR,[5,6]],
[TENSOR,[5,7]],[15,-1,0,0,3,-1,0,0,3,3,0,-1,-1,0,0,0,0,0,0],
[TENSOR,[16,6]],
[TENSOR,[16,7]],[45,-3,0,0,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(14,17)(15,18)(16,19),( 3, 4)( 7, 8)( 9,10)(12,13)(15,16)(18,19)]);
ARC("j3m4","CAS",[rec(name:="j3m4",
permchars:=( 2, 7, 3, 4,10, 8, 5,13,12,11, 9, 6),
permclasses:=( 3, 4, 5)( 6,10)( 7,12,14,11)( 8,13,15,16,17, 9),
text:="maximal subgroup of j3")]);
ARC("j3m4","tomfusion",rec(name:="2^4:(3xA5)",map:=[1,2,4,4,3,11,15,15,5,5,6,
16,16,13,35,35,13,35,35],text:=[
"fusion map is unique"
]));
ALF("j3m4","J3",[1,2,3,3,2,5,8,8,3,3,4,8,8,6,16,16,7,17,17],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("j3m4","2^4:(3xA5).2",[1,2,3,3,4,5,6,6,7,7,8,9,9,10,11,12,10,12,11],[
"fusion map is unique up to table automorphisms"
]);
ALF("j3m4","L3(4).3",[1,2,9,10,2,4,13,14,9,10,3,13,14,5,15,16,6,17,18],[
"fusion map is unique up to table aut."
]);
ALN("j3m4",["2^4:(3xA5)","AGL(2,4)"]);
MOT("j3m6",
[
"origin: CAS library,\n",
"maximal subgroup of j3, (3 x a6):2 \n",
"tests: 1.o.r., pow[2,3,5]"
],
[2160,1080,48,24,27,27,27,24,12,30,30,15,15,20,8,8,10,10],
[,[1,2,1,2,5,7,6,3,4,11,10,13,12,1,8,8,10,11],[1,1,3,3,1,1,1,8,8,11,10,11,10,
14,16,15,18,17],,[1,2,3,4,5,7,6,8,9,1,1,2,2,14,16,15,14,14]],
0,
[(15,16),(10,11)(12,13)(17,18),(6,7)],
["ConstructIndexTwoSubdirectProduct","C3","S3","A6","A6.2_2",
[29,30,31,32,33],(2,3,5,10,7)(4,8)(6,11,9)(17,18),(3,4,15,8,14,6,11,18,10,17,
9,13,5,16,7,12)]);
ARC("j3m6","tomfusion",rec(name:="(3xA6):2_2",map:=[1,4,2,12,5,6,6,8,25,
10,10,28,28,3,16,16,21,21],text:=[
"fusion map is unique"
]));
ALF("j3m6","J3",[1,3,2,8,4,3,3,5,15,6,7,16,17,2,9,9,14,13],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("j3m6","(3xM10):2",[1,2,3,4,5,6,6,7,8,9,9,10,10,14,15,15,16,16],[
"fusion map is unique"
]);
ALF("j3m6","A6.2_2",[1,1,2,2,3,3,3,4,4,5,6,5,6,7,8,9,11,10]);
ALF("j3m6","S3",[1,2,1,2,1,2,2,1,2,1,1,2,2,3,3,3,3,3]);
ALN("j3m6",["(3xA6):2_2","J3N3A"]);
MOT("2^10:L5(2)",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5,7,31]"
],
[10239344640,66060288,11796480,2752512,2752512,393216,393216,49152,49152,
98304,32768,98304,3072,32768,8192,8192,8064,8064,1152,1152,2880,576,288,6144,
6144,6144,6144,1024,1024,2048,2048,2048,2048,1024,1024,256,256,256,256,256,
128,128,60,20,192,192,192,192,96,96,48,48,24,84,84,84,84,64,64,64,64,48,48,48,
48,28,28,28,28,15,15,42,42,42,42,31,31,31,31,31,31],
[,[1,1,1,1,1,1,1,2,2,1,1,2,3,2,2,2,17,17,17,17,21,21,21,4,5,4,5,6,7,4,4,7,7,6,
5,9,10,14,12,11,16,15,43,43,17,17,17,17,19,19,21,22,23,54,54,56,56,30,31,32,
33,45,46,45,46,54,54,56,56,70,71,72,72,74,74,76,77,78,79,80,81],[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,1,2,2,3,1,2,3,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,4,5,6,7,8,9,10,12,13,56,57,54,55,58,59,60,61,24,25,
26,27,68,69,66,67,43,43,56,57,54,55,81,80,77,76,79,78],,[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,
37,38,39,40,41,42,1,3,45,46,47,48,49,50,51,52,53,56,57,54,55,58,59,60,61,62,
63,64,65,68,69,66,67,21,21,74,75,72,73,78,79,80,81,76,77],,[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,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,1,2,1,2,58,59,60,61,62,
63,64,65,4,5,4,5,71,70,17,18,17,18,80,81,76,77,78,79],,,,[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,
62,63,64,65,66,67,68,69,71,70,72,73,74,75,79,78,81,80,77,76],,[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,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,56,57,54,55,58,59,
60,61,62,63,64,65,68,69,66,67,71,70,74,75,72,73,79,78,81,80,77,76],,,,[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,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,56,57,54,55,
58,59,60,61,62,63,64,65,68,69,66,67,70,71,74,75,72,73,81,80,77,76,79,78],,[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,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,56,57,
54,55,58,59,60,61,62,63,64,65,68,69,66,67,70,71,74,75,72,73,80,81,76,77,78,
79],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,77,76,79,
78,81,80],,,,,,[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,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,71,70,72,73,74,75,
77,76,79,78,81,80],,[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,
49,50,51,52,53,56,57,54,55,58,59,60,61,62,63,64,65,68,69,66,67,70,71,74,75,72,
73,1,1,1,1,1,1],,,,,,[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,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,71,70,72,73,
74,75,81,80,77,76,79,78],,,,[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,
46,47,48,49,50,51,52,53,56,57,54,55,58,59,60,61,62,63,64,65,68,69,66,67,71,70,
74,75,72,73,78,79,80,81,76,77]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1],[30,30,30,14,14,14,14,14,14,6,6,6,6,6,6,6,6,6,6,6,0,0,0,6,6,6,6,6,6,
2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,2,2,2,2,2,2,0,0,0,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[124,124,124,28,28,28,28,28,28,12,12,12,
12,12,12,12,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,-1,-1,1,1,1,1,
1,1,0,0,0,-2,-2,-2,-2,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,1,1,1,1,0,0,0,0,0,0],[155,
155,155,27,27,27,27,27,27,-5,-5,-5,-5,-5,-5,-5,8,8,8,8,5,5,5,3,3,3,3,3,3,-5,
-5,-5,-5,-5,-5,-5,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,-1,-1,-1,-1,
0,0,0,0,-1,-1,-1,-1,0,0,1,1,1,1,0,0,0,0,0,0],[217,217,217,-7,-7,-7,-7,-7,-7,9,
9,9,9,9,9,9,7,7,7,7,4,4,4,-7,-7,-7,-7,-7,-7,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,-1,
-1,-1,-1,-1,-1,0,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,0,0,0,0,-1,-1,0,0,0,0,0,0,0,
0,0,0],[280,280,280,56,56,56,56,56,56,8,8,8,8,8,8,8,7,7,7,7,-5,-5,-5,8,8,8,8,
8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1],[315,315,315,-21,-21,-21,-21,-21,
-21,3,3,3,3,3,3,3,0,0,0,0,0,0,0,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
E(31)+E(31)^2+E(31)^4+E(31)^8+E(31)^16,E(31)^15+E(31)^23+E(31)^27+E(31)^29
+E(31)^30,E(31)^5+E(31)^9+E(31)^10+E(31)^18+E(31)^20,E(31)^11+E(31)^13
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[19530,3402,-630,-294,
-294,-102,-102,-6,42,66,2,-30,-6,34,18,-14,0,0,0,0,0,0,0,-6,18,-6,18,2,-6,-10,
6,-10,6,-2,-2,2,2,-2,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[868,-28,4,84,-28,-12,4,-4,4,44,-4,4,0,-12,
-4,4,7,-7,-1,1,10,2,-2,4,-4,-4,4,0,0,8,0,-4,4,-4,0,0,4,0,0,-4,0,0,3,-1,3,-1,
-3,1,-1,1,2,-2,0,0,0,0,0,2,-2,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
868,-28,4,-28,84,4,-12,-4,4,4,-12,44,0,-4,4,-4,7,-7,-1,1,10,2,-2,-4,4,4,-4,0,
0,4,-4,0,8,0,-4,0,0,4,-4,0,0,0,3,-1,-1,3,1,-3,-1,1,-2,2,0,0,0,0,0,0,0,2,-2,-1,
1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4340,-140,20,308,-28,-44,4,-20,20,52,
-28,-4,0,12,-12,12,14,-14,-2,2,-10,-2,2,12,-12,-12,12,0,0,4,-4,0,8,0,-4,0,0,
-4,4,0,0,0,0,0,2,2,-2,-2,-2,2,-2,2,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[4340,-140,20,196,84,-28,-12,-20,20,12,-36,36,0,20,-4,4,-7,7,
1,-1,20,4,-4,4,-4,-4,4,0,0,0,-8,4,12,4,-8,0,-4,0,0,4,0,0,0,0,1,-3,-1,3,1,-1,0,
0,0,0,0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4340,-140,20,
-28,308,4,-44,-20,20,-4,12,52,0,-28,12,-12,14,-14,-2,2,-10,-2,2,-12,12,12,-12,
0,0,8,0,-4,4,-4,0,0,-4,0,0,4,0,0,0,0,2,2,-2,-2,-2,2,2,-2,0,0,0,0,0,-2,2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4340,-140,20,84,196,-12,-28,-20,20,36,
20,12,0,-36,4,-4,-7,7,1,-1,20,4,-4,-4,4,4,-4,0,0,12,4,-8,0,-8,4,0,0,-4,4,0,0,
0,0,0,-3,1,3,-1,1,-1,0,0,0,0,0,0,0,0,0,-2,2,-1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[7812,-252,36,84,420,-12,-60,-36,36,-36,-20,84,0,4,12,-12,0,0,0,0,0,
0,0,-12,12,12,-12,0,0,0,-8,4,12,4,-8,0,4,0,0,-4,0,0,-3,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[7812,-252,36,420,84,
-60,-12,-36,36,84,4,-36,0,-20,-12,12,0,0,0,0,0,0,0,12,-12,-12,12,0,0,12,4,-8,
0,-8,4,0,0,4,-4,0,0,0,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[8680,-280,40,392,168,-56,-24,-40,40,-40,-8,-56,0,40,
-8,8,7,-7,-1,1,10,2,-2,8,-8,-8,8,0,0,-16,0,8,-8,8,0,0,0,0,0,0,0,0,0,0,-1,3,1,
-3,-1,1,2,-2,0,0,0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
8680,-280,40,168,392,-24,-56,-40,40,-56,40,-40,0,-8,8,-8,7,-7,-1,1,10,2,-2,-8,
8,8,-8,0,0,-8,8,0,-16,0,8,0,0,0,0,0,0,0,0,0,3,-1,-3,1,-1,1,-2,2,0,0,0,0,0,0,0,
0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[13020,-420,60,364,-420,-52,60,
4,-4,84,4,60,0,-52,4,-4,21,-21,-3,3,0,0,0,-4,4,4,-4,0,0,-8,0,4,-4,4,0,0,4,0,0,
-4,0,0,0,0,1,-3,-1,3,1,-1,0,0,0,0,0,0,0,-2,2,0,0,-1,1,1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[13020,-420,60,-420,364,60,-52,4,-4,60,-52,84,0,4,-4,4,21,-21,
-3,3,0,0,0,4,-4,-4,4,0,0,-4,4,0,-8,0,4,0,0,4,-4,0,0,0,0,0,-3,1,3,-1,1,-1,0,0,
0,0,0,0,0,0,0,-2,2,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[13020,-420,60,
-308,252,44,-36,4,-4,36,20,-84,0,-4,-12,12,21,-21,-3,3,0,0,0,-4,4,4,-4,0,0,0,
8,12,4,-4,-8,0,-4,0,0,4,0,0,0,0,1,-3,-1,3,1,-1,0,0,0,0,0,0,0,2,-2,0,0,-1,1,1,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[13020,-420,60,252,-308,-36,44,4,-4,-84,
-4,36,0,20,12,-12,21,-21,-3,3,0,0,0,4,-4,-4,4,0,0,4,12,8,0,-8,-4,0,0,-4,4,0,0,
0,0,0,-3,1,3,-1,1,-1,0,0,0,0,0,0,0,0,0,2,-2,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[13888,-448,64,448,448,-64,-64,-64,64,0,0,0,0,0,0,0,-14,14,2,-2,-20,
-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,-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],[26040,-840,120,56,-168,-8,
24,8,-8,120,24,-24,0,-56,-8,8,-21,21,3,-3,0,0,0,-8,8,8,-8,0,0,-8,8,16,0,0,-8,
0,0,0,0,0,0,0,0,0,-1,3,1,-3,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[26040,-840,120,-168,56,24,-8,8,-8,-24,-56,120,0,24,8,-8,
-21,21,3,-3,0,0,0,8,-8,-8,8,0,0,0,16,8,-8,-8,0,0,0,0,0,0,0,0,0,0,3,-1,-3,1,-1,
1,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[39060,
-1260,180,84,-252,-12,36,12,-12,-108,68,-36,0,-20,20,-20,0,0,0,0,0,0,0,12,-12,
-12,12,0,0,4,-4,0,8,0,-4,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[39060,-1260,180,-252,84,36,-12,12,
-12,-36,-20,-108,0,68,-20,20,0,0,0,0,0,0,0,-12,12,12,-12,0,0,8,0,-4,4,-4,0,0,
4,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[39060,-1260,180,-588,420,84,-60,12,-12,36,20,12,0,-36,4,-4,0,
0,0,0,0,0,0,12,-12,-12,12,0,0,-4,-12,-8,0,8,4,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[39060,-1260,
180,420,-588,-60,84,12,-12,12,-36,36,0,20,-4,4,0,0,0,0,0,0,0,-12,12,12,-12,0,
0,0,-8,-12,-4,4,8,0,-4,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(76,81,78,77,80,79),(54,56)(55,57)(66,68)(67,69)(72,74)(73,75),(70,71),
(76,79,80,77,78,81)]);
ALF("2^10:L5(2)","J4",[1,2,3,2,3,3,2,5,6,2,3,5,7,5,6,6,4,9,10,11,4,10,11,6,7,
5,7,7,6,6,6,5,6,7,7,16,6,14,14,7,15,16,8,18,10,11,11,10,21,22,10,21,23,13,
25,12,24,16,15,14,16,22,23,21,23,25,27,24,26,28,28,33,56,32,55,43,43,44,
44,45,45],[
"fusion map is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^10:L5(2)","O10+(2)",[1,2,4,2,3,4,5,11,13,4,5,10,17,11,13,14,7,23,
26,30,8,28,32,11,12,13,15,17,18,13,14,18,16,17,15,37,17,36,35,18,38,37,20,
45,26,29,30,31,50,54,32,53,57,34,58,34,59,37,38,40,39,50,52,54,56,59,60,
58,60,65,65,71,88,72,89,83,82,85,84,87,86],[
"fusion map is unique up to table automorphisms,\n",
"compatible with Brauer tables"
]);
ALF("2^10:L5(2)","L5(2)",[1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,
6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,9,9,10,10,10,10,10,10,11,11,11,12,12,
13,13,14,14,14,14,15,15,15,15,16,16,17,17,18,19,20,20,21,21,22,23,24,25,
26,27]);
ALN("2^10:L5(2)",["O10+(2)M3"]);
ARC("2^10:L5(2)","CAS",[rec(name:="l52m10",
permchars:=( 7,12,11, 8, 9,10)(13,15)(14,16),
permclasses:=(17,46,51,43,60,38,31,18,47,52,44,61,39,32,19,48,53,45,50,55,65,
59,37,30)(20,49,54,64,58,36,23,42,35,22,41,34,21,40,33)(56,70,62)(57,71,63)
(68,72)(69,73)(77,81)(79,80),
text:="")]);
MOT("O10+(2)M4",
0,
0,
0,
0,
0,
["ConstructPermuted",["2^10:L5(2)"]]);
ALF("O10+(2)M4","O10+(2)",[1,2,4,2,3,4,5,11,13,4,5,10,17,11,13,14,7,23,26,
30,8,28,32,11,12,13,15,17,18,13,14,18,16,17,15,37,17,36,35,18,38,37,20,45,
26,29,30,31,50,54,32,53,57,34,59,34,58,37,38,40,39,50,52,54,56,58,60,59,
60,65,65,72,89,71,88,82,83,84,85,86,87],[
"fusion 2^10:L5(2) -> O10+(2) mapped under O10+(2).2"
]);
MOT("(3xO8-(2)):2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct',\n",
"5th maximal subgroup of O10+(2)"
],
[1184440320,1105920,276480,18432,362880,6480,3888,9216,9216,1152,384,1080,3456
,2160,1728,432,432,144,126,192,192,54,180,120,288,144,72,270,270,51,51,63,90,
592220160,552960,138240,9216,181440,3240,1944,4608,4608,576,192,540,1728,1080,
864,216,216,72,63,96,96,27,180,180,60,144,72,36,270,270,135,51,51,51,51,63,63,
90,90,2903040,9216,7680,4608,768,768,256,4320,1296,288,216,144,72,192,64,16,60
,288,96,72,24,24,14,18,20,24,30],
[,[1,1,1,1,5,6,7,2,2,3,4,12,5,6,5,7,6,6,19,8,9,22,12,12,13,15,16,28,29,30,31,
32,28,34,34,34,34,38,39,40,35,35,36,37,45,38,39,38,40,39,39,52,41,42,55,45,45,
45,46,48,49,62,63,64,65,66,67,68,69,70,62,63,1,1,3,3,2,3,3,5,7,5,6,7,6,8,9,11,
12,15,15,17,16,17,19,22,24,25,29],[1,2,3,4,1,1,1,8,9,10,11,12,2,2,3,2,3,4,19,
20,21,7,23,24,8,10,9,12,12,31,30,19,23,1,2,3,4,1,1,1,8,9,10,11,12,2,2,3,2,3,4,
19,20,21,7,23,23,24,8,10,9,12,12,12,31,31,30,30,19,19,23,23,73,74,75,76,77,78,
79,73,73,74,73,74,74,86,87,88,89,76,75,76,77,78,95,81,97,86,89],,[1,2,3,4,5,6,
7,8,9,10,11,1,13,14,15,16,17,18,19,20,21,22,2,3,25,26,27,6,5,31,30,32,14,34,35
,36,37,38,39,40,41,42,43,44,34,46,47,48,49,50,51,52,53,54,55,35,35,36,59,60,61
,39,39,38,68,67,65,66,70,69,47,47,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87
,88,73,90,91,92,93,94,95,96,75,98,80],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
,17,18,1,20,21,22,23,24,25,26,27,28,29,31,30,5,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,34,53,54,55,57,56,58,59,60,61,63,62,64,68,67,65,66,
38,38,72,71,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
73,96,97,98,99],,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,1,1,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47
,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,34,34,34,34,70,69,71,72,73
,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99
]],
0,
[(69,70),(56,57)(62,63)(71,72),(65,66)(67,68),(30,31)(65,67,66,68)],
["ConstructIndexTwoSubdirectProduct","C3","S3","O8-(2)","O8-(2).2",[154,155,
156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,
175,176,177,178,179,180],(),()]);
ALF("(3xO8-(2)):2","S3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3]);
ALF("(3xO8-(2)):2","O8-(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,23,24,25,26,27,28,28,29,30,30,31,31,
32,32,33,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60]);
ALF("(3xO8-(2)):2","O10+(2)",[1,2,3,5,6,7,9,11,10,12,16,19,21,23,22,25,29,
31,34,36,35,41,43,44,47,49,48,64,63,66,67,73,80,6,21,22,24,7,9,8,47,46,49,
51,63,26,25,29,28,27,33,73,75,74,42,78,79,81,50,52,53,61,62,64,92,93,94,
95,71,72,76,77,3,5,12,12,14,15,15,22,27,24,29,33,31,36,35,39,44,49,49,52,
55,56,60,68,70,75,81],[
"fusion map is unique up to table automorphisms",
]);
ALN("(3xO8-(2)):2",["O10+(2)M5"]);
MOT("(A5xU4(2)):2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct',\n",
"8th maximal subgroup of O10+(2)"
],
[3110400,69120,11520,38880,12960,6480,5760,960,600,4320,2160,2160,1440,540,720
,207360,4608,768,2592,864,432,384,64,40,288,144,144,96,36,48,155520,3456,576,
1944,648,324,288,48,30,216,108,108,72,27,36,129600,2880,480,3240,3240,540,270,
240,40,25,360,360,180,180,90,60,45,45,60,60,8640,576,576,192,216,216,72,48,60,
72,2880,192,192,64,72,72,24,16,20,24,4320,288,288,96,108,108,36,24,30,36],
[,[1,1,1,4,5,6,2,3,9,4,5,6,5,14,10,1,1,1,4,5,6,2,3,9,4,5,6,5,14,10,31,31,31,34
,35,36,32,33,39,34,35,36,35,44,40,46,46,46,49,50,51,52,47,48,55,49,50,51,51,52
,51,62,63,56,57,1,1,3,3,5,6,6,7,9,13,16,16,18,18,20,21,21,22,24,28,31,31,33,33
,35,36,36,37,39,43],[1,2,3,1,1,1,7,8,9,2,2,2,3,4,7,16,17,18,16,16,16,22,23,24,
17,17,17,18,19,22,1,2,3,1,1,1,7,8,9,2,2,2,3,4,7,46,47,48,46,46,46,46,53,54,55,
47,47,47,47,47,48,50,49,53,53,66,67,68,69,66,66,67,73,74,68,76,77,78,79,76,76,
77,83,84,78,66,67,68,69,66,66,67,73,74,68],,[1,2,3,4,5,6,7,8,1,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,16,25,26,27,28,29,30,31,32,33,34,35,36,37,38,31,40,
41,42,43,44,45,1,2,3,4,4,5,6,7,8,1,10,10,11,11,12,13,14,14,15,15,66,67,68,69,
70,71,72,73,66,75,76,77,78,79,80,81,82,83,76,85,86,87,88,89,90,91,92,93,86,95]
],
0,
[(49,50)(56,57)(58,59)(62,63)(64,65)],
["ConstructIndexTwoSubdirectProduct","A5","A5.2","U4(2)","U4(2).2",[116,117,
118,119,120,121,122,123,124,125,141,142,143,144,145,146,147,148,149,150,166,
167,168,169,170,171,172,173,174,175],(),()]);
ALF("(A5xU4(2)):2","A5.2",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7]);
ALF("(A5xU4(2)):2","U4(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,4,
5,6,7,8,9,10,10,11,11,12,13,14,14,15,15,16,17,18,19,20,21,22,23,24,25,16,
17,18,19,20,21,22,23,24,25,16,17,18,19,20,21,22,23,24,25]);
ALF("(A5xU4(2)):2","O10+(2)",[1,2,3,9,6,7,10,12,19,25,21,23,22,41,48,3,5,
5,27,22,29,14,15,44,33,24,31,24,68,55,6,21,22,8,7,9,46,49,63,28,26,25,29,
42,53,19,43,44,61,62,63,64,69,70,20,76,77,78,79,80,81,90,91,96,97,3,5,12,
12,22,29,31,35,44,49,12,15,16,18,49,52,56,38,70,51,22,24,49,49,29,27,33,
74,81,52],[
"fusion map is unique up to table automorphisms",
]);
ALN("(A5xU4(2)):2",["O10+(2)M8"]);
MOT("mx1j4",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5,7,11,23]"
],
[501397585920,1816657920,283115520,2752512,491520,491520,393216,34560,4032,
245760,98304,98304,43008,8192,6144,6144,2048,2048,1024,1024,768,768,480,34560,
2304,2304,576,192,192,96,96,168,168,768,512,256,128,64,64,480,80,80,80,22,192,
192,48,48,48,48,24,24,56,56,28,28,30,30,32,80,80,21,21,22,23,23,48,48,28,28,
30,30],
[,[1,1,1,1,1,1,1,8,9,3,3,3,2,3,4,4,4,4,7,7,5,6,23,8,8,8,9,8,8,9,9,32,33,12,12,
11,14,17,18,23,23,23,23,44,26,26,25,27,28,28,30,31,32,33,33,32,57,58,35,40,40,
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,
28,29,30,31,33,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,54,
53,56,55,58,57,59,61,60,63,62,64,65,66,67,68,70,69,72,71],,,,[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,33,32,34,
35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,54,53,56,55,57,58,59,61,
60,63,62,64,66,65,68,67,70,69,71,72],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,33,32,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,54,53,56,55,57,58,59,60,61,63,62,64,66,65,68,67,
70,69,71,72],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,61,60,62,63,64,1,1,67,68,69,70,71,72],,,,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
58,57,59,60,61,62,63,64,65,66,68,67,69,70,72,71]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[23,23,
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0,-1,-1,0,0,0,0],[45,45,45,-3,5,5,-3,0,3,5,-3,-3,-3,5,-3,-3,1,1,1,-3,1,1,0,0,
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0],
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+E(23)^8+E(23)^9+E(23)^12+E(23)^13+E(23)^16+E(23)^18,E(23)^5+E(23)^7+E(23)^10
+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20+E(23)^21+E(23)^22,-1,
-1,0,0,0,0],
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2,0,0,0,0,0,0,0,0,0,0,0],[34155,2475,-405,-213,75,75,-21,0,0,75,-21,27,3,-5,
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-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,-E(7)^3-E(7)^5-E(7)^6,
-E(7)-E(7)^2-E(7)^4,0,0,1,0,0,0,0,0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,0,0],
[GALOIS,[40,3]],[34155,2475,-405,-165,-45,-45,27,0,0,-45,27,75,-45,3,3,3,7,-9,
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0,0,0,0,0,-E(7)^3-E(7)^5-E(7)^6,-E(7)-E(7)^2-E(7)^4,0,0],
[GALOIS,[42,3]],[41216,-1792,256,0,128,128,0,-40,14,-128,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,2,2,0,0,1,0,0,0,0,0,0,0,0],[42504,3080,-504,168,120,120,168,-39,0,120,
40,40,-56,-8,8,8,0,0,0,8,0,0,4,9,-7,9,0,-3,-3,0,0,0,0,-8,0,0,0,0,0,-4,0,0,0,0,
1,1,1,0,-1,-1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,-1,-1],[48576,3520,-576,
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-E(5)^4,0,0,1,0,0,0,0,0,0,0,0],
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0],[79695,5775,-945,63,-105,-105,255,45,0,-105,-65,-17,7,7,-17,-17,-5,11,3,7,
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0,-1,0,0,0,0,0,0,0,1,1,0,0,0,0],[85008,-3696,528,112,288,-96,-16,30,0,-96,-16,
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2,-2,0,0,2,-2,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0],[85008,-3696,528,
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0,0,0,0,0,0],[91080,6600,-1080,104,120,120,104,-45,0,120,-24,-24,8,-8,-8,-8,0,
0,0,-8,0,0,0,-45,3,3,0,-1,-1,0,0,3,3,8,0,0,0,0,0,0,0,0,0,0,3,3,-1,0,1,1,0,0,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,0,0],[127512,-5544,792,168,-48,16,
-24,0,21,16,-24,24,0,0,24,-24,-4,-4,4,0,4,-4,-3,0,0,0,-3,0,0,-3,1,0,0,0,0,0,0,
2,-2,-3,1,-3,1,0,0,0,0,1,0,0,1,-1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0],[
127512,-5544,792,168,16,-48,-24,0,21,16,-24,24,0,0,-24,24,-4,-4,4,0,-4,4,-3,0,
0,0,-3,0,0,1,-3,0,0,0,0,0,0,2,-2,-3,1,1,-3,0,0,0,0,1,0,0,-1,1,0,0,0,0,0,0,0,1,
1,0,0,0,0,0,0,0,0,0,0,0],[141680,-6160,880,-112,-160,-160,16,20,14,160,16,-16,
0,0,0,0,8,8,-8,0,0,0,0,-20,-4,4,-2,-4,4,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,
-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[154560,-6720,960,-448,0,
0,64,30,0,0,64,-64,0,0,0,0,0,0,0,0,0,0,0,-30,-6,6,0,2,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-1,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-2*E(12)^7+2*E(12)^11,
2*E(12)^7-2*E(12)^11,0,0,0,0],
[GALOIS,[64,5]],[159390,11550,-1890,462,-90,-90,78,-45,0,-90,14,-82,14,6,-10,
-10,-6,-6,-6,6,6,6,0,-45,3,3,0,3,3,0,0,0,0,-2,2,2,-2,0,0,0,0,0,0,0,-1,-1,-1,0,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0],[185472,-8064,1152,0,192,
-64,0,0,-21,-64,0,0,0,0,0,0,0,0,0,0,8,-8,-3,0,0,0,3,0,0,3,-1,0,0,0,0,0,0,0,0,
-3,1,-3,1,1,0,0,0,-1,0,0,-1,1,0,0,0,0,0,0,0,1,1,0,0,-1,0,0,0,0,0,0,0,0],[
185472,-8064,1152,0,-64,192,0,0,-21,-64,0,0,0,0,0,0,0,0,0,0,-8,8,-3,0,0,0,3,0,
0,-1,3,0,0,0,0,0,0,0,0,-3,1,1,-3,1,0,0,0,-1,0,0,1,-1,0,0,0,0,0,0,0,1,1,0,0,-1,
0,0,0,0,0,0,0,0],[226688,-9856,1408,0,64,-192,0,-40,-7,64,0,0,0,0,0,0,0,0,0,0,
-8,8,3,40,8,-8,1,0,0,1,-3,0,0,0,0,0,0,0,0,3,-1,-1,3,0,0,0,0,1,0,0,1,-1,0,0,0,
0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0],[226688,-9856,1408,0,-192,64,0,-40,-7,64,
0,0,0,0,0,0,0,0,0,0,8,-8,3,40,8,-8,1,0,0,-3,1,0,0,0,0,0,0,0,0,3,-1,3,-1,0,0,0,
0,1,0,0,-1,1,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0],[239085,17325,-2835,
-483,-75,-75,93,0,0,-75,-99,45,21,5,21,21,9,-7,1,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,
0,-3,5,-3,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0],[239085,17325,-2835,-147,45,45,-339,0,0,45,45,-3,21,-3,-3,-3,-3,13,5,5,
-3,-3,0,0,0,0,0,0,0,0,0,0,0,-3,-7,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(67,68),(65,66),(60,61),(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)]);
ALF("mx1j4","J4",[1,3,2,2,2,3,3,4,4,5,5,6,7,6,6,5,6,6,7,7,6,7,8,9,11,10,
10,10,11,10,11,12,13,15,16,14,16,16,15,17,18,17,18,20,21,22,23,21,21,22,
22,23,26,27,25,24,28,28,29,30,31,32,33,35,36,36,37,38,40,39,42,42],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("mx1j4","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]);
MOT("(A4xA5):2",
[
"origin: Dixon's Algorithm,\n",
"6th maximal subgroup of J2.2"
],
[1440,480,96,32,180,72,9,60,24,12,20,15,15,24,24,8,8,12,12],
[,[1,1,1,1,5,6,7,8,6,5,8,12,13,1,2,3,4,6,9],[1,2,3,4,1,1,1,8,2,3,11,8,8,14,15,
16,17,14,15],,[1,2,3,4,5,6,7,1,9,10,2,5,5,14,15,16,17,18,19]],
0,
[(12,13)],
["ConstructIndexTwoSubdirectProduct","a4","Symm(4)","A5","A5.2",[26,27,28,33,
34,35],(2,3,6,4,8,11,7,9,5)(15,16,18,17),(3,10,12,14,4,6,8)(5,7,9,11,13)(15,
19,18,17)]);
ARC("(A4xA5):2","tomfusion",rec(name:="(A4xA5):2",map:=[1,2,3,4,6,7,8,22,
24,28,47,67,67,5,13,21,19,27,56],text:=[
"fusion map is unique"
]));
ALF("(A4xA5):2","A9",[1,2,2,3,4,4,6,9,10,10,15,17,18,2,7,7,8,10,16],[
"fusion map is unique up to table autom."
]);
ALF("(A4xA5):2","J2.2",[1,3,2,3,4,5,5,7,10,9,13,16,16,17,19,18,19,20,24],[
"fusion map is unique",
]);
ALF("(A4xA5):2","(A5x3):2",[1,1,2,2,5,3,7,4,3,6,4,8,9,10,10,11,11,12,12]);
ALF("(A4xA5):2","Symm(4)",[1,2,1,2,3,1,3,1,2,3,2,3,3,4,5,4,5,4,5]);
ALF("(A4xA5):2","A5.2",[1,1,2,2,1,3,3,4,3,2,4,4,4,5,5,6,6,7,7]);
MOT("(A5xD10).2",
[
"origin: Dixon's Algorithm,\n",
"7th maximal subgroup of J2.2"
],
[1200,80,60,300,50,25,25,20,15,240,16,12,10,24,24,8,8,12,12],
[,[1,1,3,4,5,6,7,4,9,1,1,3,5,10,10,11,11,12,12],[1,2,1,4,5,6,7,8,4,10,11,10,
13,15,14,17,16,15,14],,[1,2,3,1,1,1,1,2,3,10,11,12,10,14,15,16,17,18,19]],
0,
[( 6, 7),(14,15)(16,17)(18,19)],
["ConstructIndexTwoSubdirectProduct","D10","5:4","A5","A5.2",[19,20,21,33,34,
35],(4,5)(6,8)(7,9)(15,16,18,17),(3,15,5,6,11,9)(4,7,10,14,12,8)]);
ARC("(A5xD10).2","tomfusion",rec(name:="(A5xD10).2",map:=[1,3,5,11,12,13,
14,24,33,2,4,17,25,7,7,10,10,30,30],text:=[
"fusion map is unique up to table autom."
]));
ALF("(A5xD10).2","J2.2",[1,3,4,7,8,8,7,13,16,2,3,9,14,18,18,19,19,23,23],[
"compatible with a5xd10 -> J2"
]);
ALF("(A5xD10).2","5:4",[1,1,1,2,1,2,2,2,2,4,4,4,4,3,5,3,5,3,5]);
ALF("(A5xD10).2","A5.2",[1,2,3,1,4,4,4,2,3,1,2,3,4,5,5,6,6,7,7]);
ALF("(A5xD10).2","G2(4).2",[1,3,4,9,10,9,10,17,22,2,3,11,16,26,26,27,27,
33,33],[
"fusion of the 5AB normalizer determined up to table aut."
]);
ALF("(A5xD10).2","He",[1,2,4,9,9,9,9,18,25,2,3,10,18,6,6,7,7,19,19],[
"fusion map determined by factorization through S4(4).2"
]);
ALF("(A5xD10).2","Suz",[1,3,4,12,11,11,12,25,37,2,3,13,24,9,9,10,10,29,29],[
"fusion map is unique up to table aut."
]);
ALF("(A5xD10).2","5:4xS5",[1,2,3,8,4,11,11,9,10,22,23,24,25,19,33,20,34,
21,35],[
"fusion map is unique up to table aut."
]);
ALF("(A5xD10).2","O8+(2)",[1,3,7,18,18,19,20,41,51,3,6,24,41,14,14,17,17,
48,48]);
ALN("(A5xD10).2",["O8+(2)N5A","SuzN5B"]);
MOT("(D10xA5).2",
[
"normalizer of a defect 5-subgroup of type 5CD in G2(4).2"
],
0,
0,
0,
0,
["ConstructPermuted",["(A5xD10).2"]]);
ALF("(D10xA5).2","G2(4).2",[1,2,5,10,9,9,10,16,23,3,3,12,17,27,27,27,27,
34,34],[
"fusion of the 5CD normalizer determined up to table aut."
]);
ALF("(D10xA5).2","O8+(2)",[1,4,8,19,19,18,20,42,52,4,6,25,42,15,15,17,17,
49,49]);
ALN("(D10xA5).2",["O8+(2)N5B"]);
MOT("O8+(2)N5C",
0,
0,
0,
0,
0,
["ConstructPermuted",["(A5xD10).2"]]);
ALF("O8+(2)N5C","O8+(2)",[1,5,9,20,20,18,19,43,53,5,6,26,43,16,16,17,17,
50,50]);
MOT("(A5xA5):2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct'"
],
[7200,480,360,300,480,32,24,20,360,24,18,15,300,20,15,25,25,72,24,36,24,8,12,
36,12,18],
[,[1,1,3,4,1,1,3,4,9,9,11,12,13,13,15,16,17,1,2,3,5,6,7,9,10,11],[1,2,1,4,5,6,
5,8,1,2,1,4,13,14,13,16,17,18,19,18,21,22,21,18,19,18],,[1,2,3,1,5,6,7,5,9,10,
11,9,1,2,3,1,1,18,19,20,21,22,23,24,25,26]],
0,
[(16,17),( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15)(19,21)(20,24)(23,25)],
["ConstructIndexTwoSubdirectProduct","A5","A5.2","A5","A5.2",[33,34,35,40,41,
42,47,48,49],(),()]);
ALF("(A5xA5):2","A5.2",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,5,5,5,6,6,6,7,7,
7]);
ALF("(A5xA5):2","G2(4).2",[1,2,5,9,3,3,12,17,4,11,5,22,10,16,23,9,10,25,
26,29,27,27,34,28,33,29],[
"fusion map is unique up to table aut."
]);
MOT("(2.A5xA5):2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct'"
],
[14400,14400,480,720,720,600,600,960,960,32,48,48,40,40,720,720,24,36,36,30,30
,600,600,20,30,30,50,50,50,50,72,48,48,72,72,24,16,16,24,24,36,24,24,36,36],
[,[1,1,2,4,4,6,6,1,1,2,4,4,6,6,15,15,16,18,18,20,20,22,22,23,25,25,27,28,27,28
,2,3,3,5,5,9,10,10,12,12,16,17,17,19,19],[1,2,3,1,2,6,7,8,9,10,8,9,13,14,1,2,3
,1,2,6,7,22,23,24,22,23,27,28,29,30,31,33,32,31,31,36,38,37,36,36,31,33,32,31,
31],,[1,2,3,4,5,1,2,8,9,10,11,12,8,9,15,16,17,18,19,15,16,1,2,3,4,5,1,1,2,2,31
,33,32,35,34,36,38,37,40,39,41,43,42,45,44]],
0,
[(32,33)(37,38)(42,43),(27,28)(29,30),(34,35)(39,40)(44,45)],
["ConstructIndexTwoSubdirectProduct","A5","A5.2","2.A5","Isoclinic(2.A5.2)",[
56,57,58,59,60,68,69,70,71,72,80,81,82,83,84],(),()]);
ALF("(2.A5xA5):2","A5.2",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,
4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7]);
ALF("(2.A5xA5):2","Isoclinic(2.A5.2)",[1,2,3,4,5,6,7,1,2,3,4,5,6,7,1,2,3,
4,5,6,7,1,2,3,4,5,6,6,7,7,8,9,10,11,12,8,9,10,11,12,8,9,10,11,12]);
ALF("(2.A5xA5):2","(A5xA5):2",[1,1,2,3,3,4,4,5,5,6,7,7,8,8,9,9,10,11,11,
12,12,13,13,14,15,15,16,17,16,17,18,19,19,20,20,21,22,22,23,23,24,25,25,
26,26]);
MOT("L3(2).2x2",
[
"8th maximal subgroup of J2.2"
],
0,
0,
0,
[(11,12)(13,14)(15,16)(17,18),(15,17)(16,18)],
["ConstructDirectProduct",[["L3(2).2"],["Cyclic",2]]]);
ARC("L3(2).2x2","tomfusion",rec(name:="L3(2).2x2",map:=[1,2,4,3,7,23,11,9,
24,45,5,6,17,19,32,27,32,27],text:=[
"fusion map is unique up to table autom."
]));
ALF("L3(2).2x2","J2.2",[1,17,2,17,5,20,6,18,11,25,3,17,10,20,12,22,12,22],[
"fusion map is unique up to table automorphisms"
]);
LIBTABLE.LOADSTATUS.ctomaxi6:="userloaded";
#############################################################################
##
#E
