Impressum ctomaxi1.tbl
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#############################################################################
##
#W ctomaxi1.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 simple Mathieu groups.
##
#H ctbllib history
#H ---------------
#H $Log: ctomaxi1.tbl,v $
#H Revision 4.45 2012/06/20 14:45:31 gap
#H added tables and fusions, as documented in ctbldiff.dat
#H TB
#H
#H Revision 4.44 2012/04/23 16:16:11 gap
#H next step of consolidation:
#H
#H - removed a few unnecessary duplicate tables,
#H and changed some related fusions, names of maxes, table constructions
#H - make sure that duplicate tables arise only via `ConstructPermuted'
#H constructions
#H - added some relative names
#H - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H L2(41) -> M, (A5xA12):2 -> A17,
#H - added maxes of A12.2, L6(2), 2.M22.2
#H - added table of QD16.2,
#H - fixed the syntax of two `ALN' calls
#H TB
#H
#H Revision 4.43 2012/01/30 08:31:55 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.42 2011/09/28 14:32:21 gap
#H removed revision entry and SET_TABLEFILENAME call
#H TB
#H
#H Revision 4.41 2010/11/15 16:38:35 gap
#H replaced fusion 2.M12M4 -> A6.2^2 by fusion 2.M12M4 -> M12M4
#H TB
#H
#H Revision 4.40 2010/09/15 08:03:50 gap
#H the fusion 3^2.2.S4 -> M12 belongs to the 134th class of subgroups in the
#H table of marks not to the 133rd
#H TB
#H
#H Revision 4.39 2010/05/05 13:20:05 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 4.38 2009/03/02 16:43:19 gap
#H added table of 3.M22.2M3
#H TB
#H
#H Revision 4.37 2009/01/07 09:36:11 gap
#H added fusion 2xL2(11).2 -> 2.M12.2 (preimage of novelty L2(11).2 < M12.2)
#H TB
#H
#H Revision 4.36 2007/07/03 08:50:15 gap
#H added fusions,
#H encoded several tables as index two subdirect products
#H TB
#H
#H Revision 4.35 2004/11/24 15:20:20 gap
#H added missing maxes of U4(3) --Max had asked for them--
#H and their class fusions,
#H fixed construction entry for "(2xA6).2^2",
#H fixed fusion "2.U4(3).2_2' -> U4(3).2_2"
#H TB
#H
#H Revision 4.34 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 4.33 2004/03/01 17:56:52 gap
#H added a few factor fusions (needed for automatic construction of some
#H compatible central extensions)
#H TB
#H
#H Revision 4.32 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 4.31 2003/11/17 15:49:55 gap
#H added a few obvious fusions
#H TB
#H
#H Revision 4.30 2003/06/20 15:02:58 gap
#H added several fusions
#H TB
#H
#H Revision 4.29 2003/06/10 16:19:08 gap
#H store in several fusions between character tables to which subgroup number
#H in the table of marks of the supergroup the subgroup belongs
#H (in order to make the commutative diagrams testable)
#H TB
#H
#H Revision 4.28 2003/05/15 17:38:07 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 4.27 2003/03/31 16:33:22 gap
#H added fusions BN31 -> B, L2(31) -> B,
#H added some names and tables of maxes of 2.B,
#H added table of 2.(S3xFi22.2) < 2.B (J. An had asked for it)
#H TB
#H
#H Revision 4.26 2003/03/07 15:53:35 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 4.25 2003/01/29 15:51:51 gap
#H added admissible names, fusions, tables for certain maxes (which are
#H available in Rob's ATLAS and thus should be available in the table
#H library, too)
#H TB
#H
#H Revision 4.24 2003/01/24 15:57:31 gap
#H replaced several fusions by ones that are compatible with Brauer tables
#H TB
#H
#H Revision 4.23 2003/01/22 12:31:03 gap
#H removed a line from an `InfoText' value
#H TB
#H
#H Revision 4.22 2003/01/21 16:25:31 gap
#H further standardizations of `InfoText' strings,
#H added and corrected `Maxes' infos,
#H added some fusions
#H TB
#H
#H Revision 4.21 2003/01/14 17:28:49 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 4.20 2002/11/04 16:33:47 gap
#H added fusions of maxes of U3(3).2,
#H added fusion U3(3).2 -> Fi24' (this took me a whole afternoon ...)
#H TB
#H
#H Revision 4.19 2002/10/22 12:44:07 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 4.18 2002/09/23 14:48:59 gap
#H replaced 2xS5 by a ``construction'' table
#H TB
#H
#H Revision 4.17 2002/09/18 15:22:00 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 4.16 2002/08/21 14:50:18 gap
#H removed names s2m11, s2m12,
#H added fusion M22.2M4 -> M22.2
#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 2002/03/04 17:01:45 gap
#H added some fusions
#H TB
#H
#H Revision 4.11 2001/05/04 16:48:01 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.11 of ctbllib coincides with Rev. 4.10 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctomaxi1.tbl,v
#H Working file: ctomaxi1.tbl
#H head: 4.10
#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: 4.8.0.2
#H keyword substitution: kv
#H total revisions: 14; selected revisions: 14
#H description:
#H ----------------------------
#H revision 4.10
#H date: 2000/07/08 10:07:46; author: gap; state: Exp; lines: +30 -11
#H added some maxes of 2.HS (not yet complete ...) and corresponding fusions
#H
#H TB
#H ----------------------------
#H revision 4.9
#H date: 1999/10/21 14:15:47; author: gap; state: Exp; lines: +8 -3
#H added many `tomidentifer' and `tomfusion' values, which yields a better
#H interface between `tom' and `tbl';
#H
#H added maxes of McL.2,
#H
#H unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 1999/07/14 11:39:39; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1999/03/25 12:32:28; author: gap; state: Exp; lines: +4 -4
#H added fusions and tables for completing maxes of M12.2
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 1998/03/11 08:05:31; author: gap; state: Exp; lines: +36 -11
#H mainly new fusions to tables of marks added
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1997/11/25 16:17:21; author: gap; state: Exp; lines: +4 -4
#H fixed succession of maxes for Fi22.2, J3.2, M12.2, M22.2
#H (The simple group itself had not been contained before.)
#H TB
#H ----------------------------
#H revision 4.4
#H date: 1997/11/25 15:44:56; author: gap; state: Exp; lines: +19 -2
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1997/08/05 15:03:44; author: gap; state: Exp; lines: +6 -6
#H removed unnecessary (and ugly) `return' statements in the calls of
#H `ConstructPermuted' and `ConstructSubdirect'
#H ----------------------------
#H revision 4.2
#H date: 1997/08/01 15:43:02; author: gap; state: Exp; lines: +177 -2
#H added table of 2^7:S6(2)
#H (subgroup of Fi22.2; stored using Clifford matrices);
#H added tables of A14 mod p for p = 2, 11, 13
#H (moved ordinary table from `ctomisc1.tbl' to `ctoalter.tbl' for that);
#H added maxes of 2.M12;
#H updated the ``table of contents''.
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:41:17; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.4
#H date: 1997/04/04 12:19:54; author: sam; state: Exp; lines: +13 -39
#H added 'ConstructPermuted', 'ConstructSubdirect',
#H changed table constructions involving 'CharTable', 'RecFields'
#H 'Sort...' up to now
#H ----------------------------
#H revision 1.3
#H date: 1996/10/29 13:56:20; author: sam; state: Exp; lines: +26 -5
#H added table of S4xS3,
#H 2x2^3:L3(2) is also table of a maximal subgroup of M22.2
#H (added fusion and name).
#H ----------------------------
#H revision 1.2
#H date: 1996/10/23 15:34:30; author: sam; state: Exp; lines: +81 -4
#H added lines in some text components,
#H added tables of 6.M22M7 and 12.M22M7.
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:59:47; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("2^4:s5",
[
"origin: CAS library,\n",
"maximal subgroup of M22,\n",
"test: 1.OR,JAMES,JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5]"
],
[1920,128,32,32,16,6,5,48,16,8,8,6],
[,[1,1,1,2,2,6,7,1,2,3,4,6],[1,2,3,4,5,1,7,8,9,10,11,8],,[1,2,3,4,5,6,1,8,9,
10,11,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,-1,-1,-1,-1,-1],[4,4,0,0,0,1,-1,2,2,
0,0,-1],
[TENSOR,[3,2]],[5,5,1,1,1,-1,0,1,1,-1,-1,1],
[TENSOR,[5,2]],[6,6,-2,-2,-2,0,1,0,0,0,0,0],[15,-1,3,-1,-1,0,0,3,-1,1,-1,0],
[TENSOR,[8,2]],[15,-1,-1,3,-1,0,0,3,-1,-1,1,0],
[TENSOR,[10,2]],[30,-2,-2,-2,2,0,0,0,0,0,0,0]],
[]);
ARC("2^4:s5","projectives",["2.M22M5",[[6,-2,-2,2,0,0,1,0,0,-2,0,0],[6,-2,2,
-2,0,0,1,0,0,0,-2*E(4),0],[10,2,2,2,0,1,0,2,2,0,0,-1],[10,2,-2,-2,0,1,0,-4,0,
0,0,-1],[20,4,0,0,0,-1,0,-2,2,0,0,1],[24,-8,0,0,0,0,-1,0,0,0,0,
0]],"4.M22M5",[[16,0,0,0,0,-2,1,0,0,0,0,0],[16,0,0,0,0,1,1,0,0,0,0,
E(3)-E(3)^2],[24,0,0,0,0,0,-1,0,0,0,2*E(8),0]],]);
ARC("2^4:s5","tomfusion",rec(name:="2^4:S5`",map:=[1,2,4,12,15,5,20,3,14,18,
38,22],text:=[
"fusion map is unique"
]));
ALF("2^4:s5","L3(4).2_2",[1,2,2,4,5,3,6,9,10,10,12,11],[
"fusion map is unique"
]);
ALF("2^4:s5","M22",[1,2,2,4,5,3,6,2,4,5,10,7],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^4:s5","A5.2",[1,1,2,2,2,3,4,5,5,6,6,7]);
ALF("2^4:s5","M22.2M4",[1,2,3,4,5,6,7,8,9,10,11,12],[
"fusion map is unique up to table aut."
]);
MOT("2.M22M5",
[
"5th maximal subgroup of 2.M22,\n",
"constructed by S. Irnich using tables of M22, 2.M22, M22M5"
],
[3840,3840,256,256,64,64,64,64,16,12,12,10,10,96,96,32,32,16,16,16,16,12,12],
[,[1,1,1,1,1,1,3,3,4,10,10,12,12,1,1,3,3,6,6,7,7,10,10],[1,2,3,4,5,6,7,8,9,1,
2,12,13,14,15,16,17,18,19,21,20,14,15],,[1,2,3,4,5,6,7,8,9,10,11,1,2,14,15,16,
17,18,19,20,21,22,23]],
0,
[(20,21),(18,19),(14,15)(16,17)(22,23)],
["ConstructProj",[["2^4:s5",[]],["2.M22M5",[]]]]);
ALF("2.M22M5","2^4:s5",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12]);
ALF("2.M22M5","2.M22",[1,2,3,4,3,4,7,8,9,5,6,10,11,3,4,7,8,9,9,18,19,12,
13],[
"fusion map is unique up to table automorphisms"
]);
ALF("2.M22M5","A5.2",[1,1,1,1,2,2,2,2,2,3,3,4,4,5,5,5,5,6,6,6,6,7,7]);
MOT("2.S4",
[
"origin: CAS library, tests: 1.o.r., pow[2,3]"
],
[48,48,8,4,8,8,6,6],
[,[1,1,2,1,3,3,7,7],[1,2,3,4,5,6,1,2]],
[[1,1,1,1,1,1,1,1],[1,1,1,-1,-1,-1,1,1],[2,2,2,0,0,0,-1,-1],[3,3,-1,1,-1,-1,0,
0],[4,-4,0,0,0,0,1,-1],[2,-2,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,-1,1],
[TENSOR,[6,2]],
[TENSOR,[4,2]]],
[(5,6)]);
ARC("2.S4","CAS",[rec(name:="2.s4",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("2.S4","tomfusion",rec(name:="M8:S3",map:=[1,2,6,3,11,11,4,7],text:=[
"fusion map is unique"
]));
ALF("2.S4","2.A5.2",[1,2,3,8,9,10,4,5],[
"fusion map is unique up to table aut."
]);
ALF("2.S4","M11",[1,2,4,2,7,8,3,6],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("2.S4",["M11C2","M11C2A","M11N2A","M8:S3"]);
MOT("23:11",
[
"origin: CAS library,\n",
"maximal subgroup of M23,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[11,23]"
],
0,
0,
0,
[( 4, 5, 7,11, 8,13,12,10, 6, 9),(2,3)],
["ConstructPermuted",["P:Q",[23,11]]]);
ARC("23:11","tomfusion",rec(name:="23:11",map:=[1,3,3,2,2,2,2,2,2,2,2,2,2],
text:=[
"fusion map is unique"
]));
ALF("23:11","L2(23)",[1,13,14,6,8,7,10,9,9,10,7,8,6],[
"fusion map is unique up to table autom."
]);
ALF("23:11","M23",[1,16,17,10,11,10,10,10,11,11,11,10,11],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("23:11","M24",[1,25,26,16,16,16,16,16,16,16,16,16,16],[
"fusion is unique up to table automorphisms"
]);
ALF("23:11","Co3",[1,38,39,24,25,24,24,24,25,25,25,24,25],[
"fusion is unique up to table automorphisms"
]);
ALF("23:11","Co2",[1,53,54,33,33,33,33,33,33,33,33,33,33],[
"fusion is unique up to table automorphisms"
]);
ALF("23:11","Co1",[1,78,79,44,44,44,44,44,44,44,44,44,44],[
"fusion is unique up to table automorphisms"
]);
ALF("23:11","Fi23",[1,80,81,41,41,41,41,41,41,41,41,41,41],[
"fusion map is unique up to table automorphisms"
]);
ALF("23:11","F3+",[1,74,75,37,37,37,37,37,37,37,37,37,37],[
"fusion is unique up to table automorphisms"
]);
ALN("23:11",["M23N23","M24N23","Co3N23","Co2N23","Co1N23","Fi23N23",
"F3+N23"]);
MOT("2^3:sl(3,2)",
[
"origin: CAS library,\n",
"maximal subgroup of M22,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly,\n",
"constructions: AGL(3,2),\n",
"tests: 1.o.r., pow[2,3,7]"
],
[1344,192,32,32,16,8,8,6,6,7,7],
[,[1,1,1,1,2,3,4,8,8,10,11],[1,2,3,4,5,6,7,1,2,11,10],,,,[1,2,3,4,5,6,7,8,9,1,
1]],
[[1,1,1,1,1,1,1,1,1,1,1],[3,3,-1,-1,-1,1,1,0,0,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[2,3]],[6,6,2,2,2,0,0,0,0,-1,-1],[7,7,-1,-1,-1,-1,-1,1,1,0,0],[8,8,0,
0,0,0,0,-1,-1,1,1],[7,-1,3,-1,-1,1,-1,1,-1,0,0],[7,-1,-1,3,-1,-1,1,1,-1,0,0],[
14,-2,2,2,-2,0,0,-1,1,0,0],[21,-3,1,-3,1,-1,1,0,0,0,0],[21,-3,-3,1,1,1,-1,0,0,
0,0]],
[(10,11),(3,4)(6,7)]);
ARC("2^3:sl(3,2)","tomfusion",rec(name:="2^3:L3(2)",map:=[1,2,3,4,13,17,18,5,
19,22,22],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^3:sl(3,2)","A8",[1,2,2,3,6,6,7,5,10,11,12],[
"fusion map is unique up to table autom."
],"tom:134");
ALF("2^3:sl(3,2)","M22",[1,2,2,2,4,4,5,3,7,8,9],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^3:sl(3,2)","M23",[1,2,2,2,4,4,4,3,6,7,8],[
"fusion map is unique up to table aut."
]);
ALF("2^3:sl(3,2)","L3(2)",[1,1,2,2,2,4,4,3,3,5,6]);
ALF("2^3:sl(3,2)","2x2^3:L3(2)",[1,3,5,7,9,11,13,15,17,19,21],[
"fusion map is unique up to table aut."
]);
ALN("2^3:sl(3,2)",["AGL(3,2)"]);
MOT("2^4:(3xA5).2",
[
"source: H. Pahlings,\n",
"6th maximal subgroup of M23,\n",
"4th maximal subgroup of J3.2,\n",
"table is sorted w.r. to normal series 2^4.3.A5.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[5760,384,180,96,32,12,36,18,12,15,15,15,48,16,8,8,6],
[,[1,1,3,1,2,3,7,8,7,10,11,12,1,2,4,5,8],[1,2,1,4,5,4,1,1,2,10,10,10,13,14,15,
16,13],,[1,2,3,4,5,6,7,8,9,1,3,3,13,14,15,16,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1],[6,6,6,-2,-2,-2,0,0,0,1,1,1,0,0,0,0,0],[4,4,4,0,0,0,1,1,1,-1,-1,-1,2,2,0,
0,-1],
[TENSOR,[4,2]],[5,5,5,1,1,1,-1,-1,-1,0,0,0,1,1,-1,-1,1],
[TENSOR,[6,2]],[2,2,-1,2,2,-1,-1,2,-1,2,-1,-1,0,0,0,0,0],[6,6,-3,-2,-2,1,0,0,
0,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,
0,0],
[GALOIS,[9,7]],[8,8,-4,0,0,0,-1,2,-1,-2,1,1,0,0,0,0,0],[10,10,-5,2,2,-1,1,-2,
1,0,0,0,0,0,0,0,0],[15,-1,0,3,-1,0,3,0,-1,0,0,0,-3,1,-1,1,0],
[TENSOR,[13,2]],[30,-2,0,6,-2,0,-3,0,1,0,0,0,0,0,0,0,0],[45,-3,0,-3,1,0,0,0,0,
0,0,0,3,-1,-1,1,0],
[TENSOR,[16,2]]],
[(11,12)]);
ARC("2^4:(3xA5).2","CAS",[rec(name:="2^4:(3xa5):2",
permchars:=( 3,10, 9, 8)( 6, 7)(16,17),
permclasses:=( 3, 5, 8, 7, 6,13, 4)( 9,12,17,14)(10,11,16,15),
text:=[
"maximal subgroup of M23,\n",
"Berechnet 6.6.88 mit Cayley.\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly."])]);
ARC("2^4:(3xA5).2","tomfusion",rec(name:="2^4:(3xA5).2",map:=[1,2,5,3,13,
22,6,7,21,18,63,63,4,14,17,42,24],text:=[
"fusion map is unique"
]));
ALF("2^4:(3xA5).2","J3.2",[1,2,3,2,5,7,3,4,7,6,14,14,18,19,19,22,20],[
"fusion map is unique"
]);
ALF("2^4:(3xA5).2","L3(4).3.2_2",[1,2,8,2,4,10,8,3,10,5,11,12,15,16,16,18,
17],[
"fusion map is unique up to table autom."
]);
ALF("2^4:(3xA5).2","M23",[1,2,3,2,4,6,3,3,6,5,14,15,2,4,4,9,6],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^4:(3xA5).2","(A5x3):2",[1,1,5,2,2,6,7,3,7,4,8,9,10,10,11,11,12]);
ALN("2^4:(3xA5).2",["2^4:(3xa5):2"]);
MOT("2^4:a6",
[
"origin: CAS library,\n",
"maximal subgroup of M22,\n",
"test: OR.1, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5]"
],
[5760,384,32,32,16,36,12,9,8,8,5,5],
[,[1,1,1,2,2,6,6,8,3,4,12,11],[1,2,3,4,5,1,2,1,9,10,12,11],,[1,2,3,4,5,6,7,8,
9,10,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1],[5,5,1,1,1,2,2,-1,-1,-1,0,0],[5,5,1,1,1,-1,-1,2,-1,
-1,0,0],[8,8,0,0,0,-1,-1,-1,0,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4],
[GALOIS,[4,2]],[9,9,1,1,1,0,0,0,1,1,-1,-1],[10,10,-2,-2,-2,1,1,1,0,0,0,0],[15,
-1,3,-1,-1,3,-1,0,1,-1,0,0],[15,-1,-1,3,-1,3,-1,0,-1,1,0,0],[30,-2,2,2,-2,-3,
1,0,0,0,0,0],[45,-3,1,-3,1,0,0,0,-1,1,0,0],[45,-3,-3,1,1,0,0,0,1,-1,0,0]],
[(11,12)]);
ARC("2^4:a6","CAS",[rec(name:="2^4.a6",
permclasses:=( 4, 5, 6, 9)( 7,12,11,10),
permchars:=( 2, 3)( 4, 5)(11,12),
text:=[
"names:group1; g[2]..\n",
"order: 2^7.3^2.5 = 5,760\n",
"number of classes: 12\n",
"source:magliveras, s.s.\n",
"the subgroup structure of the\n",
"higman-sims simple group\n",
"univ. of birmingham [1970]\n",
"test: 1. o.r., sym 2 decompose correctly\n",
"comments: -"])]);
ARC("2^4:a6","projectives",["2.M22M2",[[6,-2,2,-2,0,3,1,0,0,0,1,1],[10,2,2,2,
0,1,-1,1,2,0,0,0],[10,2,2,2,0,1,-1,1,-2,0,0,0],[10,2,-2,-2,0,1,-1,1,0,2*E(4),
0,0],
[GALOIS,[4,3]],[18,-6,-2,2,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[GALOIS,[6,2]],[24,-8,0,0,0,3,1,0,0,0,-1,-1],[30,-10,2,-2,0,-3,-1,0,0,0,0,0],[
40,8,0,0,0,-2,2,1,0,0,0,0],[40,8,0,0,0,1,-1,-2,0,0,0,0]],"3.M22M2",[[3,3,-1,
-1,-1,0,0,0,1,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[GALOIS,[1,2]],[6,6,2,2,2,0,0,0,0,0,1,1],[9,9,1,1,1,0,0,0,1,1,-1,-1],[15,-1,
-1,3,-1,0,2,0,-1,1,0,0],[15,-1,3,-1,-1,0,2,0,1,-1,0,0],[15,15,-1,-1,-1,0,0,0,
-1,-1,0,0],[30,-2,2,2,-2,0,-2,0,0,0,0,0],[45,-3,-3,1,1,0,0,0,1,-1,0,0],[45,-3,
1,-3,1,0,0,0,-1,1,0,0]],"4.M22M2",[[16,0,0,0,0,-2,0,-2,0,0,1,1],[16,0,0,0,0,4,
0,1,0,0,1,1],[32,0,0,0,0,2,0,-1,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4],
[GALOIS,[3,2]],[40,0,0,0,0,-2,0,1,0,2*E(8),0,0],
[GALOIS,[5,5]]],"6.M22M2",[[6,-2,2,-2,0,0,-2,0,0,0,1,1],[18,-6,-2,2,0,0,0,0,0,
0,-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[GALOIS,[2,2]],[24,-8,0,0,0,0,-2,0,0,0,-1,-1],[30,-10,2,-2,0,0,2,0,0,0,0,0],[
30,6,-2,-2,0,0,0,0,-2,0,0,0],[30,6,-2,-2,0,0,0,0,2,0,0,0],[30,6,2,2,0,0,0,0,0,
-2*E(4),0,0],
[GALOIS,[8,3]]],"12.M22M2",[[24,0,0,0,0,0,0,0,0,2*E(8),-1,-1],
[GALOIS,[1,5]],[48,0,0,0,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[GALOIS,[3,2]]],]);
ARC("2^4:a6","tomfusion",rec(name:="2^4:A6",map:=[1,2,3,11,15,4,18,5,16,
32,17,17],text:=[
"fusion map is unique"
]));
ALF("2^4:a6","A6",[1,1,2,2,2,3,3,4,5,5,6,7],[
"factor fusion equal to that on the CAS table"
]);
ALF("2^4:a6","M22",[1,2,2,4,5,3,7,3,4,10,6,6],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^4:a6","2^4.s6",[1,2,3,4,5,7,8,6,9,10,11,11],[
"fusion map is unique"
]);
ALF("2^4:a6","2^4:a7",[1,2,3,4,4,6,7,5,8,9,10,10],[
"fusion map is unique"
]);
ALF("2^4:a6","U4(3)",[1,2,2,7,8,4,11,6,8,15,9,9],[
"fusion map is unique up to table autom."
],"tom:371");
ALF("2^4:a6","M22.2M3",[1,2,3,4,5,6,7,8,9,10,11,11],[
"fusion map is unique"
]);
ALN("2^4:a6",["2^4.a6"]);
MOT("2.M22M2",
[
"2nd maximal subgroup of 2.M22,\n",
"constructed by Stefan Irnich using GAP"
],
0,
0,
0,
0,
["ConstructPermuted",["P21/G1/L1/V1/ext2"],(2,4)(6,7,8)(12,13)(17,18,19),(8,
13,14,15,16,17,23,11,20,9,19)(10,18,22,12,21)]);
ALF("2.M22M2","2^4:a6",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12]);
ALF("2.M22M2","2.M22",[1,2,3,4,3,4,7,8,9,5,6,12,13,5,6,7,8,18,19,10,11,10,
11]);
ALF("2.M22M2","A6",[1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,5,5,5,5,6,6,7,7]);
MOT("3.M22M2",
[
"2nd maximal subgroup of 3.M22,\n",
"constructed by Stefan Irnich using GAP"
],
[17280,17280,17280,1152,1152,1152,96,96,96,96,96,96,48,48,48,36,36,36,36,9,24,
24,24,24,24,24,15,15,15,15,15,15],
[,[1,3,2,1,3,2,1,3,2,4,6,5,4,6,5,16,16,16,16,20,7,9,8,10,12,11,30,32,31,27,29,
28],[1,1,1,4,4,4,7,7,7,10,10,10,13,13,13,1,4,4,4,1,21,21,21,24,24,24,30,30,30,
27,27,27],,[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,16,17,19,18,20,21,23,22,24,26,
25,1,3,2,1,3,2]],
0,
[(27,30)(28,31)(29,32),( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(18,19)(22,23)
(25,26)(28,29)(31,32)],
["ConstructProj",[["2^4:a6",[]],,["3.M22M2",[-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1]]]]);
ALF("3.M22M2","2^4:a6",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,7,7,7,8,9,9,9,10,
10,10,11,11,11,12,12,12]);
ALF("3.M22M2","3.M22",[1,2,3,4,5,6,4,5,6,8,9,10,11,12,13,7,17,18,19,7,8,9,
10,26,27,28,14,15,16,14,15,16],[
"fusion map is unique up to table automorphisms"
]);
ALF("3.M22M2","3.A6",[1,2,3,1,2,3,4,5,6,4,5,6,4,5,6,7,7,7,7,8,9,10,11,9,
10,11,12,13,14,15,16,17]);
ALF("3.M22M2","2^4:3.S6",[1,3,3,2,4,4,5,8,8,6,9,9,7,10,10,11,12,13,13,14,
15,17,17,16,18,18,19,20,21,19,21,20],[
"fusion map is unique up to table aut."
]);
MOT("4.M22M2",
[
"2nd maximal subgroup of 4.M22,\n",
"constructed by Stefan Irnich using GAP"
],
[23040,23040,23040,23040,768,768,64,64,64,64,16,144,144,144,144,24,24,36,36,
36,36,16,16,32,32,32,32,20,20,20,20,20,20,20,20],
[,[1,3,1,3,1,3,1,3,5,5,6,12,14,12,14,12,14,18,20,18,20,7,7,9,9,9,9,32,34,32,
34,28,30,28,30],[1,4,3,2,5,6,7,8,9,10,11,1,4,3,2,5,6,1,4,3,2,22,23,25,24,27,
26,32,35,34,33,28,31,30,29],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,26,27,24,25,1,2,3,4,1,2,3,4]],
0,
[(24,26)(25,27),(22,23),(28,32)(29,33)(30,34)(31,35),( 2, 4)(13,15)(19,21)
(24,25)(26,27)(29,31)(33,35)],
["ConstructProj",[["2^4:a6",[]],["2.M22M2",[]],,["4.M22M2",[-1,-1,-1,-1,-1,
-1]]]]);
ALF("4.M22M2","2.M22M2",[1,2,1,2,3,4,5,6,7,8,9,10,11,10,11,12,13,14,15,14,
15,16,17,18,19,18,19,20,21,20,21,22,23,22,23]);
ALF("4.M22M2","2^4:a6",[1,1,1,1,2,2,3,3,4,4,5,6,6,6,6,7,7,8,8,8,8,9,9,10,
10,10,10,11,11,11,11,12,12,12,12]);
ALF("4.M22M2","4.M22",[1,2,3,4,5,6,5,6,11,12,13,7,8,9,10,18,19,7,8,9,10,
11,12,28,29,30,31,14,15,16,17,14,15,16,17],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("4.M22M2","A6",[1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,
6,6,6,6,7,7,7,7]);
MOT("6.M22M2",
[
"2nd maximal subgroup of 6.M22,\n",
"constructed by Stefan Irnich using GAP"
],
[34560,34560,34560,34560,34560,34560,2304,2304,2304,2304,2304,2304,192,192,
192,192,192,192,192,192,192,192,192,192,48,48,48,72,72,72,72,72,72,72,72,18,
18,48,48,48,48,48,48,48,48,48,48,48,48,30,30,30,30,30,30,30,30,30,30,30,30],
[,[1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,7,9,11,7,9,11,10,12,8,28,28,28,28,28,
28,28,28,36,36,13,15,17,13,15,17,19,21,23,19,21,23,56,58,60,56,58,60,50,52,54,
50,52,54],[1,4,1,4,1,4,7,10,7,10,7,10,13,16,13,16,13,16,19,22,19,22,19,22,25,
25,25,1,4,7,10,7,10,7,10,1,4,38,41,38,41,38,41,47,44,47,44,47,44,56,59,56,59,
56,59,50,53,50,53,50,53],,[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,19,24,
23,22,21,20,25,27,26,28,29,30,35,34,33,32,31,36,37,38,43,42,41,40,39,44,49,48,
47,46,45,1,6,5,4,3,2,1,6,5,4,3,2]],
0,
[(44,47)(45,48)(46,49),(38,41)(39,42)(40,43),(50,56)(51,57)(52,58)(53,59)
(54,60)(55,61),( 2, 6)( 3, 5)( 8,12)( 9,11)(14,18)(15,17)(20,24)(21,23)(26,27)
(31,35)(32,34)(39,43)(40,42)(45,49)(46,48)(51,55)(52,54)(57,61)(58,60)],
["ConstructProj",[["2^4:a6",[]],["2.M22M2",[]],["3.M22M2",[-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1]],,,["6.M22M2",[-1,-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("6.M22M2","2.M22M2",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,8,7,8,7,8,
9,9,9,10,11,12,13,12,13,12,13,14,15,16,17,16,17,16,17,18,19,18,19,18,19,
20,21,20,21,20,21,22,23,22,23,22,23]);
ALF("6.M22M2","3.M22M2",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,10,
11,12,13,14,15,16,16,17,18,19,17,18,19,20,20,21,22,23,21,22,23,24,25,26,
24,25,26,27,28,29,27,28,29,30,31,32,30,31,32]);
ALF("6.M22M2","2^4:a6",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,
5,5,6,6,7,7,7,7,7,7,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,
12,12,12,12,12,12]);
ALF("6.M22M2","6.M22",[1,2,3,4,5,6,7,8,9,10,11,12,7,8,9,10,11,12,15,16,17,
18,19,20,21,22,23,13,14,30,31,32,33,34,35,13,14,15,16,17,18,19,20,48,49,
50,51,52,53,24,25,26,27,28,29,24,25,26,27,28,29],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("6.M22M2","3.A6",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,4,5,6,4,5,6,4,5,
6,7,7,7,7,7,7,7,7,8,8,9,10,11,9,10,11,9,10,11,9,10,11,12,13,14,12,13,14,
15,16,17,15,16,17]);
MOT("12.M22M2",
[
"2nd maximal subgroup of 12.M22,\n",
"constructed by Stefan Irnich using GAP"
],
[69120,69120,69120,69120,69120,69120,69120,69120,69120,69120,69120,69120,2304,
2304,2304,2304,2304,2304,192,192,192,192,192,192,192,192,192,192,192,192,48,
48,48,144,144,144,144,72,72,72,72,72,72,36,36,36,36,48,48,48,48,48,48,96,96,
96,96,96,96,96,96,96,96,96,96,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,
60,60,60,60,60,60,60,60],
[,[1,3,5,7,9,11,1,3,5,7,9,11,1,3,5,7,9,11,1,3,5,7,9,11,13,15,17,13,15,17,16,
18,14,34,36,34,36,34,36,34,36,34,36,44,46,44,46,19,21,23,19,21,23,25,27,29,25,
27,29,25,27,29,25,27,29,78,80,82,84,86,88,78,80,82,84,86,88,66,68,70,72,74,76,
66,68,70,72,74,76],[1,4,7,10,1,4,7,10,1,4,7,10,13,16,13,16,13,16,19,22,19,22,
19,22,25,28,25,28,25,28,31,31,31,1,4,7,10,13,16,13,16,13,16,1,4,7,10,48,51,48,
51,48,51,63,54,57,60,63,54,57,60,63,54,57,60,78,81,84,87,78,81,84,87,78,81,84,
87,66,69,72,75,66,69,72,75,66,69,72,75],,[1,6,11,4,9,2,7,12,5,10,3,8,13,18,17,
16,15,14,19,24,23,22,21,20,25,30,29,28,27,26,31,33,32,34,35,36,37,38,43,42,41,
40,39,44,45,46,47,48,53,52,51,50,49,60,65,58,63,56,61,54,59,64,57,62,55,1,6,
11,4,9,2,7,12,5,10,3,8,1,6,11,4,9,2,7,12,5,10,3,8]],
0,
[(66,78)(67,79)(68,80)(69,81)(70,82)(71,83)(72,84)(73,85)(74,86)(75,87)(76,88)
(77,89),(48,51)(49,52)(50,53),(54,60)(55,61)(56,62)(57,63)(58,64)(59,65),
( 2, 6)( 3,11)( 5, 9)( 8,12)(14,18)(15,17)(20,24)(21,23)(26,30)(27,29)(32,33)
(39,43)(40,42)(49,53)(50,52)(55,59)(56,64)(58,62)(61,65)(67,71)(68,76)(70,74)
(73,77)(79,83)(80,88)(82,86)(85,89),( 2, 8)( 4,10)( 6,12)(35,37)(45,47)(54,57)
(55,64)(56,59)(58,61)(60,63)(62,65)(67,73)(69,75)(71,77)(79,85)(81,87)
(83,89)],
["ConstructProj",[["2^4:a6",[]],["2.M22M2",[]],["3.M22M2",[-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1]],["4.M22M2",[-1,-1,-1,-1,-1,-1]],,["6.M22M2",[-1,-1,-1,-1,-1,-1,
-1,-1,-1]],,,,,,["12.M22M2",[[29,19,11],[29,19,11],[29,19,11],[29,19,11]]]]]);
ALF("12.M22M2","2^4:a6",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,
4,4,4,4,4,4,5,5,5,6,6,6,6,7,7,7,7,7,7,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,
10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,
12,12,12,12,12,12,12]);
ALF("12.M22M2","2.M22M2",[1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,
7,8,7,8,7,8,9,9,9,10,11,10,11,12,13,12,13,12,13,14,15,14,15,16,17,16,17,
16,17,18,19,18,19,18,19,18,19,18,19,18,19,20,21,20,21,20,21,20,21,20,21,
20,21,22,23,22,23,22,23,22,23,22,23,22,23]);
ALF("12.M22M2","4.M22M2",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,5,6,5,6,7,8,7,8,7,8,
9,10,9,10,9,10,11,11,11,12,13,14,15,16,17,16,17,16,17,18,19,20,21,22,23,
22,23,22,23,24,25,26,27,24,25,26,27,24,25,26,27,28,29,30,31,28,29,30,31,
28,29,30,31,32,33,34,35,32,33,34,35,32,33,34,35]);
ALF("12.M22M2","3.M22M2",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,
10,11,12,10,11,12,13,14,15,16,16,16,16,17,18,19,17,18,19,20,20,20,20,21,
22,23,21,22,23,24,25,26,24,25,26,24,25,26,24,25,26,27,28,29,27,28,29,27,
28,29,27,28,29,30,31,32,30,31,32,30,31,32,30,31,32]);
ALF("12.M22M2","6.M22M2",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,28,29,30,31,32,33,34,35,36,37,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,44,45,46,47,48,49,50,51,52,53,
54,55,50,51,52,53,54,55,56,57,58,59,60,61,56,57,58,59,60,61]);
ALF("12.M22M2","12.M22",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,13,
14,15,16,17,18,23,24,25,26,27,28,29,30,31,19,20,21,22,44,45,46,47,48,49,
19,20,21,22,23,24,25,26,27,28,74,75,76,77,78,79,80,81,82,83,84,85,32,33,
34,35,36,37,38,39,40,41,42,43,32,33,34,35,36,37,38,39,40,41,42,43],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("12.M22M2","3.A6",[1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,4,
5,6,4,5,6,4,5,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,9,10,11,9,10,11,9,10,11,9,10,
11,9,10,11,9,10,11,12,13,14,12,13,14,12,13,14,12,13,14,15,16,17,15,16,17,
15,16,17,15,16,17]);
MOT("2^4:3.S6",
[
"origin: Dixon's Algorithm,\n",
"3rd maximal subgroup of 3.M22.2"
],
[34560,2304,17280,1152,192,192,96,96,96,48,72,72,36,18,48,48,24,24,15,15,15,
384,128,96,192,64,16,16,12,12,6],
[,[1,1,3,3,1,2,2,3,4,4,11,11,11,14,5,6,8,9,19,20,21,1,1,2,1,2,5,6,11,12,14],[1
,2,1,2,5,6,7,5,6,7,1,2,2,1,15,16,15,16,19,19,19,22,23,24,25,26,27,28,22,24,25]
,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,3,3,22,23,24,25,26,27,28,29,
30,31]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[5,5,5,5,1,1,1,1,
1,1,2,2,2,-1,-1,-1,-1,-1,0,0,0,3,3,3,-1,-1,1,1,0,0,-1],
[TENSOR,[3,2]],[5,5,5,5,1,1,1,1,1,1,-1,-1,-1,2,-1,-1,-1,-1,0,0,0,-1,-1,-1,3,3
,1,1,-1,-1,0],
[TENSOR,[5,2]],[16,16,16,16,0,0,0,0,0,0,-2,-2,-2,-2,0,0,0,0,1,1,1,0,0,0,0,0,0
,0,0,0,0],[9,9,9,9,1,1,1,1,1,1,0,0,0,0,1,1,1,1,-1,-1,-1,3,3,3,3,3,-1,-1,0,0,0]
,
[TENSOR,[8,2]],[10,10,10,10,-2,-2,-2,-2,-2,-2,1,1,1,1,0,0,0,0,0,0,0,2,2,2,-2,
-2,0,0,-1,-1,1],
[TENSOR,[10,2]],[6,6,-3,-3,-2,-2,-2,1,1,1,0,0,0,0,2,2,-1,-1,1,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,0,0,0
,0,0,0,0],
[GALOIS,[12,7]],[12,12,-6,-6,4,4,4,-2,-2,-2,0,0,0,0,0,0,0,0,2,-1,-1,0,0,0,0,0
,0,0,0,0,0],[18,18,-9,-9,2,2,2,-1,-1,-1,0,0,0,0,2,2,-1,-1,-2,1,1,0,0,0,0,0,0,0
,0,0,0],[30,30,-15,-15,-2,-2,-2,1,1,1,0,0,0,0,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,
0,0],[15,-1,15,-1,3,-1,-1,3,-1,-1,3,-1,-1,0,1,-1,1,-1,0,0,0,7,-1,-1,3,-1,1,-1,
1,-1,0],[15,-1,15,-1,-1,3,-1,-1,3,-1,3,-1,-1,0,-1,1,-1,1,0,0,0,-5,3,-1,3,-1,-1
,1,1,-1,0],
[TENSOR,[17,2]],
[TENSOR,[18,2]],[30,-2,30,-2,2,2,-2,2,2,-2,-3,1,1,0,0,0,0,0,0,0,0,2,2,-2,6,-2
,0,0,-1,1,0],
[TENSOR,[21,2]],[30,-2,-15,1,6,-2,-2,-3,1,1,0,4,-2,0,2,-2,-1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0],[30,-2,-15,1,-2,6,-2,1,-3,1,0,4,-2,0,-2,2,1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0],[45,-3,45,-3,1,-3,1,1,-3,1,0,0,0,0,-1,1,-1,1,0,0,0,9,1,-3,-3,1,-1,1,0
,0,0],
[TENSOR,[25,2]],[45,-3,45,-3,-3,1,1,-3,1,1,0,0,0,0,1,-1,1,-1,0,0,0,3,-5,3,3,
-1,-1,1,0,0,0],
[TENSOR,[27,2]],[60,-4,-30,2,4,4,-4,-2,-2,2,0,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[90,-6,-45,3,2,-6,2,-1,3,-1,0,0,0,0,-2,2,1,-1,0,0,0,0,0,0,0,0,0,0,0
,0,0],[90,-6,-45,3,-6,2,2,3,-1,-1,0,0,0,0,2,-2,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
],
[(20,21)]);
ALF("2^4:3.S6","3.M22.2",[1,3,2,4,3,6,8,4,7,9,5,12,13,5,6,18,7,19,10,11,
11,23,24,25,23,26,26,28,27,30,27],[
"fusion map is unique"
]);
MOT("2^4:a7",
[
"origin: CAS library,\n",
"maximal subgroup of M23,\n",
"maximal subgroup of McL,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[40320,2688,96,32,36,36,12,8,8,5,12,14,14,14,14],
[,[1,1,1,2,5,6,6,3,4,10,5,12,12,14,14],[1,2,3,4,1,1,2,8,9,10,3,14,15,12,13],,[
1,2,3,4,5,6,7,8,9,1,11,14,15,12,13],,[1,2,3,4,5,6,7,8,9,10,11,1,2,1,2]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[6,6,2,2,3,0,0,0,0,1,-1,-1,-1,-1,-1],[10,10,
-2,-2,1,1,1,0,0,0,1,E(7)+E(7)^2+E(7)^4,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],
[GALOIS,[3,3]],[14,14,2,2,2,-1,-1,0,0,-1,2,0,0,0,0],[14,14,2,2,-1,2,2,0,0,-1,
-1,0,0,0,0],[15,15,-1,-1,3,0,0,-1,-1,0,-1,1,1,1,1],[21,21,1,1,-3,0,0,-1,-1,1,
1,0,0,0,0],[35,35,-1,-1,-1,-1,-1,1,1,0,-1,0,0,0,0],[15,-1,3,-1,0,3,-1,1,-1,0,
0,1,-1,1,-1],[45,-3,-3,1,0,0,0,1,-1,0,0,E(7)+E(7)^2+E(7)^4,-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],
[GALOIS,[11,3]],[90,-6,6,-2,0,0,0,0,0,0,0,-1,1,-1,1],[105,-7,-3,1,0,3,-1,-1,1,
0,0,0,0,0,0],[120,-8,0,0,0,-3,1,0,0,0,0,1,-1,1,-1]],
[(12,14)(13,15)]);
ARC("2^4:a7","projectives",["3.2^4:a7",[[6,6,2,2,0,0,0,0,0,1,2,-1,-1,-1,-1],[
15,15,-1,-1,0,0,0,-1,-1,0,2,1,1,1,1],[15,15,3,3,0,0,0,1,1,0,0,1,1,1,1],[21,21,
1,1,0,0,0,-1,-1,1,-2,0,0,0,0],[21,21,-3,-3,0,0,0,1,1,1,0,0,0,0,0],[24,24,0,0,
0,0,0,0,0,-1,0,E(7)+E(7)^2+E(7)^4,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],
[GALOIS,[6,3]],[15,-1,3,-1,0,0,2,1,-1,0,0,1,-1,1,-1],[45,-3,-3,1,0,0,0,1,-1,0,
0,E(7)+E(7)^2+E(7)^4,-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],
[GALOIS,[9,3]],[90,-6,6,-2,0,0,0,0,0,0,0,-1,1,-1,1],[105,-7,-3,1,0,0,2,-1,1,0,
0,0,0,0,0],[120,-8,0,0,0,0,-2,0,0,0,0,1,-1,1,-1]],]);
ARC("2^4:a7","tomfusion",rec(name:="2^4:A7",map:=[1,2,3,10,4,5,15,12,30,
13,14,18,49,18,49],text:=[
"fusion map is unique"
]));
ALF("2^4:a7","M23",[1,2,2,4,3,3,6,4,9,5,6,7,12,8,13],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^4:a7","McL",[1,2,2,5,4,4,9,5,12,7,9,10,19,11,20],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^4:a7","A7",[1,1,2,2,3,4,4,5,5,6,7,8,8,9,9],[
"factor fusion equal to that on the CAS table"
]);
ALF("2^4:a7","2^4:a8",[1,2,5,6,7,8,9,14,15,16,17,20,21,22,23],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("3.2^4:a7",
[
"9th maximal subgroup of 3.McL,\n",
"table constructed 1996/09/10 by Thomas Breuer using the tables of McL,\n",
"3.McL, and 2^4:a7"
],
[120960,120960,120960,8064,8064,8064,288,288,288,96,96,96,36,36,36,36,36,24,
24,24,24,24,24,15,15,15,36,36,36,42,42,42,42,42,42,42,42,42,42,42,42],
[,[1,3,2,1,3,2,1,3,2,4,6,5,13,14,14,14,14,7,9,8,10,12,11,24,26,25,13,13,13,30,
32,31,30,32,31,36,38,37,36,38,37],[1,1,1,4,4,4,7,7,7,10,10,10,1,1,4,4,4,18,18,
18,21,21,21,24,24,24,7,7,7,36,36,36,39,39,39,30,30,30,33,33,33],,[1,3,2,4,6,5,
7,9,8,10,12,11,13,14,15,17,16,18,20,19,21,23,22,1,3,2,27,29,28,36,38,37,39,41,
40,30,32,31,33,35,34],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,1,2,3,4,5,6,1,2,3,4,5,6]],
0,
[(30,36)(31,37)(32,38)(33,39)(34,40)(35,41),( 2, 3)( 5, 6)( 8, 9)(11,12)
(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)],
["ConstructProj",[["2^4:a7",[]],,["3.2^4:a7",[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1]]]]);
ALF("3.2^4:a7","2^4:a7",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,7,7,7,8,8,8,9,9,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15]);
ALF("3.2^4:a7","3.McL",[1,2,3,4,5,6,4,5,6,11,12,13,10,10,23,24,25,11,12,
13,32,33,34,17,18,19,23,24,25,26,27,28,49,50,51,29,30,31,52,53,54],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.2^4:a7","3.A7",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,8,8,8,9,10,11,9,10,11,
12,13,14,15,16,17,18,19,20,18,19,20,21,22,23,21,22,23]);
ALF("3.2^4:a7","Ly",[1,3,3,2,8,8,2,8,8,5,19,19,4,4,9,10,10,5,19,19,12,31,
31,7,24,24,9,10,10,11,27,28,21,49,50,11,28,27,21,50,49],[
"fusion map is unique up to table aut."
]);
MOT("3.McLM10",
[
"10th maximal subgroup of 3.McL,\n",
"differs from 3.McLM9 = 3.2^4:a7 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3.2^4:a7"]]);
ALF("3.McLM10","3.McL",[1,2,3,4,5,6,4,5,6,11,12,13,10,10,23,24,25,11,12,
13,32,33,34,17,18,19,23,24,25,29,30,31,52,53,54,26,27,28,49,50,51],[
"fusion map is unique up to table automorphisms,\n",
"equals the map from 3.McLM9, mapped under the outer autom."
]);
ALF("3.McLM10","3.A7",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,8,8,8,9,10,11,9,10,11,
12,13,14,15,16,17,18,19,20,18,19,20,21,22,23,21,22,23]);
ALF("3.McLM10","McLM10",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,7,7,7,8,8,8,9,9,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15]);
MOT("2xA7",
[
"3rd and 4th maximal subgroup of 2.M22"
],
0,
0,
0,
[(15,17)(16,18)],
["ConstructDirectProduct",[["A7"],["Cyclic",2]]]);
ALF("2xA7","2.M22",[1,2,4,3,5,6,5,6,9,9,10,11,13,12,14,15,16,17],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2xA7","A7xS3",[1,3,4,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27],[
"fusion map is unique up to table aut."
]);
MOT("2x(3.A7)",
[
"3rd and 4th maximal subgroup of 6.M22"
],
0,
0,
0,
[(3,5)(4,6)(9,11)(10,12)(19,21)(20,22)(25,27)(26,28)(31,33)(32,34)(37,39)(38,
40)(43,45)(44,46),(35,41)(36,42)(37,43)(38,44)(39,45)(40,46)],
["ConstructDirectProduct",[["3.A7"],["Cyclic",2]]]);
ALF("2x(3.A7)","6.M22",[1,4,5,2,3,6,10,7,8,11,12,9,13,14,13,14,21,21,22,
22,23,23,24,27,28,25,26,29,33,30,31,34,35,32,36,39,40,37,38,41,42,45,46,
43,44,47],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2x(3.A7)","2xA7",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,7,8,9,10,9,10,9,10,11,
12,11,12,11,12,13,14,13,14,13,14,15,16,15,16,15,16,17,18,17,18,17,18]);
MOT("2.(2xA7)",
[
"3rd and 4th maximal subgroup of 4.M22"
],
0,
0,
0,
[(15,17)(16,18),(25,29)(26,30)(27,31)(28,32),(2,4)(8,10)(12,14)(16,18)(20,22)
(26,28)(30,32)],
["ConstructIsoclinic",[["2.A7"],["Cyclic",2]]]);
ALF("2.(2xA7)","4.M22",[1,2,3,4,6,5,7,8,9,10,7,8,9,10,13,13,13,13,14,15,
16,17,19,18,20,21,22,23,24,25,26,27],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(2xA7)","A7",[1,1,1,1,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,8,8,
8,8,9,9,9,9]);
ALF("2.(2xA7)","2xA7",[1,2,1,2,3,4,5,6,5,6,7,8,7,8,9,10,9,10,11,12,11,12,
13,14,15,16,15,16,17,18,17,18]);
MOT("2.(2x3.A7)",
[
"3rd and 4th maximal subgroup of 12.M22"
],
0,
0,
0,
[(57,69)(58,70)(59,71)(60,72)(61,73)(62,74)(63,75)(64,76)(65,77)(66,78)(67,79)
(68,80),(27,33)(28,34)(29,35)(30,36)(31,37)(32,38),(3,11)(4,12)(5,9)(6,10)(15,
17)(16,18)(29,37)(30,38)(31,35)(32,36)(41,49)(42,50)(43,47)(44,48)(53,55)(54,
56)(59,67)(60,68)(61,65)(62,66)(71,79)(72,80)(73,77)(74,78),(2,8)(4,10)(6,12)
(20,22)(24,26)(28,34)(30,36)(32,38)(40,46)(42,48)(44,50)(58,64)(60,66)(62,68)
(70,76)(72,78)(74,80)],
["ConstructIsoclinic",[["6.A7"],["Cyclic",2]]]);
ALF("2.(2x3.A7)","12.M22",[1,10,11,8,9,6,7,4,5,2,3,12,16,13,14,17,18,15,
19,20,21,22,19,20,21,22,29,29,30,30,31,31,29,29,30,30,31,31,32,41,42,39,
40,37,38,35,36,33,34,43,47,44,45,48,49,46,50,59,60,57,58,55,56,53,54,51,
52,61,62,71,72,69,70,67,68,65,66,63,64,73],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(2x3.A7)","3.A7",[1,1,2,2,3,3,1,1,2,2,3,3,4,4,5,5,6,6,7,7,7,7,8,8,
8,8,9,9,10,10,11,11,9,9,10,10,11,11,12,12,13,13,14,14,12,12,13,13,14,14,
15,15,16,16,17,17,18,18,19,19,20,20,18,18,19,19,20,20,21,21,22,22,23,23,
21,21,22,22,23,23]);
ALF("2.(2x3.A7)","2.(2xA7)",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,5,6,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,15,16,17,18,15,16,17,18,19,20,21,22,19,20,21,22,
19,20,21,22,23,24,23,24,23,24,25,26,27,28,25,26,27,28,25,26,27,28,29,30,
31,32,29,30,31,32,29,30,31,32]);
MOT("3x2^4:s5",
[
"5th maximal subgroup of 3.M22"
],
0,
0,
0,
[(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",[["2^4:s5"],["Cyclic",3]]]);
ALF("3x2^4:s5","3.M22",[1,2,3,4,5,6,4,5,6,8,9,10,11,12,13,7,7,7,14,15,16,
4,5,6,8,9,10,11,12,13,26,27,28,17,18,19],[
"fusion map is unique up to table automorphisms"
]);
ALF("3x2^4:s5","(2^4:S5x3).2",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,
13,14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,24],[
"fusion map is unique"
]);
MOT("4.M22M5",
[
"5th maximal subgroup of 4.M22,\n",
"constructed by Stefan Irnich using GAP"
],
[7680,7680,7680,7680,256,256,64,64,64,64,16,24,24,24,24,20,20,20,20,96,96,32,
32,16,16,32,32,32,32,24,24,24,24],
[,[1,3,1,3,1,3,1,3,5,5,6,12,14,12,14,16,18,16,18,1,3,5,5,8,8,9,9,9,9,12,14,12,
14],[1,4,3,2,5,6,7,8,9,10,11,1,4,3,2,16,19,18,17,20,21,22,23,24,25,27,26,29,
28,20,21,20,21],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,20,21,22,23,24,
25,28,29,26,27,32,33,30,31]],
0,
[(26,28)(27,29),(24,25),(30,32)(31,33),( 2, 4)(13,15)(17,19)(26,27)(28,29)
(31,33)],
["ConstructProj",[["2^4:s5",[]],["2.M22M5",[]],,["4.M22M5",[-1,-1,-1]]]]);
ALF("4.M22M5","2.M22M5",[1,2,1,2,3,4,5,6,7,8,9,10,11,10,11,12,13,12,13,14,
15,16,17,18,19,20,21,20,21,22,23,22,23]);
ALF("4.M22M5","2^4:s5",[1,1,1,1,2,2,3,3,4,4,5,6,6,6,6,7,7,7,7,8,8,9,9,10,
10,11,11,11,11,12,12,12,12]);
ALF("4.M22M5","4.M22",[1,2,3,4,5,6,5,6,11,12,13,7,8,9,10,14,15,16,17,5,6,
11,12,13,13,28,29,30,31,18,19,18,19],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("4.M22M5","A5.2",[1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,
6,6,6,7,7,7,7]);
MOT("3x2.M22M5",
[
"5th maximal subgroup of 6.M22"
],
0,
0,
0,
[(58,61)(59,62)(60,63),(52,55)(53,56)(54,57),(40,43)(41,44)(42,45)(46,49)(47,
50)(48,51)(64,67)(65,68)(66,69),(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)(50,51)(53,54)
(56,57)(59,60)(62,63)(65,66)(68,69)],
["ConstructDirectProduct",[["2.M22M5"],["Cyclic",3]]]);
ALF("3x2.M22M5","6.M22",[1,3,5,4,6,2,7,9,11,10,12,8,7,9,11,10,12,8,15,17,
19,18,20,16,21,23,22,13,13,13,14,14,14,24,26,28,27,29,25,7,9,11,10,12,8,
15,17,19,18,20,16,21,23,22,21,23,22,48,50,52,51,53,49,30,32,34,33,35,31],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("3x4.M22M5",
[
"5th maximal subgroup of 12.M22"
],
0,
0,
0,
[(76,82)(77,83)(78,84)(79,85)(80,86)(81,87),(70,73)(71,74)(72,75),(88,94)(89,
95)(90,96)(91,97)(92,98)(93,99),(4,10)(5,11)(6,12)(37,43)(38,44)(39,45)(49,55)
(50,56)(51,57)(76,79)(77,80)(78,81)(82,85)(83,86)(84,87)(91,97)(92,98)(93,99),
(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)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)
(71,72)(74,75)(77,78)(80,81)(83,84)(86,87)(89,90)(92,93)(95,96)(98,99)],
["ConstructDirectProduct",[["4.M22M5"],["Cyclic",3]]]);
ALF("3x4.M22M5","12.M22",[1,9,5,10,6,2,7,3,11,4,12,8,13,15,17,16,18,14,13,
15,17,16,18,14,23,25,27,26,28,24,29,31,30,19,19,19,20,20,20,21,21,21,22,
22,22,32,40,36,41,37,33,38,34,42,35,43,39,13,15,17,16,18,14,23,25,27,26,
28,24,29,31,30,29,31,30,74,82,78,83,79,75,80,76,84,77,85,81,44,46,48,47,
49,45,44,46,48,47,49,45],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3x4.M22M5","3x2.M22M5",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,28,29,30,31,32,
33,34,35,36,37,38,39,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,58,59,60,61,62,63,64,65,66,67,68,
69,64,65,66,67,68,69]);
MOT("2x2^3:L3(2)",
[
"6th maximal subgroup of 2.M22,\n",
"maximal subgroup of M22.2"
],
0,
0,
0,
[( 5, 7)( 6, 8)(11,13)(12,14),(19,21)(20,22)],
["ConstructDirectProduct",[["2^3:sl(3,2)"],["Cyclic",2]]]);
ARC("2x2^3:L3(2)","projectives",["4.M22M6",[[8,8*E(4),0,0,0,0,0,0,0,0,0,0,0,0,
-1,-E(4),-E(3)+E(3)^2,-E(12)^7+E(12)^11,1,E(4),1,E(4)],
[GALOIS,[1,5]],[8,8*E(4),0,0,0,0,0,0,0,0,0,0,0,0,2,2*E(4),0,0,1,E(4),1,E(4)],[
24,24*E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6,
E(28)^3+E(28)^19+E(28)^27,E(7)+E(7)^2+E(7)^4,E(28)^11+E(28)^15+E(28)^23],
[GALOIS,[4,5]]],]);
ARC("2x2^3:L3(2)","tomfusion",rec(name:="2^3:L3(2)x2",map:=[1,2,3,4,6,5,8,7,
22,26,34,41,39,40,9,50,45,46,52,148,52,148],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2x2^3:L3(2)","2.M22",[1,2,3,4,3,4,4,3,8,7,7,8,9,9,5,6,12,13,14,15,16,
17],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2x2^3:L3(2)","M22.2",[1,12,2,12,2,12,2,13,4,15,4,15,5,14,3,16,7,16,8,
20,9,21],[
"fusion map is unique up to table automorphisms"
]);
ALF("2x2^3:L3(2)","L3(2)",[1,1,1,1,2,2,2,2,2,2,4,4,4,4,3,3,3,3,5,5,6,6]);
ALN("2x2^3:L3(2)",["2^3:L3(2)x2","M22.2C2B","M22.2N2B"]);
MOT("2x2^3:L3(2)x2",
[
"5th maximal subgroup of 2.M22.2"
],
0,
0,
0,
[(5,7)(6,8)(11,13)(12,14)(27,29)(28,30)(33,35)(34,36),(23,24)(25,26)(27,28)
(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44),(19,21)(20,22)(41,
43)(42,44),(2,23)(4,25)(6,27)(8,29)(10,31)(12,33)(14,35)(16,37)(18,39)(20,41)
(22,43)],
["ConstructDirectProduct",[["Cyclic",2],["2x2^3:L3(2)"]]]);
ALF("2x2^3:L3(2)x2","2.M22.2",[1,2,3,4,3,4,4,3,8,7,7,8,9,9,5,6,12,13,14,
15,16,17,21,22,22,21,21,22,23,23,26,26,26,26,24,25,27,28,28,27,34,35,36,
37],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("(2xA6).2^2",
[
"6th maximal subgroup of 2.M22.2"
],
0,
0,
0,
[(19,20),(11,12)(14,15)(22,23),(17,18)(22,23)],
["ConstructIsoclinic",[["A6.D8"]],[1..15]]);
ALF("(2xA6).2^2","2.M22.2",[1,2,3,4,5,6,8,7,10,11,21,22,26,27,28,23,
29,29,30,31,9,18,18],[
"fusion map is unique up to table automorphisms"
]);
MOT("3x2^3:L3(2)",
[
"6th maximal subgroup of 3.M22"
],
0,
0,
0,
[(7,10)(8,11)(9,12)(16,19)(17,20)(18,21),(2,3)(5,6)(8,9)(11,12)(14,15)(17,18)
(20,21)(23,24)(26,27)(29,30)(32,33),(28,31)(29,32)(30,33)],
["ConstructDirectProduct",[["2^3:sl(3,2)"],["Cyclic",3]]]);
ALF("3x2^3:L3(2)","3.M22",[1,2,3,4,5,6,4,5,6,4,5,6,8,9,10,8,9,10,11,12,13,
7,7,7,17,18,19,20,21,22,23,24,25],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3x2^3:L3(2)","2^3:L3(2)xS3",[1,2,2,4,5,5,7,8,8,10,11,11,13,14,14,16,
17,17,19,20,20,22,23,23,25,26,26,28,29,29,31,32,32],[
"fusion map is unique up to table aut."
]);
MOT("4.M22M6",
[
"6th maximal subgroup of 4.M22"
],
[5376,5376,5376,5376,384,384,64,64,64,64,32,32,16,16,16,16,24,24,24,24,24,24,
24,24,28,28,28,28,28,28,28,28],
[,[1,1,2,2,1,2,1,2,2,1,5,5,7,7,9,9,17,17,18,18,17,17,18,18,25,25,26,26,29,29,
30,30],[1,2,4,3,5,6,7,8,9,10,11,12,13,14,15,16,1,2,4,3,5,5,6,6,29,30,32,31,25,
26,28,27],,,,[1,2,4,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,19,21,22,24,23,
1,2,4,3,1,2,4,3]],
0,
[(25,29)(26,30)(27,31)(28,32),(21,22)(23,24),(3,4)(19,20)(23,24)(27,28)(31,
32)],
["ConstructProj",[["2x2^3:L3(2)",[]],["4.M22M6",[]]]]);
ALF("4.M22M6","2x2^3:L3(2)",[1,1,2,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,16,
16,17,17,18,18,19,19,20,20,21,21,22,22]);
ALF("4.M22M6","4.M22",[1,3,2,4,5,6,5,6,6,5,12,11,11,12,13,13,7,9,8,10,18,
18,19,19,20,22,21,23,24,26,25,27],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("4.M22M6","L3(2)",[1,1,1,1,1,1,2,2,2,2,2,2,4,4,4,4,3,3,3,3,3,3,3,3,5,
5,5,5,6,6,6,6]);
MOT("6x2^3:L3(2)",
[
"6th maximal subgroup of 6.M22"
],
0,
0,
0,
[(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(31,37)(32,38)(33,39)(34,40)(35,41)
(36,42),(2,6)(3,5)(8,12)(9,11)(14,18)(15,17)(20,24)(21,23)(26,30)(27,29)(32,
36)(33,35)(38,42)(39,41)(44,48)(45,47)(50,54)(51,53)(56,60)(57,59)(62,66)(63,
65),(55,61)(56,62)(57,63)(58,64)(59,65)(60,66)],
["ConstructDirectProduct",[["2^3:sl(3,2)"],["Cyclic",6]]]);
ALF("6x2^3:L3(2)","6.M22",[1,2,3,4,5,6,7,8,9,10,11,12,7,8,9,10,11,12,10,
11,12,7,8,9,18,19,20,15,16,17,15,16,17,18,19,20,21,22,23,21,22,23,13,14,
13,14,13,14,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("6x2^3:L3(2)","2x2^3:L3(2)",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,8,
7,8,7,8,9,10,9,10,9,10,11,12,11,12,11,12,13,14,13,14,13,14,15,16,15,16,15,
16,17,18,17,18,17,18,19,20,19,20,19,20,21,22,21,22,21,22]);
MOT("3x4.M22M6",
[
"6th maximal subgroup of 12.M22"
],
0,
0,
0,
[(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)
(84,96),(61,64)(62,65)(63,66)(67,70)(68,71)(69,72),(7,10)(8,11)(9,12)(55,58)
(56,59)(57,60)(67,70)(68,71)(69,72)(79,82)(80,83)(81,84)(91,94)(92,95)(93,96),
(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)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)
(71,72)(74,75)(77,78)(80,81)(83,84)(86,87)(89,90)(92,93)(95,96)],
["ConstructDirectProduct",[["4.M22M6"],["Cyclic",3]]]);
ALF("3x4.M22M6","12.M22",[1,5,9,7,11,3,10,2,6,4,8,12,13,17,15,16,14,18,13,
17,15,16,14,18,16,14,18,13,17,15,26,24,28,23,27,25,23,27,25,26,24,28,29,
30,31,29,30,31,19,19,19,21,21,21,20,20,20,22,22,22,44,48,46,44,48,46,47,
45,49,47,45,49,50,54,58,56,60,52,59,51,55,53,57,61,62,66,70,68,72,64,71,
63,67,65,69,73],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("(4xA6).2_3",
[
"subdirect product of M10 and C8,\n",
"7th maximal subgroup of 4.M22"
],
0,
0,
0,
[(25,29)(26,30)(27,31)(28,32),(21,23)(22,24)(25,27)(26,28)(29,31)(30,32),
( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(21,22)(23,24)(25,26)(27,28)(29,30)
(31,32)],
["ConstructSubdirect",[["A6.2_3"],["Cyclic",8]],[1,3,5,7,9,11,13,15,17,19,21,
23,25,27,29,31,33,35,37,39,42,44,46,48,50,52,54,56,58,60,62,64]]);
ALF("(4xA6).2_3","4.M22",[1,2,3,4,5,6,5,6,7,8,9,10,12,11,12,11,14,15,16,
17,13,13,13,13,28,29,30,31,28,29,30,31],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(4xA6).2_3","(2xA6).2_3",[1,2,1,2,3,4,3,4,5,6,5,6,7,8,7,8,9,10,9,10,
11,12,11,12,13,14,13,14,15,16,15,16]);
ALF("(4xA6).2_3","A6.2_3",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,
6,7,7,7,7,8,8,8,8]);
MOT("6.M22M7",
[
"subdirect product of 3.A6.2_3 and C4,\n",
"7th maximal subgroup of 6.M22"
],
0,
0,
0,
0,
["ConstructPermuted",["Isoclinic(3.A6.2_3x2)"],(),()]);
ALF("6.M22M7","(2xA6).2_3",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,7,8,7,8,7,8,9,10,
9,10,9,10,11,12,11,12,11,12,13,14,13,14,13,14,15,16,15,16,15,16]);
ALF("6.M22M7","3.A6.2_3",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,
12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22]);
ALF("6.M22M7","C4",[1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,2,
4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4]);
ALF("6.M22M7","6.M22",[1,4,5,2,3,6,7,10,11,8,9,12,13,14,18,15,16,19,20,17,
24,27,28,25,26,29,21,21,22,22,23,23,48,51,52,49,50,53,48,51,52,49,50,53],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("12.M22M7",
[
"subdirect product of 3.A6.2_3 and C8,\n",
"7th maximal subgroup of 12.M22"
],
0,
0,
0,
[(65,77)(66,78)(67,79)(68,80)(69,81)(70,82)(71,83)(72,84)(73,85)(74,86)(75,87)
(76,88),(53,55)(54,56)(57,59)(58,60)(61,63)(62,64)(65,67)(66,68)(69,71)(70,72)
(73,75)(74,76)(77,79)(78,80)(81,83)(82,84)(85,87)(86,88),( 5, 9)( 6,10)( 7,11)
( 8,12)(17,21)(18,22)(19,23)(20,24)(33,37)(34,38)(35,39)(36,40)(45,49)(46,50)
(47,51)(48,52)(57,61)(58,62)(59,63)(60,64)(69,73)(70,74)(71,75)(72,76)(81,85)
(82,86)(83,87)(84,88),( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)
(34,36)(38,40)(42,44)(46,48)(50,52)(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)],
["ConstructSubdirect",[["3.A6.2_3"],["Cyclic",8]],
[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,
55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,
106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138,140,142,
144,146,148,150,152,154,156,158,160,162,164,166,168,170,172,174,176]]);
ALF("12.M22M7","(4xA6).2_3",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,7,8,5,6,7,8,5,6,
7,8,9,10,11,12,13,14,15,16,13,14,15,16,13,14,15,16,17,18,19,20,17,18,19,
20,17,18,19,20,21,22,23,24,21,22,23,24,21,22,23,24,25,26,27,28,25,26,27,
28,25,26,27,28,29,30,31,32,29,30,31,32,29,30,31,32]);
ALF("12.M22M7","3.A6.2_3",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,
6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,
14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19,
20,20,20,20,21,21,21,21,22,22,22,22]);
ALF("12.M22M7","12.M22",[1,10,7,4,5,2,11,8,9,6,3,12,13,16,13,16,17,14,17,
14,15,18,15,18,19,20,21,22,26,23,26,23,24,27,24,27,28,25,28,25,32,41,38,
35,36,33,42,39,40,37,34,43,29,29,29,29,30,30,30,30,31,31,31,31,74,83,80,
77,78,75,84,81,82,79,76,85,74,83,80,77,78,75,84,81,82,79,76,85],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("2xL2(11)",
[
"8th maximal subgroup of 2.M22"
],
0,
0,
0,
[(13,15)(14,16),(7,9)(8,10)],
["ConstructDirectProduct",[["L2(11)"],["Cyclic",2]]]);
ALF("2xL2(11)","2.M22",[1,2,4,3,5,6,10,11,10,11,13,12,20,21,22,23],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("2xL2(11).2",
[
"2nd maximal subgroup of 2.M12.2 (preimage of novelty L2(11).2 < M12.2),\n",
"7th maximal subgroup of 2.M22.2"
],
0,
0,
0,
[(23,25)(24,26),(7,9)(8,10)(19,21)(20,22),(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)],
["ConstructDirectProduct",[["L2(11).2"],["Cyclic",2]]]);
ALF("2xL2(11).2","2.M12.2",[1,2,4,5,6,7,11,12,11,12,14,15,19,20,21,21,22,
23,27,27,28,28,31,32,33,34],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("2xL2(11).2","2.M22.2",[1,2,4,3,5,6,10,11,10,11,13,12,19,20,23,23,24,
25,30,31,31,30,32,33,32,33],[
"fusion map is unique up to table automorphisms"
]);
ALN("2xL2(11).2",["2.M12.2M2"]);
MOT("3xL2(11)",
[
"8th maximal subgroup of 3.M22"
],
0,
0,
0,
[(19,22)(20,23)(21,24),(2,3)(5,6)(8,9)(11,12)(14,15)(17,18)(20,21)(23,24),(10,
13)(11,14)(12,15)],
["ConstructDirectProduct",[["L2(11)"],["Cyclic",3]]]);
ALF("3xL2(11)","3.M22",[1,2,3,4,5,6,7,7,7,14,15,16,14,15,16,17,18,19,29,
30,31,32,33,34],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3xL2(11)","(L2(11)x3).2",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,
13,14,15,13,15,14],[
"fusion map is unique up to table aut."
]);
MOT("2.(2xL2(11))",
[
"8th maximal subgroup of 4.M22"
],
0,
0,
0,
[(19,21)(20,22),(11,15)(12,16)(13,17)(14,18),(23,27)(24,28)(25,29)(26,30),(2,
4)(8,10)(12,14)(16,18)(20,22)(24,26)(28,30)],
["ConstructIsoclinic",[["2.L2(11)"],["Cyclic",2]]]);
ALF("2.(2xL2(11))","4.M22",[1,2,3,4,6,5,7,8,9,10,14,15,16,17,14,15,16,17,
19,18,19,18,32,33,34,35,36,37,38,39],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(2xL2(11))","2xL2(11)",[1,2,1,2,3,4,5,6,5,6,7,8,7,8,9,10,9,10,11,
12,11,12,13,14,13,14,15,16,15,16]);
ALF("2.(2xL2(11))","L2(11)",[1,1,1,1,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,
7,7,7,7,8,8,8,8]);
MOT("6xL2(11)",
[
"8th maximal subgroup of 6.M22"
],
0,
0,
0,
[(37,43)(38,44)(39,45)(40,46)(41,47)(42,48),(2,6)(3,5)(8,12)(9,11)(14,18)(15,
17)(20,24)(21,23)(26,30)(27,29)(32,36)(33,35)(38,42)(39,41)(44,48)(45,47),(19,
25)(20,26)(21,27)(22,28)(23,29)(24,30)],
["ConstructDirectProduct",[["L2(11)"],["Cyclic",6]]]);
ALF("6xL2(11)","6.M22",[1,2,3,4,5,6,10,11,12,7,8,9,13,14,13,14,13,14,24,
25,26,27,28,29,24,25,26,27,28,29,33,34,35,30,31,32,54,55,56,57,58,59,60,
61,62,63,64,65],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("6xL2(11)","3xL2(11)",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,
10,11,12,13,14,15,13,14,15,16,17,18,16,17,18,19,20,21,19,20,21,22,23,24,
22,23,24]);
ALF("6xL2(11)","2xL2(11)",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,8,7,8,7,
8,9,10,9,10,9,10,11,12,11,12,11,12,13,14,13,14,13,14,15,16,15,16,15,16]);
MOT("3x2.(2xL2(11))",
[
"8th maximal subgroup of 12.M22"
],
0,
0,
0,
[(55,61)(56,62)(57,63)(58,64)(59,65)(60,66),(31,43)(32,44)(33,45)(34,46)(35,
47)(36,48)(37,49)(38,50)(39,51)(40,52)(41,53)(42,54),(67,79)(68,80)(69,81)(70,
82)(71,83)(72,84)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90),(4,10)(5,11)(6,12)
(22,28)(23,29)(24,30)(34,40)(35,41)(36,42)(46,52)(47,53)(48,54)(58,64)(59,65)
(60,66)(70,76)(71,77)(72,78)(82,88)(83,89)(84,90),(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)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75)(77,78)(80,
81)(83,84)(86,87)(89,90)],
["ConstructDirectProduct",[["2.(2xL2(11))"],["Cyclic",3]]]);
ALF("3x2.(2xL2(11))","12.M22",[1,5,9,10,2,6,7,11,3,4,8,12,16,14,18,13,17,
15,19,19,19,20,20,20,21,21,21,22,22,22,32,36,40,41,33,37,38,42,34,35,39,
43,32,36,40,41,33,37,38,42,34,35,39,43,47,45,49,44,48,46,47,45,49,44,48,
46,86,90,94,95,87,91,92,96,88,89,93,97,98,102,106,107,99,103,104,108,100,
101,105,109],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3x2.(2xL2(11))","3xL2(11)",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,7,8,
9,7,8,9,7,8,9,7,8,9,10,11,12,10,11,12,10,11,12,10,11,12,13,14,15,13,14,15,
13,14,15,13,14,15,16,17,18,16,17,18,16,17,18,16,17,18,19,20,21,19,20,21,
19,20,21,19,20,21,22,23,24,22,23,24,22,23,24,22,23,24]);
MOT("McLM10",
[
"10th maximal subgroup of McL,\n",
"differs from McLM9 = 2^4:a7 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2^4:a7"]]);
ALF("McLM10","McL",[1,2,2,5,4,4,9,5,12,7,9,11,20,10,19],[
"fusion 2^4:a7 -> McL mapped under McL.2"
]);
ALF("McLM10","A7",[1,1,2,2,3,4,4,5,5,6,7,8,8,9,9]);
MOT("2^4:a8",
[
"origin: CAS library,\n",
"names:= 2^4:a8\n",
" order: 322,560 = 2^10 . 3^2 . 5 . 7\n",
" number of classes: 25\n",
"source: todd,j.a.\n",
" a representation of the mathieu-group m24\n",
" as a collineation group\n",
" ann.mat.pura appl [4] 71\n",
" (1966),199-238\n",
" comments: 2^4:a8 is maximal subgroup of m24\n",
" test: orth.1, min, sym(3)\n",
"constructions: AGL(4,2),\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[322560,21504,1536,512,384,128,180,72,24,384,64,64,32,16,16,15,12,12,12,14,14,
14,14,15,15],
[,[1,1,1,1,1,2,7,8,8,2,3,3,4,5,6,16,7,8,9,20,20,22,22,24,25],[1,2,3,4,5,6,1,1,
2,10,11,12,13,14,15,16,5,3,10,22,23,20,21,16,16],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,1,17,18,19,22,23,20,21,7,7],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,1,2,1,2,25,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[7,7,-1,-1,3,3,4,1,1,-1,
-1,-1,-1,1,1,2,0,-1,-1,0,0,0,0,-1,-1],[14,14,6,6,2,2,-1,2,2,6,2,2,2,0,0,-1,-1,
0,0,0,0,0,0,-1,-1],[20,20,4,4,4,4,5,-1,-1,4,0,0,0,0,0,0,1,1,1,-1,-1,-1,-1,0,
0],[21,21,-3,-3,1,1,6,0,0,-3,1,1,1,-1,-1,1,-2,0,0,0,0,0,0,1,1],[21,21,-3,-3,1,
1,-3,0,0,-3,1,1,1,-1,-1,1,1,0,0,0,0,0,0,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[6,7]],[28,28,-4,-4,4,4,1,1,1,-4,0,0,0,0,0,-2,1,-1,-1,0,0,0,0,1,1],[
35,35,3,3,-5,-5,5,2,2,3,-1,-1,-1,-1,-1,0,1,0,0,0,0,0,0,0,0],[45,45,-3,-3,-3,
-3,0,0,0,-3,1,1,1,1,1,0,0,0,0,E(7)+E(7)^2+E(7)^4,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)^6,0,0],
[GALOIS,[10,3]],[56,56,8,8,0,0,-4,-1,-1,8,0,0,0,0,0,1,0,-1,-1,0,0,0,0,1,1],[
64,64,0,0,0,0,4,-2,-2,0,0,0,0,0,0,-1,0,0,0,1,1,1,1,-1,-1],[70,70,-2,-2,2,2,-5,
1,1,-2,-2,-2,-2,0,0,0,-1,1,1,0,0,0,0,0,0],[15,-1,7,-1,3,-1,0,3,-1,-1,3,-1,-1,
1,-1,0,0,1,-1,1,-1,1,-1,0,0],[45,-3,-3,5,-3,1,0,0,0,-3,1,-3,1,1,-1,0,0,0,0,
E(7)+E(7)^2+E(7)^4,-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)^6,0,0],
[GALOIS,[16,3]],[90,-6,18,2,6,-2,0,0,0,-6,2,2,-2,0,0,0,0,0,0,-1,1,-1,1,0,0],[
105,-7,17,-7,-3,1,0,3,-1,1,1,-3,1,-1,1,0,0,-1,1,0,0,0,0,0,0],[105,-7,1,9,-3,1,
0,3,-1,-7,-3,1,1,-1,1,0,0,1,-1,0,0,0,0,0,0],[105,-7,-7,1,9,-3,0,3,-1,1,-3,1,1,
1,-1,0,0,-1,1,0,0,0,0,0,0],[120,-8,8,8,0,0,0,-3,1,-8,0,0,0,0,0,0,0,-1,1,1,-1,
1,-1,0,0],[210,-14,10,-6,6,-2,0,-3,1,2,-2,-2,2,0,0,0,0,1,-1,0,0,0,0,0,0],[315,
-21,3,-5,-9,3,0,0,0,3,-1,3,-1,1,-1,0,0,0,0,0,0,0,0,0,0],[315,-21,-21,3,3,-1,0,
0,0,3,3,-1,-1,-1,1,0,0,0,0,0,0,0,0,0,0]],
[(24,25),(20,22)(21,23)]);
ARC("2^4:a8","tomfusion",rec(name:="2^4:A8",map:=[1,2,3,4,5,33,6,7,43,32,34,
35,36,37,166,38,44,45,191,46,192,46,192,193,193],text:=[
"fusion map is unique"
]));
ALF("2^4:a8","L5(2)",[1,2,2,3,3,7,5,4,10,6,6,7,8,8,14,9,11,10,15,12,16,13,
17,19,18],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("2^4:a8","M24",[1,2,2,3,2,7,4,4,10,6,7,6,8,7,14,9,10,10,17,12,19,13,
20,22,21],[
"fusion is unique up to table automorphisms,\n",
"compatible with Brauer tables,\n",
"the map on the CAS table was not compatible"
]);
ALF("2^4:a8","A8",[1,1,2,2,3,3,4,5,5,2,6,6,6,7,7,8,9,10,10,11,11,12,12,13,
14]);
ALN("2^4:a8",["AGL(4,2)"]);
MOT("2^6:(psl(3,2)xs3)",
[
"origin: CAS library,\n",
"names:= 2^6:[psl(3,2]xs3)\n",
" order: 64,512 = 2^10 . 3^2 . 7\n",
" number of classes: 33\n",
" source/origin: pahlings,h.\n",
" comments: 2^6:(psl(3,2)xs3) is maximal subgroup of m24\n",
" test: orth.1, min, sym(3)\n",
"tests: 1.o.r., pow[2,3,7]"
],
[64512,3072,1536,256,768,128,128,72,24,504,36,12,32,96,24,42,42,12,21,21,2688,
384,128,64,32,128,32,32,16,12,12,14,14],
[,[1,1,1,1,1,2,2,8,8,10,11,11,4,5,10,16,17,15,19,20,1,2,1,2,3,2,5,4,6,8,9,16,
17],[1,2,3,4,5,6,7,1,2,1,1,3,13,14,5,17,16,14,17,16,21,22,23,24,25,26,27,28,
29,21,22,33,32],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,1,18,10,10,21,22,23,
24,25,26,27,28,29,30,31,21,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,
2,2,2,2,2,2,2,-1,-1,-1,2,2,-1,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,
-1,-1,-1,-1,0,0,3,0,0,1,1,-1,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,1,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,3,3,-1,-1,-1,-1,1,1,1,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[4,3]],
[TENSOR,[4,2]],
[TENSOR,[5,2]],[6,6,6,2,2,2,2,0,0,6,0,0,0,0,2,-1,-1,0,-1,-1,6,6,2,2,2,2,0,0,0,
0,0,-1,-1],
[TENSOR,[8,2]],[6,6,6,-2,-2,-2,-2,0,0,-3,0,0,2,2,1,2*E(7)+2*E(7)^2+2*E(7)^4,
2*E(7)^3+2*E(7)^5+2*E(7)^6,-1,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0,0,
0,0,0,0,0,0,0,0,0,0],
[GALOIS,[10,3]],[7,7,7,-1,-1,-1,-1,1,1,7,1,1,-1,-1,-1,0,0,-1,0,0,7,7,-1,-1,-1,
-1,-1,-1,-1,1,1,0,0],
[TENSOR,[12,2]],[8,8,8,0,0,0,0,-1,-1,8,-1,-1,0,0,0,1,1,0,1,1,8,8,0,0,0,0,0,0,
0,-1,-1,1,1],
[TENSOR,[14,2]],[12,12,12,4,4,4,4,0,0,-6,0,0,0,0,-2,-2,-2,0,1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0],[14,14,14,-2,-2,-2,-2,2,2,-7,-1,-1,-2,-2,1,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[16,16,16,0,0,0,0,-2,-2,-8,1,1,0,0,0,2,2,0,-1,-1,0,0,0,0,0,0,0,
0,0,0,0,0,0],[21,5,-3,5,-3,1,-3,3,-1,0,0,0,1,-3,0,0,0,0,0,0,7,-1,-1,3,-1,-1,
-1,-1,1,1,-1,0,0],
[TENSOR,[19,2]],[21,5,-3,1,9,-3,1,3,-1,0,0,0,-1,3,0,0,0,0,0,0,7,-1,3,-1,-1,3,
1,1,-1,1,-1,0,0],
[TENSOR,[21,2]],[42,10,-6,6,6,-2,-2,-3,1,0,0,0,0,0,0,0,0,0,0,0,14,-2,2,2,-2,2,
0,0,0,-1,1,0,0],
--> --------------------
--> maximum size reached
--> --------------------
[ Seitenstruktur0.124Drucken
]
|
2026-03-28
|
