|
#############################################################################
##
#W ctoline1.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables related to the
## linear groups $L_2(q)$ of the ATLAS, that is, for q in
## [ 8, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32 ]
##
#H ctbllib history
#H ---------------
#H $Log: ctoline1.tbl,v $
#H Revision 4.52 2012/06/20 14:45:30 gap
#H added tables and fusions, as documented in ctbldiff.dat
#H TB
#H
#H Revision 4.51 2012/05/07 15:20:28 gap
#H 2G2(3) is L2(8).3 not L2(8)
#H TB
#H
#H Revision 4.50 2012/04/23 16:16:07 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 4.49 2012/03/28 13:16:36 gap
#H added a permutation (of the maximal subgroups) for the fusion to the
#H table of marks of Sz(8).3, L2(11).2, HS.2, He.2, S4(5), U3(3), U4(2).2
#H TB
#H
#H Revision 4.48 2012/03/02 08:22:00 gap
#H added fusions 2.A7.2 -> 2.Suz.2, Isoclinic(2.A7.2) -> Isoclinic(2.Suz.2)
#H TB
#H
#H Revision 4.47 2012/01/30 08:23:15 gap
#H - changed fusion L2(25).2_1 -> L2(25).2^2: use the lexicogr. first map
#H - fixed ordering of maxes of L2(11).2:
#H S4 comes before D24, according to Rob's Atlas
#H - added fusions 2.L2(29) -> 2.Ru, L2(32).5 -> S10(2),
#H L2(16).4 -> O8-(2).2, L2(25).2_2 -> S12(2)
#H TB
#H
#H Revision 4.46 2011/09/28 14:32:12 gap
#H removed revision entry and SET_TABLEFILENAME call
#H TB
#H
#H Revision 4.45 2010/12/01 17:47:55 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 4.44 2010/09/15 08:08:23 gap
#H adjusted the "tom:<n>" information in some fusions
#H TB
#H
#H Revision 4.43 2010/05/05 13:20:01 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 4.42 2010/01/19 17:05:31 gap
#H added several tables of maximal subgroups of central extensions of
#H simple groups (many of them were contributed by S. Dany)
#H TB
#H
#H Revision 4.41 2009/07/29 13:59:12 gap
#H added fusion L2(25).2_3 -> 2F4(2)'.2
#H TB
#H
#H Revision 4.40 2009/04/27 08:27:21 gap
#H removed some superfluous explicit <nam>M<n> names,
#H which are created automatically
#H TB
#H
#H Revision 4.39 2009/04/22 12:39:01 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.38 2007/07/03 08:40:28 gap
#H added the table of A9M5,
#H added "maxes" of L2(13)
#H TB
#H
#H Revision 4.37 2005/04/27 07:38:45 gap
#H added fusion L2(27).6 -> S6(3).2
#H TB
#H
#H Revision 4.36 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 4.35 2004/03/23 09:50:53 gap
#H added fusion L2(17).2 -> B
#H TB
#H
#H Revision 4.34 2004/02/17 17:33:14 gap
#H added certain tables of isoclinic groups of ATLAS groups
#H (which are available in atlasrep),
#H added missing maxes of U5(2)
#H TB
#H
#H Revision 4.33 2004/01/13 08:14:56 gap
#H replaced the fusion L2(19) -> J3 by one that is compatible with the
#H Brauer tables available
#H TB
#H
#H Revision 4.32 2003/06/20 15:02:55 gap
#H added several fusions
#H TB
#H
#H Revision 4.31 2003/06/10 16:19:06 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 4.30 2003/05/15 17:38:03 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 4.29 2003/05/05 14:21:50 gap
#H adjusted fusion texts (no longer ambiguous when s.c. are used)
#H TB
#H
#H Revision 4.28 2003/04/07 16:08:38 gap
#H changed the map and mention the generality problem
#H for the fusion L2(19) -> J3 (an interesting case)
#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 2003/01/29 15:51:50 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 4.25 2003/01/27 10:03:59 gap
#H fixed two more fusions
#H TB
#H
#H Revision 4.24 2003/01/24 15:57:29 gap
#H replaced several fusions by ones that are compatible with Brauer tables
#H TB
#H
#H Revision 4.23 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 4.22 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 4.21 2002/09/26 06:42:23 gap
#H added fusion L2(13).2 -> F3+
#H (the tables of maximal subgroups of F3+ are all available,
#H so I also need the fusions;
#H this one took me half of yesterday evening ...)
#H TB
#H
#H Revision 4.20 2002/09/23 14:46:23 gap
#H removed trailing blanks
#H TB
#H
#H Revision 4.19 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 4.18 2002/08/21 14:49:03 gap
#H added fusion L2(11).2 -> M22.2
#H TB
#H
#H Revision 4.17 2002/07/26 16:58:05 gap
#H added more missing table automorphisms,
#H removed a few inconvenient names such as `c2' for `Co2'
#H (note that `c2' is used for the cyclic group of order 2,
#H which occurs in direct product constructions ...)
#H TB
#H
#H Revision 4.16 2002/07/12 06:45:55 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.15 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 4.14 2001/05/04 16:47:32 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.14 of ctbllib coincides with Rev. 4.13 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctoline1.tbl,v
#H Working file: ctoline1.tbl
#H head: 4.13
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.11.0.6
#H GAP4R2PRE2: 4.11.0.4
#H GAP4R2PRE1: 4.11.0.2
#H GAP4R1: 4.8.0.2
#H keyword substitution: kv
#H total revisions: 14; selected revisions: 14
#H description:
#H ----------------------------
#H revision 4.13
#H date: 2000/12/27 15:00:42; author: gap; state: Exp; lines: +8 -2
#H added fusions L2(13) -> S6(3) and L2(27).3 -> S6(3)
#H
#H TB
#H ----------------------------
#H revision 4.12
#H date: 2000/03/27 09:54:44; author: gap; state: Exp; lines: +25 -59
#H added some tables of maxes of 2.Suz and corresponding fusions,
#H added table of 3.Fi22M5
#H
#H TB
#H ----------------------------
#H revision 4.11
#H date: 1999/10/21 14:15:46; author: gap; state: Exp; lines: +12 -8
#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 4.10
#H date: 1999/10/04 15:57:14; author: gap; state: Exp; lines: +3 -3
#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 4.9
#H date: 1999/08/31 13:16:14; author: gap; state: Exp; lines: +6 -2
#H added missing tables and fusions of maximal subgroups of Suz.2
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 1999/06/11 14:34:47; author: gap; state: Exp; lines: +3 -3
#H fixed multiplier of L2(8)
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1999/05/21 14:30:38; author: gap; state: Exp; lines: +5 -4
#H fixed multiplier of L2(8)
#H (ATLAS misprint)
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 1999/03/25 12:32:28; author: gap; state: Exp; lines: +22 -2
#H added fusions and tables for completing maxes of M12.2
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1998/04/03 13:26:50; author: gap; state: Exp; lines: +10 -2
#H added tables of maxes of G2(3) and fusions into G2(3)
#H
#H TB
#H ----------------------------
#H revision 4.4
#H date: 1998/03/11 08:05:19; author: gap; state: Exp; lines: +26 -23
#H mainly new fusions to tables of marks added
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1997/11/25 15:44:43; author: gap; state: Exp; lines: +15 -2
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/08/01 15:42:58; author: gap; state: Exp; lines: +5 -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 15:39:49; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:59:28; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("2.L2(11)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"
],
[1320,1320,12,12,12,10,10,10,10,12,12,22,22,22,22],
[,[1,1,2,4,4,8,8,6,6,5,5,14,14,12,12],[1,2,3,1,2,8,9,6,7,3,3,12,13,14,15],,[1,
2,3,4,5,1,2,1,2,11,10,12,13,14,15],,,,,,[1,2,3,4,5,6,7,8,9,10,11,1,2,1,2]],
0,
[(12,14)(13,15),(10,11),(6,8)(7,9)],
["ConstructProj",[["L2(11)",[]],["2.L2(11)",[]]]]);
ARC("2.L2(11)","maxes",["2.A5","2.A5","2x11:5","2.D12"]);
ALF("2.L2(11)","L2(11)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8]);
ALF("2.L2(11)","2.L2(11).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,12,13],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("2.L2(11)","2.M12",[1,2,3,8,9,12,13,12,13,14,14,23,24,25,26],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2.L2(11)",["2.A1(11)","2.U2(11)","2.S2(11)","2.O3(11)"]);
MOT("2.L2(11).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"
],
[2640,2640,24,24,24,20,20,20,20,24,24,22,22,20,24,24,20,20,20,20,24,24,24,24],
[,[1,1,2,4,4,8,8,6,6,5,5,12,12,2,3,3,9,9,7,7,11,11,10,10],[1,2,3,1,2,8,9,6,7,
3,3,12,13,14,16,15,19,20,18,17,16,15,16,15],,[1,2,3,4,5,1,2,1,2,11,10,12,13,
14,16,15,14,14,14,14,24,23,22,21],,,,,,[1,2,3,4,5,6,7,8,9,10,11,1,2,14,16,15,
18,17,20,19,22,21,24,23]],
0,
[(17,18)(19,20),(10,11)(21,23)(22,24),(10,11)(17,18)(19,20)(21,23)(22,24),
(10,11)(15,16)(17,18)(19,20)(21,24)(22,23),( 6, 8)( 7, 9)(17,19,18,20),(15,16)
(21,22)(23,24)],
["ConstructProj",[["L2(11).2",[]],["2.L2(11).2",[]]]]);
ALF("2.L2(11).2","L2(11).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,10,11,11,
12,12,13,13]);
MOT("Isoclinic(2.L2(11).2)",
[
"isoclinic group of the 2.L2(11).2 given in the ATLAS"
],
0,
0,
0,
[(6,8)(7,9)(17,19,18,20),(15,16)(21,22)(23,24),(10,11)(21,23)(22,24)],
["ConstructIsoclinic",[["2.L2(11).2"]]]);
ALF("Isoclinic(2.L2(11).2)","L2(11).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,9,9,
10,10,11,11,12,12,13,13]);
MOT("2.L2(13)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"
],
[2184,2184,12,12,12,12,12,14,14,14,14,14,14,26,26,26,26],
[,[1,1,2,4,4,5,5,10,10,12,12,8,8,16,16,14,14],[1,2,3,1,2,3,3,12,13,8,9,10,11,
14,15,16,17],,,,[1,2,3,4,5,7,6,1,2,1,2,1,2,16,17,14,15],,,,,,[1,2,3,4,5,6,7,8,
9,10,11,12,13,1,2,1,2]],
0,
[(14,16)(15,17),( 8,12,10)( 9,13,11),(6,7)],
["ConstructProj",[["L2(13)",[]],["2.L2(13)",[]]]]);
ARC("2.L2(13)","maxes",["(2x13).6","2.D14","2.D12","2.L2(3)"]);
ALF("2.L2(13)","L2(13)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9]);
ALF("2.L2(13)","2.L2(13).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,14,15],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("2.L2(13)","2.G2(4)",[1,2,5,8,9,24,24,25,26,25,26,25,26,40,41,42,43],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2.L2(13)",["2.A1(13)","2.U2(13)","2.S2(13)","2.O3(13)"]);
MOT("2.L2(13).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"
],
[4368,4368,24,24,24,24,24,28,28,28,28,28,28,26,26,28,24,24,24,24,24,24,28,28,
28,28,28,28],
[,[1,1,2,4,4,5,5,10,10,12,12,8,8,14,14,2,3,3,6,6,7,7,11,11,13,13,9,9],[1,2,3,
1,2,3,3,12,13,8,9,10,11,14,15,16,18,17,18,17,18,17,27,28,23,24,25,26],,,,[1,2,
3,4,5,7,6,1,2,1,2,1,2,14,15,16,17,18,21,22,19,20,16,16,16,16,16,16],,,,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,1,2,16,18,17,20,19,22,21,24,23,26,25,28,27]],
0,
[(17,18)(19,20)(21,22),( 8,12,10)( 9,13,11)(23,28,25,24,27,26),( 6, 7)(19,21)
(20,22),( 6, 7)(19,21)(20,22)(23,24)(25,26)(27,28),( 6, 7)(17,18)(19,22)
(20,21)(23,24)(25,26)(27,28),(23,24)(25,26)(27,28)],
["ConstructProj",[["L2(13).2",[]],["2.L2(13).2",[]]]]);
ALF("2.L2(13).2","L2(13).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,10,11,11,
12,12,13,13,14,14,15,15]);
MOT("Isoclinic(2.L2(13).2)",
[
"isoclinic group of the 2.L2(13).2 given in the ATLAS"
],
0,
0,
0,
[(8,10,12)(9,11,13)(23,25,27)(24,26,28),(23,24)(25,26)(27,28),(17,18)(19,20)
(21,22),(6,7)(19,21)(20,22)],
["ConstructIsoclinic",[["2.L2(13).2"]]]);
ALF("Isoclinic(2.L2(13).2)","L2(13).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,
10,10,11,11,12,12,13,13,14,14,15,15]);
MOT("2.L2(17)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,17]"
],
[4896,4896,16,18,18,16,16,16,16,16,16,18,18,18,18,18,18,34,34,34,34],
[,[1,1,2,4,4,3,3,6,6,7,7,14,14,16,16,12,12,18,18,20,20],[1,2,3,1,2,7,6,10,11,
9,8,4,5,4,5,4,5,20,21,18,19],,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,1,2,1,2]],
0,
[(18,20)(19,21),(12,14,16)(13,15,17),(12,16,14)(13,17,15),( 6, 7)
( 8,11, 9,10),( 8, 9)(10,11)],
["ConstructProj",[["L2(17)",[]],["2.L2(17)",[]]]]);
ARC("2.L2(17)","maxes",["(2x17).8","2.Symm(4)","2.Symm(4)","2.D18","2.D16"]);
ALF("2.L2(17)","L2(17)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11]);
ALF("2.L2(17)","2.L2(17).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,18,19],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("2.L2(17)",["2.A1(17)","2.U2(17)","2.S2(17)","2.O3(17)"]);
MOT("2.L2(17).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,17]"
],
[9792,9792,32,36,36,32,32,32,32,32,32,36,36,36,36,36,36,34,34,36,36,36,32,32,
32,32,32,32,32,32,36,36,36,36,36,36],
[,[1,1,2,4,4,3,3,6,6,7,7,14,14,16,16,12,12,18,18,2,5,5,8,8,10,10,9,9,11,11,15,
15,17,17,13,13],[1,2,3,1,2,7,6,10,11,9,8,4,5,4,5,4,5,18,19,20,20,20,26,25,28,
27,29,30,24,23,21,22,21,22,21,22],,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,1,2,20,22,21,24,23,26,25,28,27,30,29,32,31,34,33,36,35]],
0,
[(21,22)(31,32)(33,34)(35,36),(12,14,16)(13,15,17)(31,33,35)(32,34,36),
(12,14,16)(13,15,17)(21,22)(31,34,35,32,33,36),( 6, 7)( 8,11, 9,10)(21,22)
(23,29,28,26,24,30,27,25)(31,32)(33,34)(35,36),( 6, 7)( 8,11, 9,10)
(23,29,28,26,24,30,27,25),(23,24)(25,26)(27,28)(29,30)],
["ConstructProj",[["L2(17).2",[]],["2.L2(17).2",[]]]]);
ALF("2.L2(17).2","L2(17).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,
12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19]);
MOT("Isoclinic(2.L2(17).2)",
[
"isoclinic group of the 2.L2(17).2 given in the ATLAS"
],
0,
0,
0,
[(6,7)(8,10,9,11)(23,25,27,30,24,26,28,29),(12,14,16)(13,15,17)(31,33,35)(32,
34,36),(21,22)(31,32)(33,34)(35,36)],
["ConstructIsoclinic",[["2.L2(17).2"]]]);
ALF("Isoclinic(2.L2(17).2)","L2(17).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,
10,10,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19]);
MOT("2.L2(19)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,19]"
],
[6840,6840,20,18,18,20,20,20,20,18,18,18,18,18,18,20,20,20,20,38,38,38,38],
[,[1,1,2,4,4,8,8,6,6,12,12,14,14,10,10,9,9,7,7,22,22,20,20],[1,2,3,1,2,8,9,6,
7,4,5,4,5,4,5,18,19,17,16,22,23,20,21],,[1,2,3,4,5,1,2,1,2,14,15,10,11,12,13,
3,3,3,3,20,21,22,23],,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,1,2,1,2]],
0,
[(20,22)(21,23),(16,17)(18,19),(10,12,14)(11,13,15),( 6, 8)( 7, 9)
(16,18,17,19),( 6, 8)( 7, 9)(16,19,17,18)],
["ConstructProj",[["L2(19)",[]],["2.L2(19)",[]]]]);
ARC("2.L2(19)","maxes",["2x19:9","2.A5","2.A5","2.D20","2.D18"]);
ALF("2.L2(19)","L2(19)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12]);
ALF("2.L2(19)","2.L2(19).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,20,21],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("2.L2(19)",["2.A1(19)","2.U2(19)","2.S2(19)","2.O3(19)"]);
MOT("2.L2(19).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,19]"
],
[13680,13680,40,36,36,40,40,40,40,36,36,36,36,36,36,40,40,40,40,38,38,36,40,
40,36,36,36,36,36,36,36,36,40,40,40,40,40,40,40,40],
[,[1,1,2,4,4,8,8,6,6,12,12,14,14,10,10,9,9,7,7,20,20,2,3,3,5,5,13,13,15,15,11,
11,19,19,16,16,18,18,17,17],[1,2,3,1,2,8,9,6,7,4,5,4,5,4,5,18,19,17,16,20,21,
22,24,23,22,22,25,26,25,26,25,26,36,35,38,37,40,39,34,33],,[1,2,3,4,5,1,2,1,2,
14,15,10,11,12,13,3,3,3,3,20,21,22,24,23,26,25,32,31,28,27,30,29,24,23,24,23,
24,23,24,23],,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,
2,22,24,23,26,25,28,27,30,29,32,31,34,33,36,35,38,37,40,39]],
0,
[(25,26)(27,28)(29,30)(31,32),(16,17)(18,19)(25,26)(27,28)(29,30)(31,32)
(33,37)(34,38)(35,39)(36,40),(16,17)(18,19)(23,24)(25,26)(27,28)(29,30)(31,32)
(33,38)(34,37)(35,40)(36,39),(10,12,14)(11,13,15)(27,29,31)(28,30,32),
(10,12,14)(11,13,15)(25,26)(27,30,31,28,29,32),( 6, 8)( 7, 9)(16,18,17,19)
(33,35,37,39)(34,36,38,40),(16,17)(18,19)(33,37)(34,38)(35,39)(36,40),(23,24)
(33,34)(35,36)(37,38)(39,40),( 6, 8)( 7, 9)(16,19,17,18)(33,39,37,35)
(34,40,38,36)],
["ConstructProj",[["L2(19).2",[]],["2.L2(19).2",[]]]]);
ALF("2.L2(19).2","L2(19).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,
11,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21]);
MOT("Isoclinic(2.L2(19).2)",
[
"isoclinic group of the 2.L2(19).2 given in the ATLAS"
],
0,
0,
0,
[(25,26)(27,28)(29,30)(31,32),(10,12,14)(11,13,15)(27,29,31)(28,30,32),(23,24)
(33,34)(35,36)(37,38)(39,40),(16,17)(18,19)(33,37)(34,38)(35,39)(36,40),(6,8)
(7,9)(16,18,17,19)(33,35,37,39)(34,36,38,40)],
["ConstructIsoclinic",[["2.L2(19).2"]]]);
ALF("Isoclinic(2.L2(19).2)","L2(19).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
10,11,11,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21]);
MOT("2.L2(23)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,23]"
],
[12144,12144,24,24,24,24,24,24,24,22,22,22,22,22,22,22,22,22,22,24,24,24,24,
46,46,46,46],
[,[1,1,2,4,4,3,3,5,5,14,14,16,16,18,18,10,10,12,12,8,8,9,9,24,24,26,26],[1,2,
3,1,2,7,6,3,3,12,13,14,15,16,17,18,19,10,11,7,6,7,6,24,25,26,27],,,,,,,,[1,2,
3,4,5,7,6,8,9,1,2,1,2,1,2,1,2,1,2,21,20,23,22,26,27,24,25],,,,,,,,,,,,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,2,1,2]],
0,
[(24,26)(25,27),(10,14,18,12,16)(11,15,19,13,17),( 8, 9)(20,22)(21,23),( 6, 7)
(20,21)(22,23),( 6, 7)( 8, 9)(20,23)(21,22),(10,18,16,14,12)(11,19,17,15,13)],
["ConstructProj",[["L2(23)",[]],["2.L2(23)",[]]]]);
ARC("2.L2(23)","maxes",["2x23:11","2.Symm(4)","2.Symm(4)","2.D24","2.D22"]);
ALF("2.L2(23)","L2(23)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12,13,13,14,14]);
ALF("2.L2(23)","2.L2(23).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,24,25],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
MOT("2.L2(23).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,23]"
],
[24288,24288,48,48,48,48,48,48,48,44,44,44,44,44,44,44,44,44,44,48,48,48,48,
46,46,44,48,48,48,48,44,44,44,44,44,44,44,44,44,44,48,48,48,48,48,48,48,48],
[,[1,1,2,4,4,3,3,5,5,14,14,16,16,18,18,10,10,12,12,8,8,9,9,24,24,2,7,7,6,6,15,
15,17,17,19,19,11,11,13,13,23,23,21,21,22,22,20,20],[1,2,3,1,2,7,6,3,3,12,13,
14,15,16,17,18,19,10,11,7,6,7,6,24,25,26,29,30,28,27,34,33,36,35,38,37,40,39,
32,31,29,30,29,30,28,27,28,27],,,,,,,,[1,2,3,4,5,7,6,8,9,1,2,1,2,1,2,1,2,1,2,
21,20,23,22,24,25,26,30,29,27,28,26,26,26,26,26,26,26,26,26,26,46,45,48,47,41,
42,43,44],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,1,2,26,28,27,30,29,32,31,34,33,36,35,38,37,40,39,42,41,44,43,46,45,48,
47]],
0,
[(27,28)(29,30)(41,42)(43,44)(45,46)(47,48),(10,14,18,12,16)(11,15,19,13,17)
(31,36,39,34,37,32,35,40,33,38),( 8, 9)(20,22)(21,23)(41,43)(42,44)(45,47)
(46,48),( 8, 9)(20,22)(21,23)(31,32)(33,34)(35,36)(37,38)(39,40)(41,43)(42,44)
(45,47)(46,48),( 6, 7)(20,21)(22,23)(27,30,28,29)(41,46,42,45)(43,48,44,47),
( 6, 7)( 8, 9)(20,23)(21,22)(27,30,28,29)(31,32)(33,34)(35,36)(37,38)(39,40)
(41,48,42,47)(43,46,44,45),(31,32)(33,34)(35,36)(37,38)(39,40)],
["ConstructProj",[["L2(23).2",[]],["2.L2(23).2",[]]]]);
ALF("2.L2(23).2","L2(23).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,
24,24,25,25]);
MOT("Isoclinic(2.L2(23).2)",
[
"isoclinic group of the 2.L2(23).2 given in the ATLAS"
],
0,
0,
0,
[(27,28)(29,30)(41,42)(43,44)(45,46)(47,48),(8,9)(20,22)(21,23)(41,43)(42,44)
(45,47)(46,48),(6,7)(20,21)(22,23)(27,29,28,30)(41,45,42,46)(43,47,44,48),(31,
32)(33,34)(35,36)(37,38)(39,40),(10,12,14,16,18)(11,13,15,17,19)(31,33,35,37,
39)(32,34,36,38,40)],
["ConstructIsoclinic",[["2.L2(23).2"]]]);
ALF("Isoclinic(2.L2(23).2)","L2(23).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,
24,24,25,25]);
MOT("2.L2(25)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"
],
[15600,15600,24,24,24,24,24,50,50,50,50,24,24,24,24,24,24,26,26,26,26,26,26,
26,26,26,26,26,26],
[,[1,1,2,4,4,3,3,8,8,10,10,5,5,13,13,12,12,28,28,26,26,20,20,18,18,24,24,22,
22],[1,2,3,1,2,7,6,8,9,10,11,3,3,7,6,7,6,26,27,28,29,18,19,20,21,22,23,24,
25],,[1,2,3,4,5,7,6,1,2,1,2,13,12,17,16,15,14,20,21,18,19,24,25,22,23,28,29,
26,27],,,,,,,,[1,2,3,4,5,7,6,8,9,10,11,12,13,15,14,17,16,1,2,1,2,1,2,1,2,1,2,
1,2]],
0,
[(18,28,22,20,26,24)(19,29,23,21,27,25),(12,13)(14,16)(15,17),( 8,10)( 9,11),
( 6, 7)(14,15)(16,17),( 6, 7)(12,13)(14,17)(15,16),(18,20)(19,21)(22,24)
(23,25)(26,28)(27,29),(18,26,22)(19,27,23)(20,28,24)(21,29,25)],
["ConstructProj",[["L2(25)",[]],["2.L2(25)",[]]]]);
ARC("2.L2(25)","maxes",["(2x5^2).12","Isoclinic(2.A5.2)","2.L2(25)M3","2.D26",
"2.D24"]);
ALF("2.L2(25)","L2(25)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15]);
ALF("2.L2(25)","2.L2(25).2_1",[1,2,3,4,5,6,7,8,9,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2.L2(25)","2.L2(25).2_2",[1,2,3,4,5,6,6,7,8,9,10,11,11,12,13,13,12,
14,15,14,15,16,17,16,17,18,19,18,19],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2.L2(25)","2.Suz",[1,2,5,10,11,16,16,17,18,19,20,29,29,50,51,50,51,
54,55,56,57,54,55,56,57,54,55,56,57],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("2.L2(25).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"
],
[31200,31200,48,48,48,48,48,50,50,48,48,48,48,48,48,52,52,52,52,52,52,52,52,
52,52,52,52,52,48,48,48,48,48,48,48,48,48,48,48,48,52,52,52,52,52,52,52,52,52,
52,52,52],
[,[1,1,2,4,4,3,3,8,8,5,5,11,11,10,10,26,26,24,24,18,18,16,16,22,22,20,20,2,6,
6,7,7,14,14,13,13,15,15,12,12,27,27,25,25,19,19,17,17,23,23,21,21],[1,2,3,1,2,
7,6,8,9,3,3,7,6,7,6,24,25,26,27,16,17,18,19,20,21,22,23,28,32,31,29,30,32,31,
29,30,29,30,32,31,50,49,52,51,42,41,44,43,46,45,48,47],,[1,2,3,4,5,7,6,1,2,11,
10,15,14,13,12,18,19,16,17,22,23,20,21,26,27,24,25,28,31,32,30,29,35,36,34,33,
40,39,37,38,43,44,42,41,47,48,46,45,51,52,50,49],,,,,,,,[1,2,3,4,5,7,6,8,9,10,
11,13,12,15,14,1,2,1,2,1,2,1,2,1,2,1,2,28,32,31,29,30,38,37,39,40,33,34,36,35,
28,28,28,28,28,28,28,28,28,28,28,28]],
0,
[(29,30)(31,32)(33,34)(35,36)(37,38)(39,40),(16,26,20,18,24,22)
(17,27,21,19,25,23)(41,51,46,44,49,47,42,52,45,43,50,48),(10,11)(12,14)(13,15)
(33,39)(34,40)(35,37)(36,38),(10,11)(12,14)(13,15)(33,39)(34,40)(35,37)(36,38)
(41,42)(43,44)(45,46)(47,48)(49,50)(51,52),( 6, 7)(12,13)(14,15)(29,31,30,32)
(33,37,34,38)(35,40,36,39),( 6, 7)(10,11)(12,15)(13,14)(29,31,30,32)
(33,35,34,36)(37,40,38,39)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52),(41,42)
(43,44)(45,46)(47,48)(49,50)(51,52),( 6, 7)(12,13)(14,15)(29,32,30,31)
(33,38,34,37)(35,39,36,40)],
["ConstructProj",[["L2(25).2_1",[]],["2.L2(25).2_1",[]]]]);
ALF("2.L2(25).2_1","L2(25).2_1",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,
11,11,12,12,13,13,14,14,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,
23,24,24,25,25,26,26,27,27]);
MOT("Isoclinic(2.L2(25).2_1)",
[
"isoclinic group of the 2.L2(25).2_1 given in the ATLAS"
],
0,
0,
0,
[(16,18)(17,19)(20,22)(21,23)(24,26)(25,27)(41,43,42,44)(45,47,46,48)(49,51,
50,52),(6,7)(12,13)(14,15)(29,31,30,32)(33,37,34,38)(35,40,36,39),(16,20,24)
(17,21,25)(18,22,26)(19,23,27)(41,45,49)(42,46,50)(43,47,51)(44,48,52),(10,
11)(12,14)(13,15)(33,39)(34,40)(35,37)(36,38)],
["ConstructIsoclinic",[["2.L2(25).2_1"]]]);
ALF("Isoclinic(2.L2(25).2_1)","L2(25).2_1",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,
9,9,10,10,11,11,12,12,13,13,14,14,15,16,16,17,17,18,18,19,19,20,20,21,21,
22,22,23,23,24,24,25,25,26,26,27,27]);
MOT("2.L2(25).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\n",
"constructions: SigmaL(2,25)"
],
[31200,31200,48,48,48,24,100,100,100,100,24,24,24,26,26,26,26,26,26,240,240,8,
12,12,20,20,20,20],
[,[1,1,2,4,4,3,7,7,9,9,5,11,11,18,18,14,14,16,16,1,2,3,4,5,7,7,10,10],[1,2,3,
1,2,6,7,8,9,10,3,6,6,18,19,14,15,16,17,20,21,22,20,21,26,25,27,28],,[1,2,3,4,
5,6,1,2,1,2,11,12,13,14,15,16,17,18,19,20,21,22,23,24,20,20,21,21],,,,,,,,[1,
2,3,4,5,6,7,8,9,10,11,13,12,1,2,1,2,1,2,20,21,22,23,24,26,25,28,27]],
0,
[(27,28),(25,26),(25,26)(27,28),(14,18,16)(15,19,17),(12,13),(12,13)(27,28)],
["ConstructProj",[["L2(25).2_2",[]],["2.L2(25).2_2",[]]]]);
ALF("2.L2(25).2_2","L2(25).2_2",[1,1,2,3,3,4,5,5,6,6,7,8,8,9,9,10,10,11,
11,12,13,14,15,16,17,17,18,18]);
MOT("Isoclinic(2.L2(25)x2)",
[
"central product of 2.L2(25) with a cyclic group of order 4,\n",
"subgroup of 4.L2(25).2_3"
],
[31200,31200,31200,31200,48,48,48,48,48,48,48,48,48,48,100,100,100,100,100,100
,100,100,48,48,48,48,48,48,48,48,48,48,48,48,52,52,52,52,52,52,52,52,52,52,52,
52,52,52,52,52,52,52,52,52,52,52,52,52],
[,[1,3,1,3,3,1,7,9,7,9,5,5,5,5,15,17,15,17,19,21,19,21,9,7,9,7,25,23,25,23,23,
25,23,25,55,57,55,57,51,53,51,53,39,41,39,41,35,37,35,37,47,49,47,49,43,45,43,
45],[1,4,3,2,5,6,1,4,3,2,13,12,11,14,15,18,17,16,19,22,21,20,5,6,5,6,13,12,11,
14,13,12,11,14,51,54,53,52,55,58,57,56,35,38,37,36,39,42,41,40,43,46,45,44,47,
50,49,48],,[1,2,3,4,5,6,7,8,9,10,13,14,11,12,1,2,3,4,1,2,3,4,25,26,23,24,33,34
,31,32,29,30,27,28,39,40,41,42,35,36,37,38,47,48,49,50,43,44,45,46,55,56,57,58
,51,52,53,54],,,,,,,,[1,2,3,4,5,6,7,8,9,10,13,14,11,12,15,16,17,18,19,20,21,22
,23,24,25,26,29,30,27,28,33,34,31,32,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1
,2,3,4]],
0,
[(23,25)(24,26)(27,31)(28,32)(29,33)(30,34),(15,19)(16,20)(17,21)(18,22),
(11,13)(12,14)(27,29)(28,30)(31,33)(32,34),
(35,39)(36,40)(37,41)(38,42)(43,47)(44,48)(45,49)(46,50)(51,55)(52,56)(53,57)
(54,58),(35,43,51)(36,44,52)(37,45,53)(38,46,54)(39,47,55)(40,48,56)(41,49,57)
(42,50,58),
( 2, 4)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30)(32,34)(36,38)(40,42)(44,46)
(48,50)(52,54)(56,58)],
["ConstructIsoclinic",[["2.L2(25)"],["Cyclic",2]]]);
ALF("Isoclinic(2.L2(25)x2)","4.L2(25).2_3",[1,2,3,2,4,5,6,7,8,7,9,10,9,11,
12,13,14,15,12,15,14,13,16,17,16,18,19,20,21,22,21,20,19,22,23,24,25,26,
23,26,25,24,27,28,29,30,27,30,29,28,31,32,33,34,31,34,33,32],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
MOT("Isoclinic(L2(25).2_3x2)",
[
"subdirect product of L2(25).2_3 with a cyclic group of order 4,\n",
"factor group of 4.L2(25).2_3"
],
[31200,31200,96,96,48,48,48,48,50,50,48,48,24,24,26,26,26,26,26,26,24,24,16,16
,16,16,24,24,24,24],
[,[1,1,1,1,5,5,3,3,9,9,5,5,11,11,19,19,15,15,17,17,4,4,8,8,8,8,12,12,12,12],[1
,2,3,4,1,2,7,8,9,10,3,4,7,8,19,20,15,16,17,18,22,21,24,23,26,25,22,21,22,21],,
[1,2,3,4,5,6,7,8,1,2,11,12,13,14,15,16,17,18,19,20,21,22,25,26,23,24,29,30,27,
28],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,1,2,1,2,21,22,25,26,23,24,27,
28,29,30]],
0,
[(27,29)(28,30),(23,25)(24,26),(21,22)(23,24)(25,26)(27,28)(29,30),
(15,17,19)(16,18,20)],
["ConstructIsoclinic",[["L2(25).2_3"],["Cyclic",2]]]);
ALF("Isoclinic(L2(25).2_3x2)","C4",[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]);
ALF("Isoclinic(L2(25).2_3x2)","L2(25).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]);
MOT("4.L2(25).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"
],
[62400,31200,62400,96,96,96,48,96,48,96,96,100,100,100,100,48,96,96,48,48,48,
48,52,52,52,52,52,52,52,52,52,52,52,52,24,24,16,16,16,16,24,24,24,24],
[,[1,3,1,3,1,6,8,6,4,4,4,12,14,12,14,8,6,6,16,16,16,16,31,33,31,33,23,25,23,25
,27,29,27,29,5,5,10,10,11,11,17,17,18,18],[1,2,3,4,5,1,2,3,9,10,11,12,15,14,13
,4,5,5,9,10,9,11,31,34,33,32,23,26,25,24,27,30,29,28,36,35,38,37,40,39,36,35,
36,35],,[1,2,3,4,5,6,7,8,9,11,10,1,2,3,2,16,18,17,19,22,21,20,23,26,25,24,27,
30,29,28,31,34,33,32,35,36,39,40,37,38,43,44,41,42],,,,,,,,[1,2,3,4,5,6,7,8,9,
11,10,12,13,14,15,16,17,18,21,22,19,20,1,2,3,2,1,2,3,2,1,2,3,2,35,36,39,40,37,
38,41,42,43,44]],
0,
[(24,26)(28,30)(32,34),(23,27,31)(24,28,32)(25,29,33)(26,30,34),(13,15),
(17,18)(19,21)(35,36)(37,38)(39,40)(41,44)(42,43),(17,18)(19,21)(41,43)(42,44)
,(10,11)(17,18)(20,22)(35,36)(37,40)(38,39)(41,44)(42,43)],
["ConstructMGA","Isoclinic(2.L2(25)x2)","Isoclinic(L2(25).2_3x2)",[[31,34],
[32,33],[35,38],[36,37],[39,42],[40,41],[43,46],[44,45],[47,50],[48,49],[51,
54],[52,53],[55,58],[56,57]],()]);
ALF("4.L2(25).2_3","Isoclinic(L2(25).2_3x2)",[1,2,1,3,4,5,6,5,7,8,8,9,10,
9,10,11,12,12,13,14,13,14,15,16,15,16,17,18,17,18,19,20,19,20,21,22,23,24,
25,26,27,28,29,30]);
ALF("4.L2(25).2_3","L2(25).2_3",[1,1,1,2,2,3,3,3,4,4,4,5,5,5,5,6,6,6,7,7,
7,7,8,8,8,8,9,9,9,9,10,10,10,10,11,11,12,12,13,13,14,14,15,15]);
MOT("2.L2(27)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"
],
[19656,19656,28,54,54,54,54,28,28,28,28,28,28,26,26,26,26,26,26,26,26,26,26,
26,26,28,28,28,28,28,28],
[,[1,1,2,6,6,4,4,12,12,8,8,10,10,22,22,24,24,20,20,16,16,18,18,14,14,13,13,9,
9,11,11],[1,2,3,1,2,1,2,10,11,12,13,8,9,16,17,18,19,14,15,22,23,24,25,20,21,
28,29,30,31,26,27],,,,[1,2,3,4,5,6,7,1,2,1,2,1,2,24,25,20,21,22,23,18,19,14,
15,16,17,3,3,3,3,3,3],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,1,2,1,2,1,2,1,2,
1,2,27,26,29,28,31,30]],
0,
[(26,27)(28,29)(30,31),(14,22,18,20,16,24)(15,23,19,21,17,25),( 8,10,12)
( 9,11,13)(26,29,30,27,28,31),(4,6)(5,7),(14,18,16)(15,19,17)(20,24,22)
(21,25,23),(14,20)(15,21)(16,22)(17,23)(18,24)(19,25)],
["ConstructProj",[["L2(27)",[]],["2.L2(27)",[]]]]);
ARC("2.L2(27)","maxes",["2x3^3:13","2.D28","2.D26","2.L2(3)"]);
ALF("2.L2(27)","L2(27)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16]);
ALF("2.L2(27)","2.L2(27).2",[1,2,3,4,5,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2.L2(27)","2.L2(27).3",[1,2,3,4,5,6,7,8,9,8,9,8,9,10,11,10,11,10,11,
12,13,12,13,12,13,14,15,14,15,14,15],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2.L2(27)","2.L2(27).6",[1,2,3,4,5,4,5,6,7,6,7,6,7,8,9,8,9,8,9,10,11,
10,11,10,11,12,13,12,13,12,13],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
MOT("2.L2(27).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"
],
[39312,39312,56,54,54,56,56,56,56,56,56,52,52,52,52,52,52,52,52,52,52,52,52,
56,56,56,56,56,56,52,56,56,52,52,52,52,52,52,52,52,52,52,52,52,56,56,56,56,56,
56,56,56,56,56,56,56],
[,[1,1,2,4,4,10,10,6,6,8,8,20,20,22,22,18,18,14,14,16,16,12,12,11,11,7,7,9,9,
2,3,3,21,21,23,23,19,19,15,15,17,17,13,13,28,28,24,24,26,26,29,29,25,25,27,
27],[1,2,3,1,2,8,9,10,11,6,7,14,15,16,17,12,13,20,21,22,23,18,19,26,27,28,29,
24,25,30,32,31,36,35,38,37,34,33,42,41,44,43,40,39,48,47,50,49,46,45,54,53,56,
55,52,51],,,,[1,2,3,4,5,1,2,1,2,1,2,22,23,18,19,20,21,16,17,12,13,14,15,3,3,3,
3,3,3,30,31,32,43,44,39,40,41,42,38,37,34,33,36,35,31,32,31,32,31,32,31,32,31,
32,31,32],,,,,,[1,2,3,4,5,6,7,8,9,10,11,1,2,1,2,1,2,1,2,1,2,1,2,25,24,27,26,
29,28,30,32,31,30,30,30,30,30,30,30,30,30,30,30,30,52,51,54,53,56,55,46,45,48,
47,50,49]],
0,
[(33,34)(35,36)(37,38)(39,40)(41,42)(43,44),(24,25)(26,27)(28,29)(33,34)
(35,36)(37,38)(39,40)(41,42)(43,44)(45,51)(46,52)(47,53)(48,54)(49,55)(50,56),
(24,25)(26,27)(28,29)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,52)
(46,51)(47,54)(48,53)(49,56)(50,55),(12,20,16,18,14,22)(13,21,17,19,15,23)
(33,41,38,40,35,43,34,42,37,39,36,44),( 6, 8,10)( 7, 9,11)(24,27,28,25,26,29)
(45,53,49,51,47,55)(46,54,50,52,48,56),(24,25)(26,27)(28,29)(45,51)(46,52)
(47,53)(48,54)(49,55)(50,56),(31,32)(45,46)(47,48)(49,50)(51,52)(53,54)
(55,56),( 6,10, 8)( 7,11, 9)(24,28,26)(25,29,27)(45,49,47)(46,50,48)(51,55,53)
(52,56,54)],
["ConstructProj",[["L2(27).2",[]],["2.L2(27).2",[]]]]);
ALF("2.L2(27).2","L2(27).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,
24,24,25,25,26,26,27,27,28,28,29,29]);
ALF("2.L2(27).2","2.L2(27).6",[1,2,3,4,5,6,7,6,7,6,7,8,9,8,9,8,9,10,11,10,
11,10,11,12,13,12,13,12,13,14,15,16,17,18,17,18,17,18,19,20,19,20,19,20,
21,22,21,22,21,22,23,24,23,24,23,24],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
MOT("Isoclinic(2.L2(27).2)",
[
"isoclinic group of the 2.L2(27).2 given in the ATLAS"
],
0,
0,
0,
[(12,18)(13,19)(14,20)(15,21)(16,22)(17,23)(33,39,34,40)(35,41,36,42)(37,43,
38,44),(12,14,16)(13,15,17)(18,20,22)(19,21,23)(33,35,37)(34,36,38)(39,41,43)
(40,42,44),(6,8,10)(7,9,11)(24,26,28)(25,27,29)(45,47,49)(46,48,50)(51,53,55)
(52,54,56),(31,32)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56),(24,25)(26,27)
(28,29)(45,51)(46,52)(47,53)(48,54)(49,55)(50,56)],
["ConstructIsoclinic",[["2.L2(27).2"]]]);
ALF("Isoclinic(2.L2(27).2)","L2(27).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,
10,10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,20,21,21,22,
22,23,23,24,24,25,25,26,26,27,27,28,28,29,29]);
MOT("2.L2(27).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\n",
"constructions: SigmaL(2,27)"
],
[58968,58968,84,162,162,162,162,28,28,26,26,26,26,28,28,72,72,72,72,12,12,18,
18,18,18,18,18,18,18],
[,[1,1,2,6,6,4,4,8,8,12,12,10,10,9,9,18,18,16,16,19,17,24,24,22,22,28,28,26,
26],[1,2,3,1,2,1,2,8,9,10,11,12,13,14,15,1,2,1,2,3,3,4,5,6,7,6,7,4,5],,,,[1,2,
3,4,5,6,7,1,2,12,13,10,11,3,3,16,17,18,19,20,21,22,23,24,25,26,27,28,
29],,,,,,[1,2,3,4,5,6,7,8,9,1,2,1,2,15,14,16,17,18,19,20,21,22,23,24,25,26,27,
28,29]],
0,
[(14,15),(10,12)(11,13),( 4, 6)( 5, 7)(16,18)(17,19)(20,21)(22,24)(23,25)
(26,28)(27,29),( 4, 6)( 5, 7)(22,26)(23,27)(24,28)(25,29)],
["ConstructProj",[["L2(27).3",[]],["2.L2(27).3",[]]]]);
ALF("2.L2(27).3","L2(27).3",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,
12,13,13,14,14,15,15,16,16]);
ALF("2.L2(27).3","2.L2(27).6",[1,2,3,4,5,4,5,6,7,8,9,10,11,12,13,25,26,27,
28,29,30,31,32,33,34,31,32,33,34],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("2.L2(27).6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"
],
[117936,117936,168,162,162,56,56,52,52,52,52,56,56,156,168,168,52,52,52,52,56,
56,56,56,144,144,144,144,24,24,18,18,18,18,12,12,24,24,24,24],
[,[1,1,2,4,4,6,6,10,10,8,8,7,7,2,3,3,11,11,9,9,12,12,13,13,27,27,25,25,28,26,
33,33,31,31,28,26,30,30,29,29],[1,2,3,1,2,6,7,8,9,10,11,12,13,14,16,15,18,17,
20,19,22,21,24,23,1,2,1,2,3,3,4,5,4,5,14,14,16,15,16,15],,,,[1,2,3,4,5,1,2,10,
11,8,9,3,3,14,15,16,19,20,18,17,15,16,15,16,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40],,,,,,[1,2,3,4,5,6,7,1,2,1,2,13,12,14,16,15,14,14,14,14,24,23,
22,21,25,26,27,28,29,30,31,32,33,34,35,36,38,37,40,39]],
0,
[(25,27)(26,28)(29,30)(31,33)(32,34)(35,36)(37,39)(38,40),(17,18)(19,20),
(12,13)(21,23)(22,24),(12,13)(17,18)(19,20)(21,23)(22,24),(12,13)(15,16)
(17,18)(19,20)(21,24)(22,23)(37,38)(39,40),( 8,10)( 9,11)(17,19,18,20),( 8,10)
( 9,11)(17,20,18,19),(15,16)(21,22)(23,24)(37,38)(39,40)],
["ConstructProj",[["L2(27).6",[]],["2.L2(27).6",[]]]]);
ALF("2.L2(27).6","L2(27).6",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,10,11,11,
12,12,13,13,14,14,15,15,16,17,18,18,19,19,20,21,22,22,23,23]);
MOT("Isoclinic(2.L2(27).6)",
[
"isoclinic group of the 2.L2(27).6 given in the ATLAS"
],
0,
0,
0,
[(8,10)(9,11)(17,19,18,20),(25,27)(26,28)(29,30)(31,33)(32,34)(35,36)(37,39)
(38,40),(15,16)(21,22)(23,24)(37,38)(39,40),(12,13)(21,23)(22,24)],
["ConstructIsoclinic",[["2.L2(27).6"]]]);
ALF("Isoclinic(2.L2(27).6)","L2(27).6",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,9,9,
10,10,11,11,12,12,13,13,14,14,15,15,16,17,18,18,19,19,20,21,22,22,23,23]);
MOT("2.L2(29)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,29]"
],
[24360,24360,28,30,30,30,30,30,30,28,28,28,28,28,28,28,28,28,28,28,28,30,30,
30,30,30,30,30,30,58,58,58,58],
[,[1,1,2,4,4,8,8,6,6,12,12,14,14,10,10,13,13,15,15,11,11,24,24,26,26,28,28,22,
22,32,32,30,30],[1,2,3,1,2,8,9,6,7,14,15,10,11,12,13,20,21,16,17,18,19,8,9,6,
7,8,9,6,7,32,33,30,31],,[1,2,3,4,5,1,2,1,2,12,13,14,15,10,11,19,18,21,20,17,
16,4,5,4,5,4,5,4,5,30,31,32,33],,[1,2,3,4,5,8,9,6,7,1,2,1,2,1,2,3,3,3,3,3,3,
28,29,22,23,24,25,26,27,30,31,32,33],,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,1,2,1,2]],
0,
[(30,32)(31,33),(22,26)(23,27)(24,28)(25,29),(16,17)(18,19)(20,21),(10,14,12)
(11,15,13)(16,21,18,17,20,19),( 6, 8)( 7, 9)(22,28,26,24)(23,29,27,25)],
["ConstructProj",[["L2(29)",[]],["2.L2(29)",[]]]]);
ARC("2.L2(29)","maxes",["(2x29).14","2.A5","2.A5","2.D30","2.D28"]);
ALF("2.L2(29)","L2(29)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17]);
ALF("2.L2(29)","2.L2(29).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,30,31],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("2.L2(29)","2.Ru",[1,2,5,6,7,16,17,16,17,20,21,20,21,20,21,36,36,38,
38,37,37,39,40,39,40,39,40,39,40,58,59,60,61],[
"fusion map is unique up to table automorphisms"
]);
MOT("2.L2(29).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,29]"
],
[48720,48720,56,60,60,60,60,60,60,56,56,56,56,56,56,56,56,56,56,56,56,60,60,
60,60,60,60,60,60,58,58,60,56,56,60,60,60,60,60,60,56,56,56,56,56,56,56,56,56,
56,56,56,60,60,60,60,60,60,60,60],
[,[1,1,2,4,4,8,8,6,6,12,12,14,14,10,10,13,13,15,15,11,11,24,24,26,26,28,28,22,
22,30,30,2,3,3,5,5,9,9,7,7,18,18,20,20,16,16,19,19,21,21,17,17,25,25,27,27,29,
29,23,23],[1,2,3,1,2,8,9,6,7,14,15,10,11,12,13,20,21,16,17,18,19,8,9,6,7,8,9,
6,7,30,31,32,34,33,32,32,40,39,37,38,46,45,42,41,44,43,52,51,48,47,50,49,40,
39,37,38,39,40,38,37],,[1,2,3,4,5,1,2,1,2,12,13,14,15,10,11,19,18,21,20,17,16,
4,5,4,5,4,5,4,5,30,31,32,34,33,36,35,32,32,32,32,50,49,52,51,48,47,44,43,46,
45,42,41,36,35,36,35,36,35,36,35],,[1,2,3,4,5,8,9,6,7,1,2,1,2,1,2,3,3,3,3,3,3,
28,29,22,23,24,25,26,27,30,31,32,33,34,36,35,39,40,38,37,33,34,33,34,33,34,33,
34,33,34,33,34,60,59,54,53,56,55,58,57],,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,1,2,32,34,33,36,
35,38,37,40,39,42,41,44,43,46,45,48,47,50,49,52,51,54,53,56,55,58,57,60,59]],
0,
[(35,36)(37,38)(39,40)(53,54)(55,56)(57,58)(59,60),(22,26)(23,27)(24,28)
(25,29)(37,38)(39,40)(53,57)(54,58)(55,59)(56,60),(22,26)(23,27)(24,28)(25,29)
(35,36)(53,58)(54,57)(55,60)(56,59),(16,17)(18,19)(20,21)(35,36)(37,38)(39,40)
(41,47)(42,48)(43,49)(44,50)(45,51)(46,52)(53,54)(55,56)(57,58)(59,60),(16,17)
(18,19)(20,21)(33,34)(35,36)(37,38)(39,40)(41,48)(42,47)(43,50)(44,49)(45,52)
(46,51)(53,54)(55,56)(57,58)(59,60),(10,14,12)(11,15,13)(16,21,18,17,20,19)
(41,51,43,47,45,49)(42,52,44,48,46,50),( 6, 8)( 7, 9)(22,28,26,24)
(23,29,27,25)(37,40,38,39)(53,59,57,55)(54,60,58,56),(16,17)(18,19)(20,21)
(41,47)(42,48)(43,49)(44,50)(45,51)(46,52),(33,34)(41,42)(43,44)(45,46)(47,48)
(49,50)(51,52),(10,14,12)(11,15,13)(16,20,18)(17,21,19)(41,45,43)(42,46,44)
(47,51,49)(48,52,50)],
["ConstructProj",[["L2(29).2",[]],["2.L2(29).2",[]]]]);
ALF("2.L2(29).2","L2(29).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,16,17,18,18,19,19,20,20,21,21,22,22,23,23,
24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31]);
MOT("Isoclinic(2.L2(29).2)",
[
"isoclinic group of the 2.L2(29).2 given in the ATLAS"
],
0,
0,
0,
[(6,8)(7,9)(22,24,26,28)(23,25,27,29)(37,39,38,40)(53,55,57,59)(54,56,58,60),
(10,12,14)(11,13,15)(16,18,20)(17,19,21)(41,43,45)(42,44,46)(47,49,51)(48,50,
52),(35,36)(37,38)(39,40)(53,54)(55,56)(57,58)(59,60),(33,34)(41,42)(43,44)
(45,46)(47,48)(49,50)(51,52),(16,17)(18,19)(20,21)(41,47)(42,48)(43,49)(44,50)
(45,51)(46,52)],
["ConstructIsoclinic",[["2.L2(29).2"]]]);
ALF("Isoclinic(2.L2(29).2)","L2(29).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,
10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,18,18,19,19,20,20,21,21,22,
22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31]);
MOT("2.L2(31)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31]"
],
[29760,29760,32,30,30,32,32,30,30,30,30,32,32,32,32,30,30,30,30,30,30,30,30,
32,32,32,32,32,32,32,32,62,62,62,62],
[,[1,1,2,4,4,3,3,10,10,8,8,7,7,6,6,18,18,20,20,22,22,16,16,13,13,15,15,12,12,
14,14,32,32,34,34],[1,2,3,1,2,7,6,10,11,8,9,14,15,13,12,10,11,8,9,10,11,8,9,
26,27,28,29,30,31,25,24,34,35,32,33],,[1,2,3,4,5,7,6,1,2,1,2,15,14,12,13,4,5,
4,5,4,5,4,5,30,31,25,24,27,26,29,28,32,33,34,35],,,,,,,,,,,,,,,,,,,,,,,,,,[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,
30,31,1,2,1,2]],
0,
[(32,34)(33,35),(16,20)(17,21)(18,22)(19,23),( 8,10)( 9,11)(16,22,20,18)
(17,23,21,19),( 6, 7)(12,15,13,14)(24,30,29,26,25,31,28,27),(24,25)(26,27)
(28,29)(30,31),(12,13)(14,15)(24,28,25,29)(26,30,27,31)],
["ConstructProj",[["L2(31)",[]],["2.L2(31)",[]]]]);
ARC("2.L2(31)","maxes",["2x31:15","2.A5","2.A5","2.D32","2.D30","2.Symm(4)",
"2.Symm(4)"]);
ALF("2.L2(31)","L2(31)",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18]);
ALF("2.L2(31)","2.L2(31).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,32,33],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
MOT("2.L2(31).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31]"
],
[59520,59520,64,60,60,64,64,60,60,60,60,64,64,64,64,60,60,60,60,60,60,60,60,
64,64,64,64,64,64,64,64,62,62,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,64,
64,64,64,64,64,64,64,64,64,64,64,64,64,64,64],
[,[1,1,2,4,4,3,3,10,10,8,8,7,7,6,6,18,18,20,20,22,22,16,16,13,13,15,15,12,12,
14,14,32,32,2,5,5,11,11,9,9,19,19,21,21,23,23,17,17,25,25,27,27,29,29,31,31,
24,24,26,26,28,28,30,30],[1,2,3,1,2,7,6,10,11,8,9,14,15,13,12,10,11,8,9,10,11,
8,9,26,27,28,29,30,31,25,24,32,33,34,34,34,40,39,37,38,40,39,37,38,39,40,38,
37,51,52,53,54,55,56,57,58,59,60,61,62,63,64,50,49],,[1,2,3,4,5,7,6,1,2,1,2,
15,14,12,13,4,5,4,5,4,5,4,5,30,31,25,24,27,26,29,28,32,33,34,36,35,34,34,34,
34,36,35,36,35,36,35,36,35,56,55,58,57,60,59,62,61,64,63,49,50,51,52,53,
54],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,1,2,34,36,35,38,37,40,39,42,41,44,43,46,
45,48,47,50,49,52,51,54,53,56,55,58,57,60,59,62,61,64,63]],
0,
[(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48),(16,20)(17,21)(18,22)
(19,23)(37,38)(39,40)(41,45)(42,46)(43,47)(44,48),(16,20)(17,21)(18,22)(19,23)
(35,36)(41,46)(42,45)(43,48)(44,47),( 8,10)( 9,11)(16,22,20,18)(17,23,21,19)
(37,40,38,39)(41,47,45,43)(42,48,46,44),( 6, 7)(12,15,13,14)(24,30,29,26,25,
31,28,27)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,56,61,51,58,63,
53,60,50,55,62,52,57,64,54,59),( 6, 7)(12,15,13,14)(24,30,29,26,25,31,28,27)
(49,56,61,51,58,63,53,60,50,55,62,52,57,64,54,59),(49,50)(51,52)(53,54)(55,56)
(57,58)(59,60)(61,62)(63,64)],
["ConstructProj",[["L2(31).2",[]],["2.L2(31).2",[]]]]);
ALF("2.L2(31).2","L2(31).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,16,17,17,18,19,19,20,20,21,21,22,22,23,23,
24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33]);
MOT("Isoclinic(2.L2(31).2)",
[
"isoclinic group of the 2.L2(31).2 given in the ATLAS"
],
0,
0,
0,
[(6,7)(12,14,13,15)(24,26,28,30,25,27,29,31)(49,51,53,55,57,59,61,63,50,52,54,
56,58,60,62,64),(8,10)(9,11)(16,18,20,22)(17,19,21,23)(37,39,38,40)(41,43,45,
47)(42,44,46,48),(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)],
["ConstructIsoclinic",[["2.L2(31).2"]]]);
ALF("Isoclinic(2.L2(31).2)","L2(31).2",[1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,
10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,19,19,20,20,21,21,22,
22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33]);
MOT("J3M3",
[
"3rd maximal subgroup of J3,\n",
"differs from J3M2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(19)"]]);
ALF("J3M3","J3",[1,2,4,7,6,11,12,10,14,13,21,20],[
"fusion L2(19) -> J3 mapped under J3.2"
]);
MOT("L2(11)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"
],
[660,12,6,5,5,6,11,11],
[,[1,1,3,5,4,3,8,7],[1,2,1,5,4,2,7,8],,[1,2,3,1,1,6,7,8],,,,,,[1,2,3,4,5,6,1,
1]],
[[1,1,1,1,1,1,1,1],[5,1,-1,0,0,1,E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,
E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10],
[GALOIS,[2,2]],[10,-2,1,0,0,1,-1,-1],[10,2,1,0,0,-1,-1,-1],[11,-1,-1,1,1,-1,0,
0],[12,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,1,1],
[GALOIS,[7,2]]],
[(7,8),(4,5)]);
ARC("L2(11)","CAS",[rec(name:="psl(2,11)",
permchars:=(4,5),
permclasses:=(),
text:=[
"names:psl[2,11]; psl2[11], psu2[11], psp2[11], pom3[11]\n",
"a1[11] 2a1[11] c1[11] b1[11] [lie-not.]\n",
"order: 2^2.3.5.11 = 660\n",
"number of classes: 8\n",
"source:generated by cas-algorithms,\n",
"aachen\n",
"comments: psl[2,11] is maximal subgroup of m12\n",
""])]);
ARC("L2(11)","projectives",["2.L2(11)",[[6,0,0,1,1,0,-E(11)-E(11)^3-E(11)^4
-E(11)^5-E(11)^9,-E(11)^2-E(11)^6-E(11)^7-E(11)^8-E(11)^10],
[GALOIS,[1,2]],[10,0,-2,0,0,0,-1,-1],[10,0,1,0,0,-E(12)^7+E(12)^11,-1,-1],
[GALOIS,[4,5]],[12,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,1,1],
[GALOIS,[6,2]]],]);
ARC("L2(11)","isSimple",true);
ARC("L2(11)","extInfo",["2","2"]);
ARC("L2(11)","tomfusion",rec(name:="L2(11)",map:=[1,2,3,5,5,8,10,10],text:=[
"fusion map is unique"
]));
ARC("L2(11)","maxes",["A5","A5","11:5","S3x2"]);
ALF("L2(11)","L2(11).2",[1,2,3,4,5,6,7,7],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("L2(11)","M11",[1,2,3,5,5,6,9,10],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L2(11)","M12",[1,2,5,8,8,9,14,15],[
"determined by permutation character (ATLAS) up to table automorphisms,\n",
"the representative is equal to the fusion on the CAS table"
]);
ALF("L2(11)","M22",[1,2,3,6,6,7,11,12],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L2(11)","J1",[1,2,3,4,5,6,10,10],[
"fusion map is unique up to table automorphisms,\n",
"unique map that is compatible with Brauer tables,\n",
"the map on the CAS table was not compatible"
]);
ALF("L2(11)","U5(2)",[1,3,9,13,13,27,33,34],[
"fusion map is unique up to table autom."
]);
ALN("L2(11)",["A1(11)","U2(11)","S2(11)","O3(11)","psl(2,11)"]);
MOT("L2(11).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11],\n",
"constructions: Aut(L2(11))"
],
[1320,24,12,10,10,12,11,20,12,10,10,12,12],
[,[1,1,3,5,4,3,7,1,2,5,4,6,6],[1,2,1,5,4,2,7,8,9,11,10,9,9],,[1,2,3,1,1,6,7,8,
9,8,8,13,12],,,,,,[1,2,3,4,5,6,1,8,9,10,11,12,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[10,2,-2,0,0,2,
-1,0,0,0,0,0,0],[10,-2,1,0,0,1,-1,0,2,0,0,-1,-1],
[TENSOR,[4,2]],[10,2,1,0,0,-1,-1,0,0,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11],
[TENSOR,[6,2]],[11,-1,-1,1,1,-1,0,1,-1,1,1,-1,-1],
[TENSOR,[8,2]],[12,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,1,2,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0],
[TENSOR,[10,2]],
[GALOIS,[10,2]],
[TENSOR,[12,2]]],
[(12,13),( 4, 5)(10,11)]);
ARC("L2(11).2","CAS",[rec(name:="pgl(2,11)",
permchars:=(),
permclasses:=(),
text:=[
"names:= pgl[2,11]\n",
" order: 2^3.3.5.11 = 1,320\n",
" number of classes: 13\n",
" source: private communication of atlas compound table\n",
" from cambridge 1980/81\n",
" test: orth.1, minus, sym[3]\n",
""])]);
ARC("L2(11).2","projectives",["2.L2(11).2",[[12,0,0,2,2,0,1,0,0,0,0,0,0],[10,
0,-2,0,0,0,-1,0,E(8)-E(8)^3,0,0,E(8)-E(8)^3,E(8)-E(8)^3],[10,0,1,0,0,
-E(12)^7+E(12)^11,-1,0,E(8)-E(8)^3,0,0,-E(24)+E(24)^11,-E(24)^17+E(24)^19],
[GALOIS,[3,7]],[12,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,1,0,0,E(20)-E(20)^9,
-E(20)^13+E(20)^17,0,0],
[GALOIS,[5,7]]],]);
ARC("L2(11).2","tomfusion",rec(name:="L2(11).2",map:=[1,2,4,8,8,9,16,3,6,
15,15,20,20],text:=[
"fusion map is unique"
],perm:=(3,4)));
ARC("L2(11).2","maxes",["L2(11)","11:10","s4","D24","D20"]);
ALF("L2(11).2","L2(121)",[1,33,23,15,27,13,2,33,18,21,9,8,28],[
"fusion map is unique up to table autom."
],"tom:57");
ALF("L2(11).2","L3(11)",[1,2,3,9,10,11,31,2,4,25,24,32,33],[
"fusion map is unique up to table autom."
]);
ALF("L2(11).2","A12.2",[1,3,7,14,14,20,29,43,47,63,63,68,68],[
"fusion map is unique"
]);
ALF("L2(11).2","M12.2",[1,3,4,7,7,9,12,13,14,17,18,20,21],[
"determined as map from novelty L2(11).2 that contains 2B elements,\n",
"and then the fusion is unique up to Galois automorphisms,\n",
"compatible with Brauer tables"
],"tom:209");
ALF("L2(11).2","M22.2",[1,2,3,6,6,7,11,13,14,18,18,19,19],[
"fusion map is unique"
]);
ALF("L2(11).2","U3(11)",[1,2,3,8,7,9,15,2,6,13,12,21,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
],"tom:115");
ALF("L2(11).2","U5(2).2",[1,3,7,11,11,19,23,31,32,38,38,39,39],[
"fusion map is unique"
]);
ALF("L2(11).2","B",[1,5,7,19,19,29,54,5,15,53,53,73,73],[
"fusion map determined using the embedding of L2(11) via M11 and L2(11).2"
]);
ALN("L2(11).2",["pgl(2,11)","U5(2).2M7"]);
MOT("L2(121)M3",
[
"3rd maximal subgroup of L2(121),\n",
"differs from L2(121)M2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(11).2"]]);
ALF("L2(121)M3","L2(121)",[1,33,23,15,27,13,3,33,18,21,9,8,28]);
MOT("M12.2M3",
[
"3rd maximal subgroup of M12.2,\n",
"differs from M12.2M2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(11).2"]]);
ALF("M12.2M3","M12.2",[1,2,5,7,7,8,12,13,15,17,18,19,19],[
"determined as extension of max. L2(11) of M12 that contains 2A elements,\n",
"and then the fusion is unique up to Galois automorphisms,\n",
"compatible with Brauer tables"
]);
MOT("U3(11)M4",
[
"4th maximal subgroup of U3(11),\n",
"differs from U3(11)M3 = L2(11).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(11).2"]]);
ALF("U3(11)M4","U3(11)",[1,2,3,8,7,9,16,2,6,13,12,21,20],[
"fusion L2(11).2 -> U3(11) mapped under U3(11).3"
]);
MOT("U3(11)M5",
[
"5th maximal subgroup of U3(11),\n",
"differs from U3(11)M3 = L2(11).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(11).2"]]);
ALF("U3(11)M5","U3(11)",[1,2,3,8,7,9,17,2,6,13,12,21,20],[
"fusion U3(11)M4 -> U3(11) mapped under U3(11).3"
]);
MOT("L2(13)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"
],
[1092,12,6,6,7,7,7,13,13],
[,[1,1,3,3,6,7,5,9,8],[1,2,1,2,7,5,6,8,9],,,,[1,2,3,4,1,1,1,9,8],,,,,,[1,2,3,
4,5,6,7,1,1]],
[[1,1,1,1,1,1,1,1,1],[7,-1,1,-1,0,0,0,-E(13)-E(13)^3-E(13)^4-E(13)^9-E(13)^10
-E(13)^12,-E(13)^2-E(13)^5-E(13)^6-E(13)^7-E(13)^8-E(13)^11],
[GALOIS,[2,2]],[12,0,0,0,-E(7)-E(7)^6,-E(7)^2-E(7)^5,-E(7)^3-E(7)^4,-1,-1],
[GALOIS,[4,3]],
[GALOIS,[4,2]],[13,1,1,1,-1,-1,-1,0,0],[14,2,-1,-1,0,0,0,1,1],[14,-2,-1,1,0,0,
0,1,1]],
[(8,9),(5,7,6)]);
ARC("L2(13)","CAS",[rec(name:="psl(2,13)",
permchars:=(),
permclasses:=(),
text:=[
"names:= psl[2,13]; psu[2,13], psp[2,13], pom[3,13]\n",
" a1[13] 2a1[13] c1[13] b1[13] [lie-not.]\n",
" order: 2^2.3.7.13 = 1,092\n",
" number of classes: 9\n",
" source: private communication of atlas compound table\n",
" from cambridge 1980/81\n",
" test: orth.1, minus, sym[3]\n",
""])]);
ARC("L2(13)","projectives",["2.L2(13)",[[6,0,0,0,-1,-1,-1,
E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6
+E(13)^7+E(13)^8+E(13)^11],
[GALOIS,[1,2]],[12,0,0,0,-E(7)-E(7)^6,-E(7)^2-E(7)^5,-E(7)^3-E(7)^4,-1,-1],
[GALOIS,[3,3]],
[GALOIS,[3,2]],[14,0,2,0,0,0,0,1,1],[14,0,-1,-E(12)^7+E(12)^11,0,0,0,1,1],
[GALOIS,[7,5]]],]);
ARC("L2(13)","maxes",["13:6","D14","S3x2","a4"]);
ARC("L2(13)","isSimple",true);
ARC("L2(13)","extInfo",["2","2"]);
ARC("L2(13)","tomfusion",rec(name:="L2(13)",map:=[1,2,3,5,8,8,8,11,11],text:=[
"fusion map is unique"
]));
ALF("L2(13)","A14",[1,4,8,26,28,28,28,48,49],[
"fusion map is unique up to table aut."
]);
ALF("L2(13)","L2(13).2",[1,2,3,4,5,6,7,8,8],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L2(13)","G2(3)",[1,2,6,12,14,14,14,22,23],[
"fusion map determined up to table automorphisms together with the fact\n",
"that the group contains 3D elements"
]);
ALF("L2(13)","G2(4)",[1,3,5,14,15,15,15,25,26],[
"fusion map is unique up to table automorphisms"
]);
ALF("L2(13)","S6(3)",[1,3,10,30,31,31,31,57,58],[
"fusion map is unique up to table automorphisms"
]);
ALN("L2(13)",["A14M9","A1(13)","U2(13)","S2(13)","O3(13)","psl(2,13)"]);
MOT("L2(13).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\n",
"constructions: Aut(L2(13))"
],
[2184,24,12,12,14,14,14,13,28,12,12,12,14,14,14],
[,[1,1,3,3,6,7,5,8,1,2,4,4,6,7,5],[1,2,1,2,7,5,6,8,9,10,10,10,15,13,14],,,,[1,
2,3,4,1,1,1,8,9,10,12,11,9,9,9],,,,,,[1,2,3,4,5,6,7,1,9,10,11,12,13,14,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1],[14,
-2,2,-2,0,0,0,1,0,0,0,0,0,0,0],[12,0,0,0,-E(7)-E(7)^6,-E(7)^2-E(7)^5,
-E(7)^3-E(7)^4,-1,2,0,0,0,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4],
[TENSOR,[4,2]],
[GALOIS,[4,3]],
[TENSOR,[6,2]],
[GALOIS,[4,2]],
[TENSOR,[8,2]],[13,1,1,1,-1,-1,-1,0,1,-1,-1,-1,1,1,1],
[TENSOR,[10,2]],[14,2,-1,-1,0,0,0,1,0,2,-1,-1,0,0,0],
[TENSOR,[12,2]],[14,-2,-1,1,0,0,0,1,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,
0,0],
[TENSOR,[14,2]]],
[(11,12),( 5, 7, 6)(13,15,14)]);
ARC("L2(13).2","CAS",[rec(name:="pgl(2,13)",
permchars:=(),
permclasses:=(),
text:=[
"names:= pgl[2,13]\n",
" order: 2^3.3.7.13 = 2,184\n",
" number of classes: 15\n",
" source: private communication of atlas compound table\n",
" from cambridge 1980/81\n",
" test: orth.1, minus, sym[3]\n",
""])]);
ARC("L2(13).2","projectives",["2.L2(13).2",[[12,0,0,0,-2,-2,-2,-1,0,0,0,0,0,0,
0],[12,0,0,0,-E(7)-E(7)^6,-E(7)^2-E(7)^5,-E(7)^3-E(7)^4,-1,0,0,0,0,
E(28)^3-E(28)^11,-E(28)^15+E(28)^27,E(28)^19-E(28)^23],
[GALOIS,[2,3]],
[GALOIS,[2,9]],[14,0,2,0,0,0,0,1,0,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,0,0,
0],[14,0,-1,-E(12)^7+E(12)^11,0,0,0,1,0,E(8)-E(8)^3,-E(24)+E(24)^11,
-E(24)^17+E(24)^19,0,0,0],
[GALOIS,[6,7]]],]);
ARC("L2(13).2","tomfusion",rec(name:="L2(13).2",map:=[1,3,4,8,11,11,11,17,
2,6,15,15,20,20,20],text:=[
"fusion map is unique"
]));
ALF("L2(13).2","G2(3).2",[1,2,5,9,11,11,11,17,18,19,23,24,25,25,25],[
"fusion map is unique up to table autom."
]);
ALF("L2(13).2","G2(4).2",[1,3,5,12,13,13,13,21,25,27,34,34,35,35,35],[
"fusion map is unique"
]);
ALF("L2(13).2","Ru",[1,2,4,11,12,12,12,20,3,6,19,19,21,23,22],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L2(13).2","F3+",[1,3,7,22,25,25,25,51,3,11,50,50,53,53,53],[
"fusion map determined by the fact that the subgroup contains elements\n",
"in the classes 2B, 3D, 7B, and 12M"
]);
ALF("L2(13).2","M",[1,3,5,17,20,20,20,45,3,9,42,42,49,49,49],[
"fusion map determined by the fact that the subgroup contains elements\n",
"in the classes 7B, 12H, and 13A"
]);
ALN("L2(13).2",["pgl(2,13)","psl(2,13):2"]);
MOT("L2(16)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17]"
],
[4080,16,15,15,15,15,15,15,15,17,17,17,17,17,17,17,17],
[,[1,1,3,5,4,8,9,7,6,12,13,11,10,16,17,15,14],[1,2,1,5,4,5,5,4,4,17,16,14,15,
10,11,12,13],,[1,2,3,1,1,3,3,3,3,16,17,15,14,11,10,13,12],,,,,,,,,,,,[1,2,3,5,
4,8,9,7,6,1,1,1,1,1,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[15,-1,0,0,0,0,0,0,0,-E(17)-E(17)^16,
-E(17)^4-E(17)^13,-E(17)^2-E(17)^15,-E(17)^8-E(17)^9,-E(17)^6-E(17)^11,
-E(17)^7-E(17)^10,-E(17)^5-E(17)^12,-E(17)^3-E(17)^14],
[GALOIS,[2,4]],
[GALOIS,[2,8]],
[GALOIS,[2,2]],
[GALOIS,[2,3]],
[GALOIS,[2,5]],
[GALOIS,[2,7]],
[GALOIS,[2,6]],[16,0,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],[17,1,-1,2,2,-1,
-1,-1,-1,0,0,0,0,0,0,0,0],[17,1,2,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,
E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)^2+E(5)^3,0,0,0,0,0,0,0,0],
[GALOIS,[12,2]],[17,1,-1,E(5)^2+E(5)^3,E(5)+E(5)^4,E(15)+E(15)^14,
E(15)^4+E(15)^11,E(15)^2+E(15)^13,E(15)^7+E(15)^8,0,0,0,0,0,0,0,0],
[GALOIS,[14,4]],
[GALOIS,[14,7]],
[GALOIS,[14,2]]],
[(10,17,13,15,11,16,12,14),(6,7)(8,9),(4,5)(6,9,7,8)]);
ARC("L2(16)","CAS",[rec(name:="psl(2,16)",
permchars:=(),
permclasses:=(),
text:=[
"names:= psl[2,16] = psu[2,16] = psp[2,16] = po[3,16] = sl[2,16]\n",
" = a1[16] = 2 a1[16] = c1[16] = b1[16] [lie-not.]\n",
" order: 4,080 = 2^4 . 3 . 5 . 17\n",
" number of classes: 17\n",
" source: private communication of atlas compound table\n",
" from cambridge 1980/81\n",
" test: orth.1, min\n",
""])]);
ARC("L2(16)","isSimple",true);
ARC("L2(16)","extInfo",["","4"]);
ARC("L2(16)","tomfusion",rec(name:="L2(16)",map:=[1,2,3,7,7,12,12,12,12,
14,14,14,14,14,14,14,14],text:=[
"fusion map is unique"
]));
ALF("L2(16)","L2(16).2",[1,2,3,4,5,6,6,7,7,8,8,9,9,10,10,11,11],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L2(16)","L2(16).4",[1,2,3,4,4,5,5,5,5,6,6,6,6,7,7,7,7],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("L2(16)",["psl(2,16)","L2(16).2M1"]);
MOT("L2(16).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17]"
],
[8160,32,30,30,30,15,15,17,17,17,17,120,8,6,10,10],
[,[1,1,3,5,4,7,6,9,8,11,10,1,2,3,5,4],[1,2,1,5,4,5,4,11,10,8,9,12,13,12,16,
15],,[1,2,3,1,1,3,3,11,10,8,9,12,13,14,12,12],,,,,,,,,,,,[1,2,3,5,4,7,6,1,1,1,
1,12,13,14,16,15]],
[[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],[30,
-2,0,0,0,0,0,-E(17)-E(17)^4-E(17)^13-E(17)^16,-E(17)^2-E(17)^8-E(17)^9
-E(17)^15,-E(17)^6-E(17)^7-E(17)^10-E(17)^11,-E(17)^3-E(17)^5-E(17)^12
-E(17)^14,0,0,0,0,0],
[GALOIS,[3,2]],
[GALOIS,[3,3]],
[GALOIS,[3,6]],[16,0,1,1,1,1,1,-1,-1,-1,-1,4,0,1,-1,-1],
[TENSOR,[7,2]],[17,1,-1,2,2,-1,-1,0,0,0,0,5,1,-1,0,0],
[TENSOR,[9,2]],[17,1,2,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,0,
0,0,0,3,-1,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[TENSOR,[11,2]],
[GALOIS,[11,2]],
[TENSOR,[13,2]],[34,2,-2,2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,-E(5)^2-E(5)^3,
-E(5)-E(5)^4,0,0,0,0,0,0,0,0,0],
[GALOIS,[15,2]]],
[( 8,11, 9,10),( 4, 5)( 6, 7)(15,16)]);
ARC("L2(16).2","CAS",[rec(name:="psl(2,16):2",
permchars:=(),
permclasses:=(),
text:=[
"names:= psl[2,16]:2\n",
" order: 8,160 = 2^5 . 3 . 5 . 17\n",
" number of classes: 16\n",
" source: private communication of atlas compound table\n",
" from cambridge 1980/81\n",
" comments: split extension of psl[2,16] with an outer\n",
" automorphism of order 2\n",
" test: orth.1, min\n",
""])]);
ARC("L2(16).2","tomfusion",rec(name:="L2(16).2",map:=[1,3,4,10,10,24,24,
28,28,28,28,2,8,13,21,21],text:=[
"fusion map is unique"
]));
ALF("L2(16).2","L2(16).4",[1,2,3,4,4,5,5,6,6,7,7,8,9,10,11,11],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("L2(16).2","J3",[1,2,3,6,7,16,17,19,19,18,18,2,5,8,13,14],[
"fusion is unique up to table automorphisms,\n",
"compatible with Brauer tables,\n",
"the map on the CAS table was not compatible"
]);
ALF("L2(16).2","O8-(2)",[1,4,6,12,12,29,30,33,32,34,35,3,11,17,25,25],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L2(16).2","S4(4)",[1,4,5,9,10,20,21,25,24,26,27,2,7,14,16,17],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
],"tom:493");
ALN("L2(16).2",["psl(2,16):2"]);
MOT("S4(4)M4",
[
"4th maximal subgroup of S4(4),\n",
"differs from S4(4)M3 = L2(16).2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(16).2"]]);
ALF("S4(4)M4","S4(4)",[1,4,6,11,12,22,23,27,26,25,24,3,7,15,18,19],[
"fusion L2(16).2 -> S4(4) mapped under S4(4).4"
]);
MOT("L2(16).4",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17],\n",
"constructions: Aut(L2(16)), PGammaL(2,16), SigmaL(2,16), PSigmaL(2,16)"
],
[16320,64,60,30,15,17,17,240,16,12,10,24,24,8,8,12,12],
[,[1,1,3,4,5,6,7,1,2,3,4,8,8,9,9,10,10],[1,2,1,4,4,7,6,8,9,8,11,13,12,15,14,
13,12],,[1,2,3,1,3,7,6,8,9,10,8,12,13,14,15,16,17],,,,,,,,,,,,[1,2,3,4,5,1,1,
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.22 Sekunden
(vorverarbeitet)
]
|
