Quelle  ctoline1.tbl   Sprache: unbekannt

#############################################################################
##
#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,
8,9,10,11,12,13,14,15,16,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,-1,-1,-1,-1,E(4),-E(4),
E(4),-E(4),E(4),-E(4)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[60,-4,0,0,0,-E(17)-E(17)^2-E(17)^4-E(17)^8-E(17)^9-E(17)^13
 -E(17)^15-E(17)^16,-E(17)^3-E(17)^5-E(17)^6-E(17)^7-E(17)^10-E(17)^11
 -E(17)^12-E(17)^14,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[5,3]],[16,0,1,1,1,-1,-1,4,0,1,-1,2,2,0,0,-1,-1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[17,1,-1,2,-1,0,0,5,1,-1,0,1,1,-1,-1,1,1],
[TENSOR,[11,2]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],[34,2,4,-1,-1,0,0,6,-2,0,1,0,0,0,0,0,0],
[TENSOR,[15,2]],[68,4,-4,-2,1,0,0,0,0,0,0,0,0,0,0,0,0]],
[(12,13)(14,15)(16,17),(6,7)]);
ARC("L2(16).4","tomfusion",rec(name:="L2(16).4",map:=[1,3,4,10,27,33,33,2,
8,12,22,9,9,18,18,26,26],text:=[
"fusion map is unique"
]));
ALF("L2(16).4","J3.2",[1,2,3,6,14,16,15,2,5,7,12,19,19,22,22,23,23],[
"fusion map determined uniquely by the Brauer tables,\n",
"(not ambiguous if one uses that J3 does not contain L2(16).4)",
]);
ALF("L2(16).4","S4(4).2",[1,4,5,9,16,18,19,2,7,12,14,21,21,26,27,29,29],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
],"tom:997");
ALF("L2(16).4","O8-(2).2",[1,4,6,12,28,30,31,3,11,17,24,39,39,49,49,55,55],[
"fusion map is unique up to table automorphisms"
]);
ALF("L2(16).4","(3xL2(16):2).2",[1,2,3,4,5,6,7,8,9,10,11,28,29,30,31,32,
33],[
"fusion map is unique up to table aut."
]);
ALN("L2(16).4",["O8-(2).2M7"]);

MOT("S4(4).2M5",
[
"5th maximal subgroup of S4(4).2,\n",
"differs from S4(4).2M4 = L2(16).4 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(16).4"]]);
ALF("S4(4).2M5","S4(4).2",[1,4,6,10,17,19,18,3,7,13,15,22,22,26,27,30,30],[
"fusion L2(16).4 -> S4(4).2 mapped under S4(4).4"
]);

MOT("L2(17)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,17]"
],
[2448,16,9,8,8,8,9,9,9,17,17],
[,[1,1,3,2,4,4,8,9,7,10,11],[1,2,1,4,6,5,3,3,3,11,10],,,,,,,,,,,,,,[1,2,3,4,5,
6,7,8,9,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1],[9,1,0,1,-1,-1,0,0,0,-E(17)-E(17)^2-E(17)^4-E(17)^8
 -E(17)^9-E(17)^13-E(17)^15-E(17)^16,-E(17)^3-E(17)^5-E(17)^6-E(17)^7-E(17)^10
 -E(17)^11-E(17)^12-E(17)^14],
[GALOIS,[2,3]],[16,0,-2,0,0,0,1,1,1,-1,-1],[16,0,1,0,0,0,E(9)^2+E(9)^4+E(9)^5
 +E(9)^7,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5,-1,-1],
[GALOIS,[5,4]],
[GALOIS,[5,2]],[17,1,-1,1,1,1,-1,-1,-1,0,0],[18,2,0,-2,0,0,0,0,0,1,1],[18,-2,
0,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,1,1],
[GALOIS,[10,3]]],
[(10,11),(7,8,9),(5,6)]);
ARC("L2(17)","CAS",[rec(name:="psl(2,17)",
permchars:=(),
permclasses:=(),
text:=[
"names:=     psl[2,17]; psu[2,17], psp[2,17], pom[3,17]\n",
"               a1[17]    2a1[17]     c1[17]     b1[17]    [lie-not.]\n",
"   order:     2^4.3^2.17 = 2,448\n",
"   number of classes: 11\n",
"   source:    private communication of atlas compound table\n",
"              from cambridge 1980/81\n",
"   test:      orth.1, minus, sym[3]\n",
""])]);
ARC("L2(17)","projectives",["2.L2(17)",[[8,0,-1,0,0,0,-1,-1,-1,
E(17)+E(17)^2+E(17)^4+E(17)^8+E(17)^9+E(17)^13+E(17)^15+E(17)^16,
E(17)^3+E(17)^5+E(17)^6+E(17)^7+E(17)^10+E(17)^11+E(17)^12+E(17)^14],
[GALOIS,[1,3]],[16,0,-2,0,0,0,1,1,1,-1,-1],[16,0,1,0,0,0,E(9)^2+E(9)^4+E(9)^5
 +E(9)^7,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5,-1,-1],
[GALOIS,[4,4]],
[GALOIS,[4,2]],[18,0,0,E(8)-E(8)^3,E(16)-E(16)^7,E(16)^3-E(16)^5,0,0,0,1,1],
[GALOIS,[7,5]],
[GALOIS,[7,7]],
[GALOIS,[7,3]]],]);
ARC("L2(17)","isSimple",true);
ARC("L2(17)","extInfo",["2","2"]);
ARC("L2(17)","tomfusion",rec(name:="L2(17)",map:=[1,2,3,6,8,8,11,11,11,15,
15],text:=[
"fusion map is unique"
]));
ARC("L2(17)","maxes",["17:8","s4","s4","D18","D16"]);
ALF("L2(17)","L2(17).2",[1,2,3,4,5,6,7,8,9,10,10],[
"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(17)","J3",[1,2,4,5,9,9,10,11,12,18,19],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L2(17)","S8(2)",[1,7,11,22,47,47,50,50,50,72,73],[
"fusion map determined up to table autom. by Brauer tables"
]);
ALN("L2(17)",["A1(17)","U2(17)","S2(17)","O3(17)","psl(2,17)","L2(17).2M1"]);

MOT("L2(17).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,17],\n",
"constructions: Aut(L2(17))"
],
[4896,32,18,16,16,16,18,18,18,17,36,18,16,16,16,16,18,18,18],
[,[1,1,3,2,4,4,8,9,7,10,1,3,5,6,5,6,8,9,7],[1,2,1,4,6,5,3,3,3,10,11,11,14,15,
16,13,12,12,12],,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,1,11,12,13,14,15,16,17,18,
19]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,-1],[18,2,0,2,-2,-2,0,0,0,1,0,0,0,0,0,0,0,0,0],[16,0,-2,0,0,0,1,1,1,
-1,2,2,0,0,0,0,-1,-1,-1],
[TENSOR,[4,2]],[16,0,1,0,0,0,E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^2-E(9)^7,
-E(9)^4-E(9)^5,-1,2,-1,0,0,0,0,-E(9)^2-E(9)^4-E(9)^5-E(9)^7,E(9)^2+E(9)^7,
E(9)^4+E(9)^5],
[TENSOR,[6,2]],
[GALOIS,[6,4]],
[TENSOR,[8,2]],
[GALOIS,[6,2]],
[TENSOR,[10,2]],[17,1,-1,1,1,1,-1,-1,-1,0,1,1,-1,-1,-1,-1,1,1,1],
[TENSOR,[12,2]],[18,2,0,-2,0,0,0,0,0,1,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,
E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0],
[TENSOR,[14,2]],[18,-2,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,1,0,0,E(16)-E(16)^7,
E(16)^3-E(16)^5,-E(16)+E(16)^7,-E(16)^3+E(16)^5,0,0,0],
[TENSOR,[16,2]],
[GALOIS,[16,5]],
[TENSOR,[18,2]]],
[( 7, 8, 9)(17,18,19),( 7, 9, 8)(17,19,18),( 5, 6)(13,16,15,14),(13,15)
(14,16)]);
ARC("L2(17).2","CAS",[rec(name:="pgl(2,17)",
permchars:=(),
permclasses:=(),
text:=[
"names:=     pgl[2,17]\n",
"   order:     2^5.3^2.17 = 4,896\n",
"   number of classes: 19\n",
"   source:    private communication of atlas compound table\n",
"              from cambridge 1980/81\n",
"   test:      orth.1, minus, sym[3]\n",
""])]);
ARC("L2(17).2","projectives",["2.L2(17).2",[[16,0,-2,0,0,0,-2,-2,-2,-1,0,0,0,
0,0,0,0,0,0],[16,0,-2,0,0,0,1,1,1,-1,0,0,0,0,0,0,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11,-E(12)^7+E(12)^11],[16,0,1,0,0,0,E(9)^2+E(9)^4+E(9)^5+E(9)^7
 ,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5,-1,0,-E(12)^7+E(12)^11,0,0,0,0,
-E(36)+E(36)^17-E(36)^25+E(36)^29,E(36)-E(36)^17,E(36)^25-E(36)^29],
[GALOIS,[3,13]],
[GALOIS,[3,11]],[18,0,0,E(8)-E(8)^3,E(16)-E(16)^7,E(16)^3-E(16)^5,0,0,0,1,0,0,
E(32)-E(32)^15,-E(32)^3+E(32)^13,-E(32)^7+E(32)^9,E(32)^5-E(32)^11,0,0,0],
[GALOIS,[6,5]],
[GALOIS,[6,7]],
[GALOIS,[6,13]]],]);
ALF("L2(17).2","B",[1,5,7,15,44,44,46,46,46,91,5,29,90,90,90,90,96,96,96],[
"fusion map determined by the fact that the group contains 8M and 9A elements"
]);
ALN("L2(17).2",["pgl(2,17)"]);

MOT("L2(19)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,19]"
],
[3420,20,9,10,10,9,9,9,10,10,19,19],
[,[1,1,3,5,4,7,8,6,5,4,12,11],[1,2,1,5,4,3,3,3,10,9,12,11],,[1,2,3,1,1,8,6,7,
2,2,11,12],,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1],[9,1,0,-1,-1,0,0,0,1,1,E(19)+E(19)^4+E(19)^5
 +E(19)^6+E(19)^7+E(19)^9+E(19)^11+E(19)^16+E(19)^17,E(19)^2+E(19)^3+E(19)^8
 +E(19)^10+E(19)^12+E(19)^13+E(19)^14+E(19)^15+E(19)^18],
[GALOIS,[2,2]],[18,-2,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-1,-1],
[GALOIS,[4,2]],[18,2,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,-1,-1],
[GALOIS,[6,2]],[19,-1,1,-1,-1,1,1,1,-1,-1,0,0],[20,0,2,0,0,-1,-1,-1,0,0,1,1],[
20,0,-1,0,0,-E(9)^2-E(9)^4-E(9)^5-E(9)^7,E(9)^2+E(9)^7,E(9)^4+E(9)^5,0,0,1,1],
[GALOIS,[10,4]],
[GALOIS,[10,2]]],
[(11,12),(6,7,8),( 4, 5)( 9,10)]);
ARC("L2(19)","CAS",[rec(name:="psl(2,19)",
permchars:=(),
permclasses:=(),
text:=[
"names:=     psl[2,19]; psu[2,19], psp[2,19], pom[3,19]\n",
"               a1[19]    2a1[19]     c1[19]     b1[19]   [lie-not.]\n",
"   order:     2^2.3^2.5.19 = 3,420\n",
"   number of classes: 12\n",
"   source:    private communication of atlas compound table\n",
"              from cambridge 1980/81\n",
"   test:      orth.1, minus, sym[3]\n",
""])]);
ARC("L2(19)","projectives",["2.L2(19)",[[10,0,1,0,0,1,1,1,0,0,
-E(19)-E(19)^4-E(19)^5-E(19)^6-E(19)^7-E(19)^9-E(19)^11-E(19)^16-E(19)^17,
-E(19)^2-E(19)^3-E(19)^8-E(19)^10-E(19)^12-E(19)^13-E(19)^14-E(19)^15-E(19)^18
 ],
[GALOIS,[1,2]],[18,0,0,-2,-2,0,0,0,0,0,-1,-1],[18,0,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,0,E(20)-E(20)^9,-E(20)^13+E(20)^17,-1,-1],
[GALOIS,[4,7]],
[GALOIS,[4,9]],
[GALOIS,[4,3]],[20,0,2,0,0,-1,-1,-1,0,0,1,1],[20,0,-1,0,0,
-E(9)^2-E(9)^4-E(9)^5-E(9)^7,E(9)^2+E(9)^7,E(9)^4+E(9)^5,0,0,1,1],
[GALOIS,[9,4]],
[GALOIS,[9,2]]],]);
ARC("L2(19)","isSimple",true);
ARC("L2(19)","extInfo",["2","2"]);
ARC("L2(19)","tomfusion",rec(name:="L2(19)",map:=[1,2,3,5,5,7,7,7,10,10,
13,13],text:=[
"fusion map is unique"
]));
ARC("L2(19)","maxes",["19:9","A5","A5","D20","D18"]);
ALF("L2(19)","L2(19).2",[1,2,3,4,5,6,7,8,9,10,11,11],[
"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(19)","J3",[1,2,4,6,7,11,12,10,13,14,20,21],[
"fusion map determined by the decomposition of the irreducible module of\n",
"dimension 110 in characteristic 19;\n",
"note that the ambiguity arises only from the Brauer tables,\n",
"the ordinary tables alone yield uniqueness up to table automorphisms;\n",
"the fusion map on the CAS table is not compatible with all Brauer tables"
]);
ALN("L2(19)",["A1(19)","U2(19)","S2(19)","O3(19)","psl(2,19)","L2(19).2M1"]);

MOT("L2(19).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,19],\n",
"constructions: Aut(L2(19))"
],
[6840,40,18,20,20,18,18,18,20,20,19,36,20,18,18,18,18,20,20,20,20],
[,[1,1,3,5,4,7,8,6,5,4,11,1,2,3,7,8,6,10,9,10,9],[1,2,1,5,4,3,3,3,10,9,11,12,
13,12,14,14,14,19,20,21,18],,[1,2,3,1,1,8,6,7,2,2,11,12,13,14,17,15,16,13,13,
13,13],,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,20,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1],[18,2,0,-2,-2,0,0,0,2,2,-1,0,0,0,0,0,0,0,0,0,0],[18,-2,
0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,0,2,0,0,0,
0,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3],
[TENSOR,[4,2]],
[GALOIS,[4,2]],
[TENSOR,[6,2]],[18,2,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,-1,0,0,0,0,0,0,E(20)-E(20)^9,-E(20)^13+E(20)^17,-E(20)+E(20)^9,
E(20)^13-E(20)^17],
[TENSOR,[8,2]],
[GALOIS,[8,7]],
[TENSOR,[10,2]],[19,-1,1,-1,-1,1,1,1,-1,-1,0,1,-1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[12,2]],[20,0,2,0,0,-1,-1,-1,0,0,1,2,0,2,-1,-1,-1,0,0,0,0],
[TENSOR,[14,2]],[20,0,-1,0,0,-E(9)^2-E(9)^4-E(9)^5-E(9)^7,E(9)^2+E(9)^7,
E(9)^4+E(9)^5,0,0,1,2,0,-1,-E(9)^2-E(9)^4-E(9)^5-E(9)^7,E(9)^2+E(9)^7,
E(9)^4+E(9)^5,0,0,0,0],
[TENSOR,[16,2]],
[GALOIS,[16,4]],
[TENSOR,[18,2]],
[GALOIS,[16,2]],
[TENSOR,[20,2]]],
[(18,20)(19,21),( 6, 7, 8)(15,16,17),( 4, 5)( 9,10)(18,19,20,21),( 4, 5)
( 9,10)(18,21,20,19)]);
ARC("L2(19).2","CAS",[rec(name:="pgl(2,19)",
permchars:=(),
permclasses:=(),
text:=[
"names:=     pgl[2,19]\n",
"   order:     2^3.3^2.5.19 = 6,840\n",
"   number of classes: 21\n",
"   source:    private communication of atlas compound table\n",
"              from cambridge 1980/81\n",
"   test:      orth.1, minus, sym[3]\n",
""])]);
ARC("L2(19).2","projectives",["2.L2(19).2",[[20,0,2,0,0,2,2,2,0,0,1,0,0,0,0,0,
0,0,0,0,0],[18,0,0,-2,-2,0,0,0,0,0,-1,0,E(8)-E(8)^3,0,0,0,0,E(8)-E(8)^3,
E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3],[18,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,
0,E(20)-E(20)^9,-E(20)^13+E(20)^17,-1,0,E(8)-E(8)^3,0,0,0,0,-E(40)^23+E(40)^37
 ,E(40)^29-E(40)^31,-E(40)^7+E(40)^13,E(40)^21-E(40)^39],
[GALOIS,[3,7]],
[GALOIS,[3,9]],
[GALOIS,[3,17]],[20,0,2,0,0,-1,-1,-1,0,0,1,0,0,0,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11,-E(12)^7+E(12)^11,0,0,0,0],[20,0,-1,0,0,
-E(9)^2-E(9)^4-E(9)^5-E(9)^7,E(9)^2+E(9)^7,E(9)^4+E(9)^5,0,0,1,0,0,
-E(12)^7+E(12)^11,-E(36)+E(36)^17-E(36)^25+E(36)^29,E(36)-E(36)^17,
E(36)^25-E(36)^29,0,0,0,0],
[GALOIS,[8,13]],
[GALOIS,[8,11]]],]);
ALF("L2(19).2","Th",[1,2,4,8,8,17,17,17,18,18,29,2,7,11,28,28,28,30,30,30,
30],[
"fusion map is unique"
]);
ALF("L2(19).2","M",[1,3,5,12,12,28,28,28,33,33,63,3,9,17,62,62,62,69,69,
69,69],[
"fusion determined uniquely by the fact that the group contains 20F and\n",
"18E elements"
]);
ALN("L2(19).2",["pgl(2,19)"]);

MOT("L2(23)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,23]"
],
[6072,24,12,12,12,11,11,11,11,11,12,12,23,23],
[,[1,1,3,2,3,8,9,10,6,7,5,5,13,14],[1,2,1,4,2,7,8,9,10,6,4,4,13,14],,,,,,,,[1,
2,3,4,5,1,1,1,1,1,11,12,14,13],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[11,-1,-1,1,-1,0,0,0,0,0,1,1,
E(23)+E(23)^2+E(23)^3+E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13
 +E(23)^16+E(23)^18,E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15
 +E(23)^17+E(23)^19+E(23)^20+E(23)^21+E(23)^22],
[GALOIS,[2,5]],[22,-2,1,-2,1,0,0,0,0,0,1,1,-1,-1],[22,2,-2,0,2,0,0,0,0,0,0,0,
-1,-1],[22,-2,1,2,1,0,0,0,0,0,-1,-1,-1,-1],[22,2,1,0,-1,0,0,0,0,0,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11,-1,-1],
[GALOIS,[7,5]],[23,-1,-1,-1,-1,1,1,1,1,1,-1,-1,0,0],[24,0,0,0,0,
E(11)+E(11)^10,E(11)^3+E(11)^8,E(11)^2+E(11)^9,E(11)^5+E(11)^6,
E(11)^4+E(11)^7,0,0,1,1],
[GALOIS,[10,4]],
[GALOIS,[10,5]],
[GALOIS,[10,2]],
[GALOIS,[10,3]]],
[(13,14),(11,12),( 6, 8,10, 7, 9)]);
ARC("L2(23)","CAS",[rec(name:="psl(2,23)",
permchars:=(),
permclasses:=(),
text:=[
"names:=     psl[2,23]; psu[2,23], psp[2,23], pom[3,23]\n",
"               a1[23]    2a1[23]     c1[23]     b1[23]    [lie-not.]\n",
"   order:     2^3.3.11.23 = 6,072\n",
"   number of classes: 14\n",
"   source:    private communication of atlas compound table\n",
"              from cambridge 1980/81\n",
"   test:      orth.1, minus, sym[3]\n",
""])]);
ARC("L2(23)","projectives",["2.L2(23)",[[12,0,0,0,0,1,1,1,1,1,0,0,
-E(23)-E(23)^2-E(23)^3-E(23)^4-E(23)^6-E(23)^8-E(23)^9-E(23)^12-E(23)^13
 -E(23)^16-E(23)^18,-E(23)^5-E(23)^7-E(23)^10-E(23)^11-E(23)^14-E(23)^15
 -E(23)^17-E(23)^19-E(23)^20-E(23)^21-E(23)^22],
[GALOIS,[1,5]],[22,0,-2,E(8)-E(8)^3,0,0,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3,-1,
-1],
[GALOIS,[3,3]],[22,0,1,-E(8)+E(8)^3,E(12)^7-E(12)^11,0,0,0,0,0,E(24)-E(24)^11,
E(24)^17-E(24)^19,-1,-1],
[GALOIS,[5,7]],
[GALOIS,[5,11]],
[GALOIS,[5,5]],[24,0,0,0,0,E(11)+E(11)^10,E(11)^3+E(11)^8,E(11)^2+E(11)^9,
E(11)^5+E(11)^6,E(11)^4+E(11)^7,0,0,1,1],
[GALOIS,[9,4]],
[GALOIS,[9,5]],
[GALOIS,[9,2]],
[GALOIS,[9,3]]],]);
ARC("L2(23)","isSimple",true);
ARC("L2(23)","extInfo",["2","2"]);
ARC("L2(23)","tomfusion",rec(name:="L2(23)",map:=[1,2,3,4,7,11,11,11,11,
11,12,12,18,18],text:=[
"fusion map is unique"
]));
ARC("L2(23)","maxes",["23:11","s4","s4","D24","D22"]);
ALF("L2(23)","Fi23",[1,4,8,12,28,41,41,41,41,41,56,56,80,81],[
"fusion map is unique up to table automorphisms"
]);
ALF("L2(23)","L2(23).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,13],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("L2(23)","M24",[1,3,5,8,11,16,16,16,16,16,18,18,25,26],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("L2(23)",["psl(2,23)"]);

MOT("L2(23).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,23],\n",
"constructions: Aut(L2(23))"
],
[12144,48,24,24,24,22,22,22,22,22,24,24,23,44,24,24,22,22,22,22,22,24,24,24,
24],
[,[1,1,3,2,3,8,9,10,6,7,5,5,13,1,4,4,8,9,10,6,7,12,11,12,11],[1,2,1,4,2,7,8,9,
10,6,4,4,13,14,16,15,18,19,20,21,17,16,16,15,15],,,,,,,,[1,2,3,4,5,1,1,1,1,1,
11,12,13,14,16,15,14,14,14,14,14,24,25,22,23],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,
10,11,12,1,14,15,16,17,18,19,20,21,22,23,24,25]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,
1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[22,-2,-2,2,-2,0,0,0,0,0,2,2,-1,0,0,0,
0,0,0,0,0,0,0,0,0],[22,-2,1,-2,1,0,0,0,0,0,1,1,-1,0,2,2,0,0,0,0,0,-1,-1,-1,
-1],
[TENSOR,[4,2]],[22,2,-2,0,2,0,0,0,0,0,0,0,-1,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,
0,0,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3],
[TENSOR,[6,2]],[22,-2,1,2,1,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,E(12)^7-E(12)^11],
[TENSOR,[8,2]],[22,2,1,0,-1,0,0,0,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,-1,0,
-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,0,0,E(24)-E(24)^11,E(24)^17-E(24)^19,
-E(24)+E(24)^11,-E(24)^17+E(24)^19],
[TENSOR,[10,2]],
[GALOIS,[10,7]],
[TENSOR,[12,2]],[23,-1,-1,-1,-1,1,1,1,1,1,-1,-1,0,1,-1,-1,1,1,1,1,1,-1,-1,-1,
-1],
[TENSOR,[14,2]],[24,0,0,0,0,E(11)+E(11)^10,E(11)^3+E(11)^8,E(11)^2+E(11)^9,
E(11)^5+E(11)^6,E(11)^4+E(11)^7,0,0,1,2,0,0,E(11)+E(11)^10,E(11)^3+E(11)^8,
E(11)^2+E(11)^9,E(11)^5+E(11)^6,E(11)^4+E(11)^7,0,0,0,0],
[TENSOR,[16,2]],
[GALOIS,[16,4]],
[TENSOR,[18,2]],
[GALOIS,[16,5]],
[TENSOR,[20,2]],
[GALOIS,[16,2]],
[TENSOR,[22,2]],
[GALOIS,[16,3]],
[TENSOR,[24,2]]],
[(15,16)(22,24)(23,25),(11,12)(22,23)(24,25),(11,12)(15,16)(22,25)(23,24),
( 6, 8,10, 7, 9)(17,19,21,18,20),( 6,10, 9, 8, 7)(17,21,20,19,18)]);
ARC("L2(23).2","CAS",[rec(name:="pgl(2,23)",
permchars:=( 3, 8, 4, 6, 5,10, 9,12)( 7,11)(14,15)(16,25,18,19,22,17)(20,21)
(23,24),
permclasses:=( 7, 8)( 9,10)(17,21,18,19,20)(22,23,25),
text:=[
"names:=     psl[2,17]\n",
"   order:     2^4.3^2.17 = 2,448\n",
"   number of classes: 11\n",
"   source:    private communication of atlas compound table\n",
"              from cambridge 1980/81\n",
"   test:      orth.1, minus, sym[3]\n",
""])]);
ARC("L2(23).2","projectives",["2.L2(23).2",[[24,0,0,0,0,2,2,2,2,2,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0],[22,0,-2,E(8)-E(8)^3,0,0,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3,
-1,0,E(16)-E(16)^7,E(16)^3-E(16)^5,0,0,0,0,0,E(16)-E(16)^7,E(16)-E(16)^7,
E(16)^3-E(16)^5,E(16)^3-E(16)^5],
[GALOIS,[2,5]],[22,0,1,-E(8)+E(8)^3,E(12)^7-E(12)^11,0,0,0,0,0,E(24)-E(24)^11,
E(24)^17-E(24)^19,-1,0,-E(16)^3+E(16)^5,E(16)-E(16)^7,0,0,0,0,0,
E(48)^31-E(48)^41,-E(48)^25+E(48)^47,-E(48)^5+E(48)^19,E(48)^35-E(48)^37],
[GALOIS,[4,17]],
[GALOIS,[4,11]],
[GALOIS,[4,5]],[24,0,0,0,0,E(11)+E(11)^10,E(11)^3+E(11)^8,E(11)^2+E(11)^9,
E(11)^5+E(11)^6,E(11)^4+E(11)^7,0,0,1,0,0,0,E(44)^7-E(44)^15,
-E(44)^23+E(44)^43,-E(44)^3+E(44)^19,-E(44)^31+E(44)^35,-E(44)^27+E(44)^39,0,
0,0,0],
[GALOIS,[8,7]],
[GALOIS,[8,5]],
[GALOIS,[8,9]],
[GALOIS,[8,19]]],]);
ALF("L2(23).2","J4",[1,2,4,6,10,20,20,20,20,20,22,22,36,3,15,15,35,35,35,
35,35,37,38,37,38],[
"fusion map is unique up to table autom. (use structure constants)\n",
"the representative is equal to that on the CAS table"
]);
ALN("L2(23).2",["pgl(2,23)"]);

MOT("L2(25)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"
],
[7800,24,12,12,25,25,12,12,12,13,13,13,13,13,13],
[,[1,1,3,2,5,6,3,7,7,15,14,11,10,13,12],[1,2,1,4,5,6,2,4,4,14,15,10,11,12,
13],,[1,2,3,4,1,1,7,9,8,11,10,13,12,15,14],,,,,,,,[1,2,3,4,5,6,7,8,9,1,1,1,1,
1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[13,1,1,-1,3,-2,1,-1,-1,0,0,0,0,0,0],[13,1,1,
-1,-2,3,1,-1,-1,0,0,0,0,0,0],[24,0,0,0,-1,-1,0,0,0,-E(13)-E(13)^12,
-E(13)^5-E(13)^8,-E(13)^4-E(13)^9,-E(13)^6-E(13)^7,-E(13)^3-E(13)^10,
-E(13)^2-E(13)^11],
[GALOIS,[4,5]],
[GALOIS,[4,3]],
[GALOIS,[4,2]],
[GALOIS,[4,4]],
[GALOIS,[4,6]],[25,1,1,1,0,0,1,1,1,-1,-1,-1,-1,-1,-1],[26,2,-1,2,1,1,-1,-1,-1,
0,0,0,0,0,0],[26,-2,2,0,1,1,-2,0,0,0,0,0,0,0,0],[26,2,-1,-2,1,1,-1,1,1,0,0,0,
0,0,0],[26,-2,-1,0,1,1,1,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,0,0,0,0,0,0],
[GALOIS,[14,5]]],
[(10,15,12,11,14,13),(8,9),(5,6),(10,11)(12,13)(14,15),(10,14,12)(11,15,13)]);
ARC("L2(25)","CAS",[rec(name:="psl(2,25)",
permchars:=(),
permclasses:=(),
text:=[
"names:=    psl[2,25] = psu[2,25] = psp[2,25] = po[3,25]\n",
"            = a1[25]  = 2 a1[25]  = c1[25]    = b1[25]\n",
" order:      7,800  =  2^3 . 3 . 5^2 . 13\n",
" number of classes:  15\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(25)","projectives",["2.L2(25)",[[12,0,0,0,-3,2,0,0,0,-1,-1,-1,-1,-1,
-1],[12,0,0,0,2,-3,0,0,0,-1,-1,-1,-1,-1,-1],[24,0,0,0,-1,-1,0,0,0,
-E(13)-E(13)^12,-E(13)^5-E(13)^8,-E(13)^4-E(13)^9,-E(13)^6-E(13)^7,
-E(13)^3-E(13)^10,-E(13)^2-E(13)^11],
[GALOIS,[3,5]],
[GALOIS,[3,3]],
[GALOIS,[3,2]],
[GALOIS,[3,4]],
[GALOIS,[3,6]],[26,0,2,E(8)-E(8)^3,1,1,0,E(8)-E(8)^3,E(8)-E(8)^3,0,0,0,0,0,0],
[GALOIS,[9,3]],[26,0,-1,E(8)-E(8)^3,1,1,E(12)^7-E(12)^11,-E(24)+E(24)^11,
-E(24)^17+E(24)^19,0,0,0,0,0,0],
[GALOIS,[11,5]],
[GALOIS,[11,11]],
[GALOIS,[11,7]]],]);
ARC("L2(25)","isSimple",true);
ARC("L2(25)","extInfo",["2","2^2"]);
ARC("L2(25)","tomfusion",rec(name:="L2(25)",map:=[1,2,3,4,8,7,9,17,17,20,
20,20,20,20,20],text:=[
"fusion map is unique up to table autom., compatible with `Maxes'"
]));
ARC("L2(25)","maxes",["5^2:12","A5.2","L2(25)M3","D26","D24"]);
ALF("L2(25)","L2(25).2_1",[1,2,3,4,5,5,6,7,8,9,10,11,12,13,14],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L2(25)","L2(25).2_2",[1,2,3,4,5,6,7,8,8,9,9,10,10,11,11],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L2(25)","L2(25).2_3",[1,2,3,4,5,5,6,7,7,8,8,9,9,10,10],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("L2(25)","Suz",[1,3,6,10,11,12,17,30,30,32,33,32,33,32,33],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L2(25)","2F4(2)'",[1,3,4,5,8,8,9,15,16,17,18,17,18,17,18],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("L2(25)",["psl(2,25)"]);

MOT("L2(25).2^2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\n",
"constructions: Aut(L2(25)), PGammaL(2,25)"
],
[31200,96,48,48,50,48,24,26,26,26,104,24,24,24,26,26,26,240,16,12,10,24,8,12],
[,[1,1,3,2,5,3,6,10,8,9,1,4,7,7,10,8,9,1,2,3,5,2,4,6],[1,2,1,4,5,2,4,10,8,9,
11,12,12,12,17,15,16,18,19,18,21,22,23,22],,[1,2,3,4,1,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,18,22,23,24],,,,,,,,[1,2,3,4,5,6,7,1,1,1,11,12,14,13,11,11,
11,18,19,20,21,22,23,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,
1,-1,-1,-1],
[TENSOR,[2,3]],[26,2,2,-2,1,2,-2,0,0,0,0,0,0,0,0,0,0,6,-2,0,1,0,0,0],
[TENSOR,[5,2]],[48,0,0,0,-2,0,0,-E(13)-E(13)^5-E(13)^8-E(13)^12,
-E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,4,0,0,0,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,0,0,0,0,0,0,0],
[TENSOR,[7,3]],
[GALOIS,[7,2]],
[TENSOR,[9,3]],
[GALOIS,[7,4]],
[TENSOR,[11,3]],[25,1,1,1,0,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,5,1,-1,0,-1,1,-1],
[TENSOR,[13,2]],
[TENSOR,[13,3]],
[TENSOR,[13,4]],[26,2,-1,2,1,-1,-1,0,0,0,0,2,-1,-1,0,0,0,4,0,1,-1,-2,0,1],
[TENSOR,[17,2]],
[TENSOR,[17,3]],
[TENSOR,[17,4]],[52,-4,4,0,2,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[52,4,-2,
-4,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[52,-4,-2,0,2,2,0,0,0,0,0,0,
-E(24)+E(24)^11+E(24)^17-E(24)^19,E(24)-E(24)^11-E(24)^17+E(24)^19,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[23,3]]],
[(13,14),( 8,10, 9)(15,17,16)]);
ARC("L2(25).2^2","CAS",[rec(name:="psl(2,25).2^2",
permclasses:=(15,17,16),
permchars:=(),
text:=[
"origin: CAS library,\n",
"maximal subgroup of sporadic simple Rudvalis group Ru,\n",
"source: received from S.Mattarei\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ALF("L2(25).2^2","Ru",[1,2,4,5,9,11,18,20,20,20,3,13,30,31,33,32,34,2,8,
11,16,6,13,19],[
"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"
]);
ALN("L2(25).2^2",["L2(25).V4","psl(2,25).2^2"]);

MOT("L2(25).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\n",
"constructions: PGL(2,25)"
],
[15600,48,24,24,25,24,24,24,26,26,26,26,26,26,52,24,24,24,24,24,24,26,26,26,
26,26,26],
[,[1,1,3,2,5,3,6,6,14,13,10,9,12,11,1,4,4,8,7,8,7,14,13,10,9,12,11],[1,2,1,4,
5,2,4,4,13,14,9,10,11,12,15,17,16,17,16,16,17,26,27,22,23,24,25],,[1,2,3,4,1,
6,8,7,10,9,12,11,14,13,15,17,16,19,18,21,20,23,22,25,24,27,26],,,,,,,,[1,2,3,
4,5,6,7,8,1,1,1,1,1,1,15,17,16,20,21,18,19,15,15,15,15,15,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,
1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[26,2,2,-2,1,2,-2,-2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,0,0,0,-1,0,0,0,-E(13)-E(13)^12,
-E(13)^5-E(13)^8,-E(13)^4-E(13)^9,-E(13)^6-E(13)^7,-E(13)^3-E(13)^10,
-E(13)^2-E(13)^11,2,0,0,0,0,0,0,E(13)+E(13)^12,E(13)^5+E(13)^8,
E(13)^4+E(13)^9,E(13)^6+E(13)^7,E(13)^3+E(13)^10,E(13)^2+E(13)^11],
[TENSOR,[4,2]],
[GALOIS,[4,5]],
[TENSOR,[6,2]],
[GALOIS,[4,3]],
[TENSOR,[8,2]],
[GALOIS,[4,2]],
[TENSOR,[10,2]],
[GALOIS,[4,4]],
[TENSOR,[12,2]],
[GALOIS,[4,6]],
[TENSOR,[14,2]],[25,1,1,1,0,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1],
[TENSOR,[16,2]],[26,2,-1,2,1,-1,-1,-1,0,0,0,0,0,0,0,2,2,-1,-1,-1,-1,0,0,0,0,0,
0],
[TENSOR,[18,2]],[26,-2,2,0,1,-2,0,0,0,0,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,
E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,0,0,0],
[TENSOR,[20,2]],[26,2,-1,-2,1,-1,1,1,0,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,0,0,0,0,0],
[TENSOR,[22,2]],[26,-2,-1,0,1,1,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,0,0,0,0,0,
0,0,-E(8)+E(8)^3,E(8)-E(8)^3,E(24)-E(24)^11,-E(24)^17+E(24)^19,
-E(24)+E(24)^11,E(24)^17-E(24)^19,0,0,0,0,0,0],
[TENSOR,[24,2]],
[GALOIS,[24,5]],
[TENSOR,[26,2]]],
[(16,17)(18,20)(19,21),( 9,14,11,10,13,12)(22,27,24,23,26,25),( 7, 8)(18,21)
(19,20),( 7, 8)(16,17)(18,19)(20,21),( 9,10)(11,12)(13,14)(22,23)(24,25)
(26,27),( 9,13,11)(10,14,12)(22,26,24)(23,27,25)]);
ARC("L2(25).2_1","CAS",[rec(name:="pgl(2,25)",
permchars:=( 5,15,11, 7)( 6,10,14, 8)( 9,13)(22,23)(24,27)(25,26),
permclasses:=(13,14)(18,21,19)(22,27,25)(23,26,24),
text:=[
"names:=    pgl[2,25]\n",
" order:      15,600  =  2^4 . 3 . 5^2 . 13\n",
" number of classes:  18\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" comments:   extension of psl[2,25] with an outer\n",
"            automorphism of order 2\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(25).2_1","projectives",["2.L2(25).2_1",[[24,0,0,0,-1,0,0,0,-2,-2,-2,
-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,0,0,0,-1,0,0,0,-E(13)-E(13)^12,
-E(13)^5-E(13)^8,-E(13)^4-E(13)^9,-E(13)^6-E(13)^7,-E(13)^3-E(13)^10,
-E(13)^2-E(13)^11,0,0,0,0,0,0,0,E(52)^9-E(52)^17,-E(52)^33+E(52)^45,
E(52)^29-E(52)^49,-E(52)^37+E(52)^41,E(52)-E(52)^25,E(52)^5-E(52)^21],
[GALOIS,[2,21]],
[GALOIS,[2,23]],
[GALOIS,[2,15]],
[GALOIS,[2,9]],
[GALOIS,[2,19]],[26,0,2,E(8)-E(8)^3,1,0,E(8)-E(8)^3,E(8)-E(8)^3,0,0,0,0,0,0,0,
E(16)-E(16)^7,-E(16)^3+E(16)^5,E(16)-E(16)^7,-E(16)^3+E(16)^5,-E(16)^3+E(16)^5
 ,E(16)-E(16)^7,0,0,0,0,0,0],
[GALOIS,[8,3]],[26,0,-1,E(8)-E(8)^3,1,E(12)^7-E(12)^11,-E(24)+E(24)^11,
-E(24)^17+E(24)^19,0,0,0,0,0,0,0,E(16)-E(16)^7,-E(16)^3+E(16)^5,
-E(48)^5+E(48)^19,-E(48)^25+E(48)^47,E(48)^31-E(48)^41,E(48)^35-E(48)^37,0,0,
0,0,0,0],
[GALOIS,[10,5]],
[GALOIS,[10,11]],
[GALOIS,[10,17]]],]);
ALF("L2(25).2_1","L2(25).2^2",[1,2,3,4,5,6,7,7,8,8,9,9,10,10,11,12,12,13,
13,14,14,15,15,16,16,17,17],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("L2(25).2_1",["pgl(2,25)","psl(2,25).2"]);

MOT("L2(25).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\n",
"constructions: PSigmaL(2,25)"
],
[15600,48,24,24,50,50,24,12,13,13,13,240,240,8,12,12,10,10],
[,[1,1,3,2,5,6,3,7,11,9,10,1,1,2,3,3,5,6],[1,2,1,4,5,6,2,4,11,9,10,12,13,14,
12,13,17,18],,[1,2,3,4,1,1,7,8,9,10,11,12,13,14,15,16,12,13],,,,,,,,[1,2,3,4,
5,6,7,8,1,1,1,12,13,14,15,16,17,18]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1],[13,1,1,-1,3,-2,1,-1,0,0,0,1,5,-1,1,-1,1,0],
[TENSOR,[3,2]],[13,1,1,-1,-2,3,1,-1,0,0,0,5,1,-1,-1,1,0,1],
[TENSOR,[5,2]],[48,0,0,0,-2,-2,0,0,-E(13)-E(13)^5-E(13)^8-E(13)^12,
-E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,0,0,0,0,0,
0,0],
[GALOIS,[7,2]],
[GALOIS,[7,4]],[25,1,1,1,0,0,1,1,-1,-1,-1,5,5,1,-1,-1,0,0],
[TENSOR,[10,2]],[26,2,-1,2,1,1,-1,-1,0,0,0,4,4,0,1,1,-1,-1],
[TENSOR,[12,2]],[26,-2,2,0,1,1,-2,0,0,0,0,6,-6,0,0,0,1,-1],
[TENSOR,[14,2]],[26,2,-1,-2,1,1,-1,1,0,0,0,4,-4,0,1,-1,-1,1],
[TENSOR,[16,2]],[52,-4,-2,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0]],
[( 9,11,10),( 5, 6)(12,13)(15,16)(17,18)]);
ARC("L2(25).2_2","projectives",["2.L2(25).2_2",[[12,0,0,0,-3,2,0,0,-1,-1,-1,0,
0,0,0,0,E(5)-E(5)^2-E(5)^3+E(5)^4,0],[12,0,0,0,2,-3,0,0,-1,-1,-1,0,0,0,0,0,0,
E(20)+E(20)^9-E(20)^13-E(20)^17],[48,0,0,0,-2,-2,0,0,-E(13)-E(13)^5-E(13)^8
 -E(13)^12,-E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)^2-E(13)^3-E(13)^10-E(13)^11
 ,0,0,0,0,0,0,0],
[GALOIS,[3,2]],
[GALOIS,[3,4]],[52,0,4,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0],[52,0,-2,0,2,2,0,
-E(24)+E(24)^11+E(24)^17-E(24)^19,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[7,7]]],]);
ARC("L2(25).2_2","tomfusion",rec(name:="L2(25).2_2",map:=[1,4,5,9,13,14,15,35,
48,48,48,3,2,12,19,18,34,31],text:=[
"unique up to table automorphisms"
]));
ALF("L2(25).2_2","L2(25).2^2",[1,2,3,4,5,5,6,7,8,9,10,18,18,19,20,20,21,
21],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("L2(25).2_2","S4(5)",[1,3,4,7,10,11,16,23,26,25,27,2,3,7,15,16,21,22],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L2(25).2_2","Suz.2",[1,3,6,10,11,12,16,28,30,30,30,38,39,41,44,45,52,
53],[
"fusion map is unique up to table automorphisms"
]);
ALF("L2(25).2_2","S12(2)",[1,10,16,49,52,53,101,252,253,253,253,6,10,49,
93,101,155,158],[
"fusion map is unique up to table automorphisms"
]);
ALN("L2(25).2_2",["S12(2)M16"]);

MOT("L2(25).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"
],
[15600,48,24,24,25,24,12,13,13,13,12,8,8,12,12],
[,[1,1,3,2,5,3,6,10,8,9,2,4,4,6,6],[1,2,1,4,5,2,4,10,8,9,11,12,13,11,11],,[1,
2,3,4,1,6,7,8,9,10,11,13,12,15,14],,,,,,,,[1,2,3,4,5,6,7,1,1,1,11,13,12,14,
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],[26,2,2,
-2,1,2,-2,0,0,0,0,0,0,0,0],[48,0,0,0,-2,0,0,-E(13)-E(13)^5-E(13)^8-E(13)^12,
-E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,0,0,0,0,
0],
[GALOIS,[4,2]],
[GALOIS,[4,4]],[25,1,1,1,0,1,1,-1,-1,-1,-1,1,1,-1,-1],
[TENSOR,[7,2]],[26,2,-1,2,1,-1,-1,0,0,0,-2,0,0,1,1],
[TENSOR,[9,2]],[26,-2,2,0,1,-2,0,0,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,0,0],
[TENSOR,[11,2]],[26,2,-1,-2,1,-1,1,0,0,0,0,0,0,E(3)-E(3)^2,-E(3)+E(3)^2],
[TENSOR,[13,2]],[52,-4,-2,0,2,2,0,0,0,0,0,0,0,0,0]],
[(14,15),(12,13),( 8,10, 9)]);
ALF("L2(25).2_3","L2(25).2^2",[1,2,3,4,5,6,7,8,9,10,22,23,23,24,24],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("L2(25).2_3","2F4(2)'.2",[1,3,4,5,8,9,14,15,15,15,20,23,23,24,25],[
"fusion map is unique up to table automorphisms"
]);

MOT("L2(27)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"
],
[9828,28,27,27,14,14,14,13,13,13,13,13,13,14,14,14],
[,[1,1,4,3,7,5,6,12,13,11,9,10,8,7,5,6],[1,2,1,1,6,7,5,9,10,8,12,13,11,15,16,
14],,,,[1,2,3,4,1,1,1,13,11,12,10,8,9,2,2,2],,,,,,[1,2,3,4,5,6,7,1,1,1,1,1,1,
14,15,16]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[13,1,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,-1,-1,
-1,0,0,0,0,0,0,1,1,1],
[GALOIS,[2,2]],[26,-2,-1,-1,-E(7)-E(7)^6,-E(7)^3-E(7)^4,-E(7)^2-E(7)^5,0,0,0,
0,0,0,-E(7)-E(7)^6,-E(7)^3-E(7)^4,-E(7)^2-E(7)^5],
[GALOIS,[4,2]],
[GALOIS,[4,3]],[26,2,-1,-1,-E(7)-E(7)^6,-E(7)^3-E(7)^4,-E(7)^2-E(7)^5,0,0,0,0,
0,0,E(7)+E(7)^6,E(7)^3+E(7)^4,E(7)^2+E(7)^5],
[GALOIS,[7,2]],
[GALOIS,[7,3]],[27,-1,0,0,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1],[28,0,1,1,0,0,0,
E(13)+E(13)^12,E(13)^3+E(13)^10,E(13)^4+E(13)^9,E(13)^5+E(13)^8,
E(13)^2+E(13)^11,E(13)^6+E(13)^7,0,0,0],
[GALOIS,[11,4]],
[GALOIS,[11,3]],
[GALOIS,[11,5]],
[GALOIS,[11,6]],
[GALOIS,[11,2]]],
[( 8,12,10,11, 9,13),( 5, 6, 7)(14,15,16),( 5, 7, 6)(14,16,15),(3,4),
( 8,10, 9)(11,13,12),( 8,11)( 9,12)(10,13)]);
ARC("L2(27)","CAS",[rec(name:="psl(2,27)",
permchars:=(),
permclasses:=(),
text:=[
"names:=    psl[2,27] = psu[2,27] = psp[2,27] = po[3,27]\n",
"            = a1[27]  = 2 a1[27]  = c1[27]    = b1[27]  [lie-not.]\n",
" order:      9,828  =  2^2 . 3^3 . 7 . 13\n",
" number of classes:  16\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(27)","projectives",["2.L2(27)",[[14,0,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,0,
0,0,1,1,1,1,1,1,0,0,0],
[GALOIS,[1,2]],[26,0,-1,-1,-2,-2,-2,0,0,0,0,0,0,0,0,0],[26,0,-1,-1,
-E(7)-E(7)^6,-E(7)^3-E(7)^4,-E(7)^2-E(7)^5,0,0,0,0,0,0,-E(28)^3+E(28)^11,
-E(28)^19+E(28)^23,E(28)^15-E(28)^27],
[GALOIS,[4,9]],
[GALOIS,[4,3]],
[GALOIS,[4,13]],
[GALOIS,[4,5]],
[GALOIS,[4,11]],[28,0,1,1,0,0,0,E(13)+E(13)^12,E(13)^3+E(13)^10,
E(13)^4+E(13)^9,E(13)^5+E(13)^8,E(13)^2+E(13)^11,E(13)^6+E(13)^7,0,0,0],
[GALOIS,[10,4]],
[GALOIS,[10,3]],
[GALOIS,[10,5]],
[GALOIS,[10,6]],
[GALOIS,[10,2]]],]);
ARC("L2(27)","isSimple",true);
ARC("L2(27)","extInfo",["2","6"]);
ARC("L2(27)","tomfusion",rec(name:="L2(27)",map:=[1,2,3,3,5,5,5,8,8,8,8,8,
8,9,9,9],text:=[
"fusion map is unique"
]));
ARC("L2(27)","maxes",["3^3:13","D28","D26","a4"]);
ALF("L2(27)","L2(27).2",[1,2,3,3,4,5,6,7,8,9,10,11,12,13,14,15],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L2(27)","L2(27).3",[1,2,3,4,5,5,5,6,6,6,7,7,7,8,8,8],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L2(27)","L2(27).6",[1,2,3,3,4,4,4,5,5,5,6,6,6,7,7,7],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("L2(27)",["psl(2,27)"]);

MOT("L2(27).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\n",
"constructions: PGL(2,27)"
],
[19656,56,27,28,28,28,26,26,26,26,26,26,28,28,28,52,28,26,26,26,26,26,26,28,
28,28,28,28,28],
[,[1,1,3,6,4,5,11,12,10,8,9,7,6,4,5,1,2,11,12,10,8,9,7,15,13,14,15,13,14],[1,
2,1,5,6,4,8,9,7,11,12,10,14,15,13,16,17,19,20,18,22,23,21,25,26,24,28,29,
27],,,,[1,2,3,1,1,1,12,10,11,9,7,8,2,2,2,16,17,23,21,22,20,18,19,17,17,17,17,
17,17],,,,,,[1,2,3,4,5,6,1,1,1,1,1,1,13,14,15,16,17,16,16,16,16,16,16,27,28,
29,24,25,26]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[26,2,-1,-2,-2,-2,0,
0,0,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[26,-2,-1,-E(7)-E(7)^6,
-E(7)^3-E(7)^4,-E(7)^2-E(7)^5,0,0,0,0,0,0,-E(7)-E(7)^6,-E(7)^3-E(7)^4,
-E(7)^2-E(7)^5,0,2,0,0,0,0,0,0,E(7)+E(7)^6,E(7)^3+E(7)^4,E(7)^2+E(7)^5,
E(7)+E(7)^6,E(7)^3+E(7)^4,E(7)^2+E(7)^5],
[TENSOR,[4,2]],
[GALOIS,[4,2]],
[TENSOR,[6,2]],
[GALOIS,[4,3]],
[TENSOR,[8,2]],[26,2,-1,-E(7)-E(7)^6,-E(7)^3-E(7)^4,-E(7)^2-E(7)^5,0,0,0,0,0,
0,E(7)+E(7)^6,E(7)^3+E(7)^4,E(7)^2+E(7)^5,0,0,0,0,0,0,0,0,E(28)^3-E(28)^11,
E(28)^19-E(28)^23,-E(28)^15+E(28)^27,-E(28)^3+E(28)^11,-E(28)^19+E(28)^23,
E(28)^15-E(28)^27],
[TENSOR,[10,2]],
[GALOIS,[10,9]],
[TENSOR,[12,2]],
[GALOIS,[10,3]],
[TENSOR,[14,2]],[27,-1,0,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1],
[TENSOR,[16,2]],[28,0,1,0,0,0,E(13)+E(13)^12,E(13)^3+E(13)^10,E(13)^4+E(13)^9,
E(13)^5+E(13)^8,E(13)^2+E(13)^11,E(13)^6+E(13)^7,0,0,0,2,0,E(13)+E(13)^12,
E(13)^3+E(13)^10,E(13)^4+E(13)^9,E(13)^5+E(13)^8,E(13)^2+E(13)^11,
E(13)^6+E(13)^7,0,0,0,0,0,0],
[TENSOR,[18,2]],
[GALOIS,[18,4]],
[TENSOR,[20,2]],
[GALOIS,[18,3]],
[TENSOR,[22,2]],
[GALOIS,[18,5]],
[TENSOR,[24,2]],
[GALOIS,[18,6]],
[TENSOR,[26,2]],
[GALOIS,[18,2]],
[TENSOR,[28,2]]],
[(24,27)(25,28)(26,29),( 7,11, 9,10, 8,12)(18,22,20,21,19,23),( 4, 5, 6)
(13,14,15)(24,28,26,27,25,29),( 7, 9, 8)(10,12,11)(18,20,19)(21,23,22),( 7,10)
( 8,11)( 9,12)(18,21)(19,22)(20,23)]);
ARC("L2(27).2","CAS",[rec(name:="psl(2,27).2",
permchars:=(),
permclasses:=(),
text:=[
"names:=    psl[2,27].2\n",
" order:      19,656  =  2^3 . 3^3 . 7 . 13\n",
" number of classes:  29\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" comments:   extension of psl[2,27] with an outer\n",
"            automorphism of order 2\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(27).2","projectives",["2.L2(27).2",[[28,0,1,0,0,0,2,2,2,2,2,2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[26,0,-1,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,E(8)-E(8)^3,
0,0,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,
E(8)-E(8)^3],[26,0,-1,-E(7)-E(7)^6,-E(7)^3-E(7)^4,-E(7)^2-E(7)^5,0,0,0,0,0,0,
-E(28)^3+E(28)^11,-E(28)^19+E(28)^23,E(28)^15-E(28)^27,0,E(8)-E(8)^3,0,0,0,0,
0,0,-E(56)^29+E(56)^55,E(56)^31-E(56)^53,-E(56)^37+E(56)^47,-E(56)^13+E(56)^15
 ,E(56)^39-E(56)^45,-E(56)^5+E(56)^23],
[GALOIS,[3,9]],
[GALOIS,[3,25]],
[GALOIS,[3,15]],
[GALOIS,[3,23]],
[GALOIS,[3,17]],[28,0,1,0,0,0,E(13)+E(13)^12,E(13)^3+E(13)^10,E(13)^4+E(13)^9,
E(13)^5+E(13)^8,E(13)^2+E(13)^11,E(13)^6+E(13)^7,0,0,0,0,0,E(52)^9-E(52)^17,
E(52)-E(52)^25,E(52)^29-E(52)^49,-E(52)^33+E(52)^45,E(52)^5-E(52)^21,
-E(52)^37+E(52)^41,0,0,0,0,0,0],
[GALOIS,[9,9]],
[GALOIS,[9,23]],
[GALOIS,[9,21]],
[GALOIS,[9,19]],
[GALOIS,[9,15]]],]);
ALF("L2(27).2","L2(27).6",[1,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,9,10,10,10,11,
11,11,12,12,12,13,13,13],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("L2(27).2",["psl(2,27).2"]);

MOT("L2(27).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\n",
"constructions: PSigmaL(2,27)"
],
[29484,84,81,81,14,13,13,14,36,36,12,12,9,9,9,9],
[,[1,1,4,3,5,7,6,5,10,9,10,9,14,13,16,15],[1,2,1,1,5,6,7,8,1,1,2,2,3,4,4,
3],,,,[1,2,3,4,1,7,6,2,9,10,11,12,13,14,15,16],,,,,,[1,2,3,4,5,1,1,8,9,10,11,
12,13,14,15,16]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,
E(3),E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[13,1,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,-1,0,0,1,1,1,1,1,E(3)^2,
E(3),E(3),E(3)^2],
[TENSOR,[4,2]],
[TENSOR,[4,3]],
[GALOIS,[4,2]],
[TENSOR,[7,2]],
[TENSOR,[7,3]],[78,-6,-3,-3,1,0,0,1,0,0,0,0,0,0,0,0],[78,6,-3,-3,1,0,0,-1,0,0,
0,0,0,0,0,0],[27,-1,0,0,-1,1,1,-1,3,3,-1,-1,0,0,0,0],
[TENSOR,[12,2]],
[TENSOR,[12,3]],[84,0,3,3,0,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)^11,0,0,0,0,0,0,0,0,0],
[GALOIS,[15,2]]],
[(6,7),( 3, 4)( 9,10)(11,12)(13,14)(15,16),( 9,10)(11,12)(13,16)(14,15)]);
ARC("L2(27).3","CAS",[rec(name:="psl(2,27).3",
permchars:=(),
permclasses:=(13,15)(14,16),
text:=[
"names:=    psl[2,27].3\n",
" order:      29,484  =  2^2 . 3^4 . 7 . 13\n",
" number of classes:  16\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" comments:   extension of psl[2,27] with an outer\n",
"            automorphism of order 3\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(27).3","projectives",["2.L2(27).3",[[14,0,-2*E(3)+E(3)^2,
E(3)-2*E(3)^2,0,1,1,0,2,2,0,0,-E(3)^2,-E(3),-E(3),-E(3)^2],
[GALOIS,[1,2]],[26,0,-1,-1,-2,0,0,0,2,2,0,0,-1,-1,-1,-1],[78,0,-3,-3,1,0,0,
-E(28)^3+E(28)^11+E(28)^15-E(28)^19+E(28)^23-E(28)^27,0,0,0,0,0,0,0,0],
[GALOIS,[4,5]],[84,0,3,3,0,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)^11,0,0,0,0,0,0,0,0,0],
[GALOIS,[6,2]]],]);
ALF("L2(27).3","L2(27).6",[1,2,3,3,4,5,6,7,14,15,16,17,18,19,18,19],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L2(27).3","S6(3)",[1,3,8,9,31,58,57,59,10,10,30,30,40,41,41,40],[
"fusion map is unique up to table automorphisms,\n",
"compatible with Brauer tables"
]);
ALN("L2(27).3",["psl(2,27).3"]);

MOT("L2(27).6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\n",
"constructions: Aut(L2(27)), PGammaL(2,27)"
],
[58968,168,81,28,26,26,28,156,84,26,26,28,28,72,72,24,24,9,9,12,12,12,12],
[,[1,1,3,4,6,5,4,1,2,6,5,7,7,15,14,15,14,19,18,15,14,17,16],[1,2,1,4,5,6,7,8,
9,10,11,12,13,1,1,2,2,3,3,8,8,9,9],,,,[1,2,3,1,6,5,2,8,9,11,10,9,9,14,15,16,
17,18,19,20,21,22,23],,,,,,[1,2,3,4,1,1,7,8,9,8,8,13,12,14,15,16,17,18,19,20,
21,22,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,-E(3),-E(3)^2,-E(3),-E(3)^2],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],[26,2,-1,-2,0,0,2,0,0,0,0,0,0,2,2,2,2,-1,-1,0,0,0,0],
[TENSOR,[7,2]],
[TENSOR,[7,3]],[78,-6,-3,1,0,0,1,0,6,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[10,2]],[78,6,-3,1,0,0,-1,0,0,0,0,E(28)^3-E(28)^11-E(28)^15+E(28)^19
 -E(28)^23+E(28)^27,-E(28)^3+E(28)^11+E(28)^15-E(28)^19+E(28)^23-E(28)^27,0,0,
0,0,0,0,0,0,0,0],
[TENSOR,[12,2]],[27,-1,0,-1,1,1,-1,1,-1,1,1,-1,-1,3,3,-1,-1,0,0,1,1,-1,-1],
[TENSOR,[14,2]],
[TENSOR,[14,3]],
[TENSOR,[14,4]],
[TENSOR,[14,5]],
[TENSOR,[14,6]],[84,0,3,0,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)^11,0,6,0,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,
0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[20,2]],
[GALOIS,[20,2]],
[TENSOR,[22,2]]],
[(14,15)(16,17)(18,19)(20,21)(22,23),(12,13),( 5, 6)(10,11)]);
ARC("L2(27).6","projectives",["2.L2(27).6",[[28,0,1,0,2,2,0,0,0,0,0,0,0,4,4,0,
0,1,1,0,0,0,0],[26,0,-1,-2,0,0,0,0,E(8)-E(8)^3,0,0,E(8)-E(8)^3,E(8)-E(8)^3,2,
2,0,0,-1,-1,0,0,E(8)-E(8)^3,E(8)-E(8)^3],[78,0,-3,1,0,0,-E(28)^3+E(28)^11
 +E(28)^15-E(28)^19+E(28)^23-E(28)^27,0,3*E(8)-3*E(8)^3,0,0,-E(56)^29+E(56)^31
 -E(56)^37+E(56)^47-E(56)^53+E(56)^55,-E(56)^5-E(56)^13+E(56)^15+E(56)^23
 +E(56)^39-E(56)^45,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[3,15]],[84,0,3,0,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)^11,0,0,0,E(52)+E(52)^9-E(52)^17
 -E(52)^25+E(52)^29-E(52)^49,E(52)^5-E(52)^21-E(52)^33-E(52)^37+E(52)^41
 +E(52)^45,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[5,15]]],]);
ALF("L2(27).6","S6(3).2",[1,3,7,23,41,40,42,51,52,72,71,73,74,8,8,22,22,
29,29,56,56,65,65],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("L2(29)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,29]"
],
[12180,28,15,15,15,14,14,14,14,14,14,15,15,15,15,29,29],
[,[1,1,3,5,4,7,8,6,7,8,6,13,14,15,12,17,16],[1,2,1,5,4,8,6,7,11,9,10,5,4,5,4,
17,16],,[1,2,3,1,1,7,8,6,10,11,9,3,3,3,3,16,17],,[1,2,3,5,4,1,1,1,2,2,2,15,12,
13,14,16,17],,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[15,-1,0,0,0,1,1,1,-1,-1,-1,0,0,0,0,
-E(29)-E(29)^4-E(29)^5-E(29)^6-E(29)^7-E(29)^9-E(29)^13-E(29)^16-E(29)^20
 -E(29)^22-E(29)^23-E(29)^24-E(29)^25-E(29)^28,-E(29)^2-E(29)^3-E(29)^8
 -E(29)^10-E(29)^11-E(29)^12-E(29)^14-E(29)^15-E(29)^17-E(29)^18-E(29)^19
 -E(29)^21-E(29)^26-E(29)^27],
[GALOIS,[2,2]],[28,0,1,-2,-2,0,0,0,0,0,0,1,1,1,1,-1,-1],[28,0,-2,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-1,-1],
[GALOIS,[5,2]],[28,0,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,
-E(15)^7-E(15)^8,-E(15)-E(15)^14,-E(15)^2-E(15)^13,-E(15)^4-E(15)^11,-1,-1],
[GALOIS,[7,7]],
[GALOIS,[7,4]],
[GALOIS,[7,2]],[29,1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0],[30,2,0,0,0,
E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,E(7)+E(7)^6,E(7)^2+E(7)^5,
E(7)^3+E(7)^4,0,0,0,0,1,1],
[GALOIS,[12,3]],
[GALOIS,[12,2]],[30,-2,0,0,0,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,
-E(7)-E(7)^6,-E(7)^2-E(7)^5,-E(7)^3-E(7)^4,0,0,0,0,1,1],
[GALOIS,[15,3]],
[GALOIS,[15,2]]],
[(16,17),(12,14)(13,15),( 6, 8, 7)( 9,11,10),( 4, 5)(12,15,14,13)]);
ARC("L2(29)","CAS",[rec(name:="psl(2,29)",
permchars:=(),
permclasses:=(),
text:=[
"names:    psl[2,29] = psu[2,29] = psp[2,29] = po[3,29]\n",
"= a1[29]  = 2 a1[29]  = c1[29]    = b1[29]   [lie-not.]\n",
"order:      12,180  =  2^2 . 3 . 5 . 7 . 29\n",
"number of classes:  17\n",
"source:     private communication of atlas compound table\n",
"from cambridge 1980/81\n",
"test:       orth.1, min,restricted characters from ru\n",
""])]);
ARC("L2(29)","projectives",["2.L2(29)",[[14,0,-1,-1,-1,0,0,0,0,0,0,-1,-1,-1,
-1,E(29)+E(29)^4+E(29)^5+E(29)^6+E(29)^7+E(29)^9+E(29)^13+E(29)^16+E(29)^20
 +E(29)^22+E(29)^23+E(29)^24+E(29)^25+E(29)^28,E(29)^2+E(29)^3+E(29)^8
 +E(29)^10+E(29)^11+E(29)^12+E(29)^14+E(29)^15+E(29)^17+E(29)^18+E(29)^19
 +E(29)^21+E(29)^26+E(29)^27],
[GALOIS,[1,2]],[28,0,1,-2,-2,0,0,0,0,0,0,1,1,1,1,-1,-1],[28,0,-2,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-1,-1],
[GALOIS,[4,2]],[28,0,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,
-E(15)^7-E(15)^8,-E(15)-E(15)^14,-E(15)^2-E(15)^13,-E(15)^4-E(15)^11,-1,-1],
[GALOIS,[6,7]],
[GALOIS,[6,4]],
[GALOIS,[6,2]],[30,0,0,0,0,2,2,2,0,0,0,0,0,0,0,1,1],[30,0,0,0,0,E(7)+E(7)^6,
E(7)^2+E(7)^5,E(7)^3+E(7)^4,E(28)^3-E(28)^11,-E(28)^15+E(28)^27,
E(28)^19-E(28)^23,0,0,0,0,1,1],
[GALOIS,[11,3]],
[GALOIS,[11,9]],
[GALOIS,[11,13]],
[GALOIS,[11,11]],
[GALOIS,[11,5]]],]);
ARC("L2(29)","isSimple",true);
ARC("L2(29)","extInfo",["2","2"]);
ARC("L2(29)","tomfusion",rec(name:="L2(29)",map:=[1,2,3,5,5,7,7,7,10,10,
10,13,13,13,13,15,15],text:=[
"fusion map is unique"
]));
ARC("L2(29)","maxes",["29:14","A5","A5","D30","D28"]);
ALF("L2(29)","L2(29).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16],[
"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(29)","Ru",[1,3,4,10,10,12,12,12,21,23,22,24,24,24,24,35,36],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("L2(29)",["psl(2,29)","L2(29).2M1"]);

MOT("L2(29).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,29],\n",
"constructions: Aut(L2(29))"
],
[24360,56,30,30,30,28,28,28,28,28,28,30,30,30,30,29,60,28,30,30,30,28,28,28,
28,28,28,30,30,30,30],
[,[1,1,3,5,4,7,8,6,7,8,6,13,14,15,12,16,1,2,3,5,4,10,11,9,10,11,9,13,14,15,
12],[1,2,1,5,4,8,6,7,11,9,10,5,4,5,4,16,17,18,17,21,20,24,22,23,27,25,26,21,
20,21,20],,[1,2,3,1,1,7,8,6,10,11,9,3,3,3,3,16,17,18,19,17,17,26,27,25,23,24,
22,19,19,19,19],,[1,2,3,5,4,1,1,1,2,2,2,15,12,13,14,16,17,18,19,21,20,18,18,
18,18,18,18,31,28,29,30],,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,1,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]],
[[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],[30,-2,0,0,
0,2,2,2,-2,-2,-2,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[28,0,1,-2,-2,0,0,0,
0,0,0,1,1,1,1,-1,2,0,-1,2,2,0,0,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[4,2]],[28,0,-2,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,2,0,2,E(5)+E(5)^4,E(5)^2+E(5)^3,
0,0,0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3],
[TENSOR,[6,2]],
[GALOIS,[6,2]],
[TENSOR,[8,2]],[28,0,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,
-E(15)^7-E(15)^8,-E(15)-E(15)^14,-E(15)^2-E(15)^13,-E(15)^4-E(15)^11,-1,2,0,
-1,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,0,0,E(15)^7+E(15)^8,E(15)+E(15)^14,
E(15)^2+E(15)^13,E(15)^4+E(15)^11],
[TENSOR,[10,2]],
[GALOIS,[10,7]],
[TENSOR,[12,2]],
[GALOIS,[10,4]],
[TENSOR,[14,2]],
[GALOIS,[10,2]],
[TENSOR,[16,2]],[29,1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,1,-1,1,1,1,-1,-1,-1,
-1,-1,-1,1,1,1,1],
[TENSOR,[18,2]],[30,2,0,0,0,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,
E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,0,0,1,0,2,0,0,0,E(7)+E(7)^6,
E(7)^2+E(7)^5,E(7)^3+E(7)^4,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,0,0],
[TENSOR,[20,2]],
[GALOIS,[20,3]],
[TENSOR,[22,2]],
[GALOIS,[20,2]],
[TENSOR,[24,2]],[30,-2,0,0,0,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,
-E(7)-E(7)^6,-E(7)^2-E(7)^5,-E(7)^3-E(7)^4,0,0,0,0,1,0,0,0,0,0,
E(28)^3-E(28)^11,-E(28)^15+E(28)^27,E(28)^19-E(28)^23,-E(28)^3+E(28)^11,
E(28)^15-E(28)^27,-E(28)^19+E(28)^23,0,0,0,0],
[TENSOR,[26,2]],
[GALOIS,[26,3]],
[TENSOR,[28,2]],
[GALOIS,[26,9]],
[TENSOR,[30,2]]],
[(22,25)(23,26)(24,27),(12,14)(13,15)(28,30)(29,31),( 6, 8, 7)( 9,11,10)
(22,27,23,25,24,26),( 4, 5)(12,15,14,13)(20,21)(28,31,30,29),( 6, 8, 7)
( 9,11,10)(22,24,23)(25,27,26)]);
ARC("L2(29).2","CAS",[rec(name:="pgl(2,29)",
permchars:=(),
permclasses:=(),
text:=[
"names:=    pgl[2,29]\n",
" order:      24,360  =  2^3 . 3 . 5 . 7 . 29\n",
" number of classes:  31\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" comments:   extension of gl[2,29] with an outer\n",
"            automorphism of order 2\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(29).2","projectives",["2.L2(29).2",[[28,0,-2,-2,-2,0,0,0,0,0,0,-2,-2,
-2,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[28,0,1,-2,-2,0,0,0,0,0,0,1,1,1,1,-1,
0,0,-E(12)^7+E(12)^11,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11,-E(12)^7+E(12)^11],[28,0,-2,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,
0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,0,0,0,
E(20)-E(20)^9,E(20)^13-E(20)^17,0,0,0,0,0,0,E(20)-E(20)^9,E(20)^13-E(20)^17,
-E(20)+E(20)^9,-E(20)^13+E(20)^17],
[GALOIS,[3,3]],[28,0,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,
-E(15)^7-E(15)^8,-E(15)-E(15)^14,-E(15)^2-E(15)^13,-E(15)^4-E(15)^11,-1,0,0,
-E(12)^7+E(12)^11,E(20)-E(20)^9,E(20)^13-E(20)^17,0,0,0,0,0,0,
E(60)^43-E(60)^47,-E(60)^11+E(60)^19,E(60)^7-E(60)^23,E(60)^31-E(60)^59],
[GALOIS,[5,23]],
[GALOIS,[5,11]],
[GALOIS,[5,13]],[30,0,0,0,0,2,2,2,0,0,0,0,0,0,0,1,0,E(8)-E(8)^3,0,0,0,
E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,0,0,0,
0],[30,0,0,0,0,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,E(28)^3-E(28)^11,
-E(28)^15+E(28)^27,E(28)^19-E(28)^23,0,0,0,0,1,0,E(8)-E(8)^3,0,0,0,
-E(56)^29+E(56)^55,-E(56)^37+E(56)^47,E(56)^31-E(56)^53,-E(56)^13+E(56)^15,
-E(56)^5+E(56)^23,E(56)^39-E(56)^45,0,0,0,0],
[GALOIS,[10,25]],
[GALOIS,[10,9]],
[GALOIS,[10,15]],
[GALOIS,[10,17]],
[GALOIS,[10,23]]],]);
ALF("L2(29).2","M",[1,3,5,12,12,20,20,20,49,49,49,52,52,52,52,97,3,10,17,
33,33,96,96,96,96,96,96,104,104,104,104],[
"fusion determined using that the subgroup contains 28D and 30G elements"
]);
ALN("L2(29).2",["pgl(2,29)"]);

MOT("L2(31)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31]"
],
[14880,32,15,16,15,15,16,16,15,15,15,15,16,16,16,16,31,31],
[,[1,1,3,2,6,5,4,4,10,11,12,9,7,8,7,8,17,18],[1,2,1,4,6,5,8,7,6,5,6,5,14,15,
16,13,18,17],,[1,2,3,4,1,1,8,7,3,3,3,3,16,13,14,15,17,
18],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[15,-1,0,-1,0,0,-1,-1,0,0,0,0,1,1,1,1,
E(31)+E(31)^2+E(31)^4+E(31)^5+E(31)^7+E(31)^8+E(31)^9+E(31)^10+E(31)^14
 +E(31)^16+E(31)^18+E(31)^19+E(31)^20+E(31)^25+E(31)^28,
E(31)^3+E(31)^6+E(31)^11+E(31)^12+E(31)^13+E(31)^15+E(31)^17+E(31)^21+E(31)^22
 +E(31)^23+E(31)^24+E(31)^26+E(31)^27+E(31)^29+E(31)^30],
[GALOIS,[2,3]],[30,-2,0,-2,0,0,2,2,0,0,0,0,0,0,0,0,-1,-1],[30,-2,0,2,0,0,0,0,
0,0,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,-1,-1],
[GALOIS,[5,3]],[30,2,0,0,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,0,-E(16)+E(16)^7,
-E(16)^3+E(16)^5,E(16)-E(16)^7,E(16)^3-E(16)^5,-1,-1],
[GALOIS,[7,5]],
[GALOIS,[7,7]],
[GALOIS,[7,3]],[31,-1,1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0],[32,0,-1,0,2,2,
0,0,-1,-1,-1,-1,0,0,0,0,1,1],[32,0,2,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,
E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,1,1],
[GALOIS,[13,2]],[32,0,-1,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,E(15)^7+E(15)^8,
E(15)+E(15)^14,E(15)^2+E(15)^13,E(15)^4+E(15)^11,0,0,0,0,1,1],
[GALOIS,[15,7]],
[GALOIS,[15,4]],
[GALOIS,[15,2]]],
[(17,18),( 9,11)(10,12),( 7, 8)(13,16,15,14),( 5, 6)( 9,12,11,10)]);
ARC("L2(31)","CAS",[rec(name:="psl(2,31)",
permchars:=(),
permclasses:=(),
text:=[
"names:=    psl[2,31] = psu[2,31] = psp[2,31] = po[3,31]\n",
"            = a1[31]  = 2 a1[31]  = c1[31]    = b1[31]   [lie-not.]\n",
" order:      14,880  =  2^5 . 3 . 5 . 31\n",
" number of classes:  18\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(31)","projectives",["2.L2(31)",[[16,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,
-E(31)-E(31)^2-E(31)^4-E(31)^5-E(31)^7-E(31)^8-E(31)^9-E(31)^10-E(31)^14
 -E(31)^16-E(31)^18-E(31)^19-E(31)^20-E(31)^25-E(31)^28,-E(31)^3-E(31)^6
 -E(31)^11-E(31)^12-E(31)^13-E(31)^15-E(31)^17-E(31)^21-E(31)^22-E(31)^23
 -E(31)^24-E(31)^26-E(31)^27-E(31)^29-E(31)^30],
[GALOIS,[1,3]],[30,0,0,E(8)-E(8)^3,0,0,E(16)-E(16)^7,E(16)^3-E(16)^5,0,0,0,0,
E(32)-E(32)^15,E(32)^3-E(32)^13,-E(32)^7+E(32)^9,E(32)^5-E(32)^11,-1,-1],
[GALOIS,[3,11]],
[GALOIS,[3,7]],
[GALOIS,[3,13]],
[GALOIS,[3,15]],
[GALOIS,[3,5]],
[GALOIS,[3,9]],
[GALOIS,[3,3]],[32,0,-1,0,2,2,0,0,-1,-1,-1,-1,0,0,0,0,1,1],[32,0,2,0,
E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0,0,0,1,1],
[GALOIS,[12,2]],[32,0,-1,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,E(15)^7+E(15)^8,
E(15)+E(15)^14,E(15)^2+E(15)^13,E(15)^4+E(15)^11,0,0,0,0,1,1],
[GALOIS,[14,7]],
[GALOIS,[14,4]],
[GALOIS,[14,2]]],]);
ARC("L2(31)","isSimple",true);
ARC("L2(31)","extInfo",["2","2"]);
ARC("L2(31)","tomfusion",rec(name:="L2(31)",map:=[1,2,3,6,7,7,11,11,15,15,
15,15,18,18,18,18,22,22],text:=[
"fusion map is unique"
]));
ARC("L2(31)","maxes",["31:15","A5","A5","D32","D30","Symm(4)","Symm(4)"]);
ALF("L2(31)","L2(31).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,17],[
"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(31)","ON",[1,2,3,5,6,6,10,10,16,17,16,17,18,19,18,19,29,30],[
"fusion is unique up to table automorphisms"
]);
ALF("L2(31)","B",[1,5,7,15,19,19,44,44,82,82,82,82,90,90,90,90,145,146],[
"determined up to table automorphisms by the fusion of 31:15"
]);
ALN("L2(31)",["psl(2,31)"]);

MOT("L2(31).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31],\n",
"constructions: Aut(L2(31))"
],
[29760,64,30,32,30,30,32,32,30,30,30,30,32,32,32,32,31,60,30,30,30,30,30,30,
30,32,32,32,32,32,32,32,32],
[,[1,1,3,2,6,5,4,4,10,11,12,9,7,8,7,8,17,1,3,6,5,10,11,12,9,13,14,15,16,13,14,
15,16],[1,2,1,4,6,5,8,7,6,5,6,5,14,15,16,13,17,18,18,21,20,21,20,21,20,27,28,
29,30,31,32,33,26],,[1,2,3,4,1,1,8,7,3,3,3,3,16,13,14,15,17,18,19,18,18,19,19,
19,19,29,30,31,32,33,26,27,28],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,1,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[
30,-2,0,-2,0,0,-2,-2,0,0,0,0,2,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[30,
-2,0,-2,0,0,2,2,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,
E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3],
[TENSOR,[4,2]],[30,-2,0,2,0,0,0,0,0,0,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,
-E(8)+E(8)^3,E(8)-E(8)^3,-1,0,0,0,0,0,0,0,0,E(16)-E(16)^7,E(16)^3-E(16)^5,
-E(16)+E(16)^7,-E(16)^3+E(16)^5,E(16)-E(16)^7,E(16)^3-E(16)^5,-E(16)+E(16)^7,
-E(16)^3+E(16)^5],
[TENSOR,[6,2]],
[GALOIS,[6,5]],
[TENSOR,[8,2]],[30,2,0,0,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,0,-E(16)+E(16)^7,
-E(16)^3+E(16)^5,E(16)-E(16)^7,E(16)^3-E(16)^5,-1,0,0,0,0,0,0,0,0,
E(32)-E(32)^15,E(32)^3-E(32)^13,-E(32)^7+E(32)^9,E(32)^5-E(32)^11,
-E(32)+E(32)^15,-E(32)^3+E(32)^13,E(32)^7-E(32)^9,-E(32)^5+E(32)^11],
[TENSOR,[10,2]],
[GALOIS,[10,11]],
[TENSOR,[12,2]],
[GALOIS,[10,7]],
[TENSOR,[14,2]],
[GALOIS,[10,13]],
[TENSOR,[16,2]],[31,-1,1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[18,2]],[32,0,-1,0,2,2,0,0,-1,-1,-1,-1,0,0,0,0,1,2,-1,2,2,-1,-1,-1,-1,
0,0,0,0,0,0,0,0],
[TENSOR,[20,2]],[32,0,2,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,1,2,2,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,0,0,
0,0],
[TENSOR,[22,2]],
[GALOIS,[22,2]],
[TENSOR,[24,2]],[32,0,-1,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,E(15)^7+E(15)^8,
E(15)+E(15)^14,E(15)^2+E(15)^13,E(15)^4+E(15)^11,0,0,0,0,1,2,-1,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(15)^7+E(15)^8,E(15)+E(15)^14,E(15)^2+E(15)^13,E(15)^4+E(15)^11
 ,0,0,0,0,0,0,0,0],
[TENSOR,[26,2]],
[GALOIS,[26,7]],
[TENSOR,[28,2]],
[GALOIS,[26,4]],
[TENSOR,[30,2]],
[GALOIS,[26,2]],
[TENSOR,[32,2]]],
[( 9,11)(10,12)(22,24)(23,25),( 7, 8)(13,16,15,14)(26,29,32,27,30,33,28,31),
( 5, 6)( 9,12,11,10)(20,21)(22,25,24,23),(26,30)(27,31)(28,32)(29,33)]);
ARC("L2(31).2","CAS",[rec(name:="pgl(2,31)",
permchars:=(),
permclasses:=(),
text:=[
"names:=    pgl[2,31]\n",
" order:      29,760  =  2^6 . 3 . 5 . 31\n",
" number of classes:  33\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" comments:   extension of psl[2,31] with an outer\n",
"            automorphism of order 2\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(31).2","projectives",["2.L2(31).2",[[32,0,2,0,2,2,0,0,2,2,2,2,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[30,0,0,E(8)-E(8)^3,0,0,E(16)-E(16)^7,
E(16)^3-E(16)^5,0,0,0,0,E(32)-E(32)^15,E(32)^3-E(32)^13,-E(32)^7+E(32)^9,
E(32)^5-E(32)^11,-1,0,0,0,0,0,0,0,0,E(64)-E(64)^31,E(64)^3-E(64)^29,
E(64)^9-E(64)^23,-E(64)^5+E(64)^27,-E(64)^15+E(64)^17,E(64)^13-E(64)^19,
-E(64)^7+E(64)^25,E(64)^11-E(64)^21],
[GALOIS,[2,21]],
[GALOIS,[2,7]],
[GALOIS,[2,19]],
[GALOIS,[2,15]],
[GALOIS,[2,5]],
[GALOIS,[2,23]],
[GALOIS,[2,29]],[32,0,-1,0,2,2,0,0,-1,-1,-1,-1,0,0,0,0,1,0,-E(12)^7+E(12)^11,
0,0,-E(12)^7+E(12)^11,-E(12)^7+E(12)^11,-E(12)^7+E(12)^11,-E(12)^7+E(12)^11,0,
0,0,0,0,0,0,0],[32,0,2,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,1,0,0,E(20)-E(20)^9,
E(20)^13-E(20)^17,E(20)-E(20)^9,E(20)^13-E(20)^17,-E(20)+E(20)^9,
-E(20)^13+E(20)^17,0,0,0,0,0,0,0,0],
[GALOIS,[11,3]],[32,0,-1,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,E(15)^7+E(15)^8,
E(15)+E(15)^14,E(15)^2+E(15)^13,E(15)^4+E(15)^11,0,0,0,0,1,0,-E(12)^7+E(12)^11
 ,E(20)-E(20)^9,E(20)^13-E(20)^17,E(60)^43-E(60)^47,-E(60)^11+E(60)^19,
E(60)^7-E(60)^23,E(60)^31-E(60)^59,0,0,0,0,0,0,0,0],
[GALOIS,[13,23]],
[GALOIS,[13,11]],
[GALOIS,[13,13]]],]);
ALN("L2(31).2",["pgl(2,31)"]);

MOT("L2(32)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,31]"
],
[32736,32,33,33,33,33,33,33,31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,33,
33,33,33,33,33,33,33,33,33],
[,[1,1,3,5,6,7,8,4,10,11,12,13,9,15,16,17,18,14,20,21,22,23,19,25,26,27,28,24,
30,31,32,33,29],[1,2,1,7,8,4,5,6,23,19,20,21,22,13,9,10,11,12,18,14,15,16,17,
7,8,4,5,6,7,8,4,5,6],,,,,,,,[1,2,3,1,1,1,1,1,16,17,18,14,15,21,22,23,19,20,11,
12,13,9,10,3,3,3,3,3,3,3,3,3,3],,,,,,,,,,,,,,,,,,,,[1,2,3,5,6,7,8,4,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,25,26,27,28,24,30,31,32,33,29]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[31,-1,1,
-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1],[31,-1,-2,
-E(11)-E(11)^10,-E(11)^2-E(11)^9,-E(11)^4-E(11)^7,-E(11)^3-E(11)^8,
-E(11)^5-E(11)^6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(11)-E(11)^10,
-E(11)^2-E(11)^9,-E(11)^4-E(11)^7,-E(11)^3-E(11)^8,-E(11)^5-E(11)^6,
-E(11)-E(11)^10,-E(11)^2-E(11)^9,-E(11)^4-E(11)^7,-E(11)^3-E(11)^8,
-E(11)^5-E(11)^6],
[GALOIS,[3,5]],
[GALOIS,[3,3]],
[GALOIS,[3,4]],
[GALOIS,[3,2]],[31,-1,1,-E(11)-E(11)^10,-E(11)^2-E(11)^9,-E(11)^4-E(11)^7,
-E(11)^3-E(11)^8,-E(11)^5-E(11)^6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(33)^8-E(33)^25,-E(33)^16-E(33)^17,-E(33)-E(33)^32,-E(33)^2-E(33)^31,
-E(33)^4-E(33)^29,-E(33)^14-E(33)^19,-E(33)^5-E(33)^28,-E(33)^10-E(33)^23,
-E(33)^13-E(33)^20,-E(33)^7-E(33)^26],
[GALOIS,[8,16]],
[GALOIS,[8,8]],
[GALOIS,[8,4]],
[GALOIS,[8,2]],
[GALOIS,[8,10]],
[GALOIS,[8,5]],
[GALOIS,[8,14]],
[GALOIS,[8,7]],
[GALOIS,[8,13]],[32,0,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1],[33,1,0,0,0,0,0,0,E(31)+E(31)^30,E(31)^2+E(31)^29,
E(31)^4+E(31)^27,E(31)^8+E(31)^23,E(31)^15+E(31)^16,E(31)^5+E(31)^26,
E(31)^10+E(31)^21,E(31)^11+E(31)^20,E(31)^9+E(31)^22,E(31)^13+E(31)^18,
E(31)^6+E(31)^25,E(31)^12+E(31)^19,E(31)^7+E(31)^24,E(31)^14+E(31)^17,
E(31)^3+E(31)^28,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[19,15]],
[GALOIS,[19,8]],
[GALOIS,[19,4]],
[GALOIS,[19,2]],
[GALOIS,[19,6]],
[GALOIS,[19,3]],
[GALOIS,[19,14]],
[GALOIS,[19,7]],
[GALOIS,[19,12]],
[GALOIS,[19,5]],
[GALOIS,[19,13]],
[GALOIS,[19,9]],
[GALOIS,[19,11]],
[GALOIS,[19,10]]],
[(24,29)(25,30)(26,31)(27,32)(28,33),( 9,23,17,11,20,14,13,22,16,10,19,18,12,
 21,15),( 4, 5, 6, 7, 8)(24,30,26,32,28,29,25,31,27,33),( 9,13,12,11,10)
(14,18,17,16,15)(19,23,22,21,20),( 9,19,14)(10,20,15)(11,21,16)(12,22,17)
(13,23,18)]);
ARC("L2(32)","isSimple",true);
ARC("L2(32)","extInfo",["","5"]);
ARC("L2(32)","tomfusion",rec(name:="L2(32)",map:=[1,2,3,15,15,15,15,15,18,18,
18,18,18,18,18,18,18,18,18,18,18,18,18,20,20,20,20,20,20,20,20,20,20],text:=[
"fusion map is unique"
]));
ALF("L2(32)","L2(32).5",[1,2,3,4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,
8,8,8,8,9,9,9,9,9],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("L2(32)",["L2(32).5M1"]);

MOT("L2(32).5",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,31],\n",
"constructions: Aut(L2(32)), PGammaL(2,32), SigmaL(2,32), PSigmaL(2,32)"
],
[163680,160,165,33,31,31,31,33,33,30,30,30,30,10,10,10,10,15,15,15,15],
[,[1,1,3,4,5,6,7,8,9,11,13,10,12,11,13,10,12,19,21,18,20],[1,2,1,4,7,5,6,4,4,
12,10,13,11,16,14,17,15,12,10,13,11],,[1,2,3,4,6,7,5,9,8,1,1,1,1,2,2,2,2,3,3,
3,3],,,,,,[1,2,3,1,6,7,5,3,3,10,11,12,13,14,15,16,17,18,19,20,
21],,,,,,,,,,,,,,,,,,,,[1,2,3,4,1,1,1,8,9,10,11,12,13,14,15,16,17,18,19,20,
21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,E(5),E(5)^2,
E(5)^3,E(5)^4,E(5),E(5)^2,E(5)^3,E(5)^4,E(5),E(5)^2,E(5)^3,E(5)^4],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],[31,-1,1,-2,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1],
[TENSOR,[6,2]],
[TENSOR,[6,3]],
[TENSOR,[6,4]],
[TENSOR,[6,5]],[155,-5,-10,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[155,-5,5,1,0,
0,0,-E(33)-E(33)^2-E(33)^4-E(33)^8-E(33)^16-E(33)^17-E(33)^25-E(33)^29
 -E(33)^31-E(33)^32,-E(33)^5-E(33)^7-E(33)^10-E(33)^13-E(33)^14-E(33)^19
 -E(33)^20-E(33)^23-E(33)^26-E(33)^28,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[12,5]],[32,0,-1,-1,1,1,1,-1,-1,2,2,2,2,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[14,2]],
[TENSOR,[14,3]],
[TENSOR,[14,4]],
[TENSOR,[14,5]],[165,5,0,0,E(31)+E(31)^2+E(31)^4+E(31)^8+E(31)^15+E(31)^16
 +E(31)^23+E(31)^27+E(31)^29+E(31)^30,E(31)^5+E(31)^9+E(31)^10+E(31)^11
 +E(31)^13+E(31)^18+E(31)^20+E(31)^21+E(31)^22+E(31)^26,
E(31)^3+E(31)^6+E(31)^7+E(31)^12+E(31)^14+E(31)^17+E(31)^19+E(31)^24+E(31)^25
 +E(31)^28,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[19,3]],
[GALOIS,[19,5]]],
[(10,11,13,12)(14,15,17,16)(18,19,21,20),(8,9),(5,7,6)]);
ARC("L2(32).5","CAS",[rec(name:="psl(2,32):5",
permchars:=(),
permclasses:=( 6, 7)(11,13,19,15,14)(12,16,17,20,18),
text:=[
"Maximal subgroup of sporadic Janko group j4\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ARC("L2(32).5","tomfusion",rec(name:="L2(32).5",map:=[1,2,3,7,10,10,10,12,
12,17,17,17,17,18,18,18,18,19,19,19,19],text:=[
"fusion map is unique"
]));
ALF("L2(32).5","J4",[1,3,4,19,43,44,45,46,47,8,8,8,8,18,18,18,18,28,28,28,
28],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L2(32).5","S10(2)",[1,8,10,92,179,180,181,182,183,35,35,35,35,91,91,
91,91,140,140,140,140],[
"fusion map is unique up to table automorphisms"
]);
ALN("L2(32).5",["psl(2,32):5","S10(2)M10"]);

MOT("L2(8)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]"
],
[504,8,9,7,7,7,9,9,9],
[,[1,1,3,5,6,4,8,9,7],[1,2,1,6,4,5,3,3,3],,,,[1,2,3,1,1,1,8,9,7]],
[[1,1,1,1,1,1,1,1,1],[7,-1,-2,0,0,0,1,1,1],[7,-1,1,0,0,0,E(9)^2+E(9)^4+E(9)^5
 +E(9)^7,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5],
[GALOIS,[3,4]],
[GALOIS,[3,2]],[8,0,-1,1,1,1,-1,-1,-1],[9,1,0,E(7)+E(7)^6,E(7)^2+E(7)^5,
E(7)^3+E(7)^4,0,0,0],
[GALOIS,[7,3]],
[GALOIS,[7,2]]],
[(7,8,9),(7,9,8),(4,6,5)]);
ARC("L2(8)","CAS",[rec(name:="psl(2,8)",
permchars:=(),
permclasses:=(),
text:=[
"names:\n",
"psl[2,8] = psu[2,8] = psp[2,8] = po[3,8] = r[3]' = [f12/3+] = sl[2,8]\n",
"         = a1[8]  = 2 a1[8]  = c1[8]    = b1[8]   = 2g2[3]    [lie-not.]\n",
" order:     504  =  2^3 . 3^2 . 7\n",
" number of classes:  9\n",
" source:    private communication of atlas compound table\n",
"           from cambridge 1980/81\n",
" test:      orth.1, min",
""])]);
ARC("L2(8)","isSimple",true);
ARC("L2(8)","extInfo",["","3"]);
ARC("L2(8)","tomfusion",rec(name:="L2(8)",map:=[1,2,3,6,6,6,8,8,8],text:=[
"fusion map is unique"
]));
ARC("L2(8)","maxes",["2^3:7","D18","D14"]);
ALF("L2(8)","L2(8).3",[1,2,3,4,4,4,5,5,5]);
ALN("L2(8)",["2G2(3)'","R(3)'","A1(8)","U2(8)","S2(8)","O3(8)","psl(2,8)"]);

MOT("L2(8).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7],\n",
"constructions: Aut(L2(8))"
],
[1512,24,27,7,9,18,18,6,6,9,9],
[,[1,1,3,4,5,7,6,7,6,11,10],[1,2,1,4,3,1,1,2,2,3,3],,,,[1,2,3,1,5,6,7,8,9,10,
11]],
[[1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[7,-1,-2,0,1,1,1,-1,-1,1,1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[21,-3,3,0,0,0,0,0,0,0,0],[8,0,-1,1,-1,2,2,0,0,-1,-1],
[TENSOR,[8,2]],
[TENSOR,[8,3]],[27,3,0,-1,0,0,0,0,0,0,0]],
[( 6, 7)( 8, 9)(10,11)]);
ARC("L2(8).3","CAS",[rec(name:="psl(2,8).3",
permchars:=(),
permclasses:=(),
text:=[
"names:=    psl[2,8].3\n",
" order:      1,512  =  2^3 . 3^3 . 7\n",
" number of classes:  11\n",
" source:     private communication of atlas compound table\n",
"            from cambridge 1980/81\n",
" comments:   extension of psl[2,8] with an outer\n",
"            automorphism of order 3\n",
" test:       orth.1, min\n",
""])]);
ARC("L2(8).3","tomfusion",rec(name:="L2(8).3",map:=[1,2,3,8,11,4,4,7,7,12,
12],text:=[
"fusion map is unique"
]));
ARC("L2(8).3","maxes",["L2(8)","2^3.7.3","9:6","7:6"]);
ALF("L2(8).3","A9",[1,3,5,12,13,6,6,11,11,13,13],[
"fusion map is unique up to table autom."
],"tom:218");
ALF("L2(8).3","S6(2)",[1,5,7,22,25,8,8,21,21,25,25],[
"fusion map is unique"
]);
ALF("L2(8).3","G2(3)",[1,2,5,14,17,7,7,13,13,18,19],[
"fusion map is unique up to table autom. (use structure constants)"
]);
ALF("L2(8).3","R(27)",[1,2,3,8,9,4,5,6,7,9,9],[
"fusion map determined using the groups"
]);
ALN("L2(8).3",["psl(2,8).3","2G2(3)","R(27)M3"]);

MOT("A9M5",
[
"5th maximal subgroup of A9,\n",
"differs from A9M4 = L2(8).3 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(8).3"]]);
ALF("A9M5","A9",[1,3,5,12,14,6,6,11,11,14,14],[
"fusion L2(8).3 -> A9 mapped under A9.2"
]);

MOT("ONM8",
[
"8th maximal subgroup of ON,\n",
"differs from ONM7 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L2(31)"]]);
ALF("ONM8","ON",[1,2,3,5,6,6,11,11,16,17,16,17,20,21,20,21,30,29],[
"fusion L2(31) -> ON mapped under ON.2"
]);

LIBTABLE.LOADSTATUS.ctoline1:="userloaded";

#############################################################################
##
#E