Quelle  ctospora.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctospora.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables related to the sporadic
##  simple groups $HS$, $McL$, $He$, $Ru$, $Suz$, $HN$, $ON$, $Ly$ and $Th$
##  of the ATLAS.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctospora.tbl,v $
#H  Revision 4.38  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 4.37  2012/01/30 08:32:01  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.36  2012/01/26 11:07:36  gap
#H  added maxes of 2.Ru
#H      TB
#H
#H  Revision 4.35  2011/09/28 14:03:15  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added tables of Isoclinic(2.HS.2), Isoclinic(2.Suz.2),
#H    Isoclinic(6.Suz.2),
#H  - added fusions from HS.2, He.2 to the tables of marks
#H      TB
#H
#H  Revision 4.34  2010/09/15 08:01:44  gap
#H  mention the compatibility with Brauer tables for the fusion 4.HS.2 -> HN.2
#H      TB
#H
#H  Revision 4.33  2010/05/05 13:20:08  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 4.32  2009/04/29 14:38:54  gap
#H  added table of 3^(1+12).2.Suz.2 (< M) and related tables
#H  (contributed by Richard Barraclough)
#H      TB
#H
#H  Revision 4.31  2009/04/27 08:27:24  gap
#H  removed some superfluous explicit <nam>M<n> names,
#H  which are created automatically
#H      TB
#H
#H  Revision 4.30  2009/04/22 12:39:07  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.29  2009/01/07 10:10:52  gap
#H  added maxes of HS.2
#H      TB
#H
#H  Revision 4.28  2006/06/07 07:54:27  gap
#H  unified ConstructMixed and ConstructMGA (for better programmatic access)
#H      TB
#H
#H  Revision 4.27  2004/01/20 10:26:13  gap
#H  added several names of the forms `<name>C<class>', `<name>N<class>'
#H      TB
#H
#H  Revision 4.26  2003/11/12 17:40:12  gap
#H  changed names of two tables:
#H  HS.2xC2 -> HS.2x2,
#H  Isoclinic(2.HSxC2) -> Isoclinic(2.HSx2)
#H      TB
#H
#H  Revision 4.25  2003/05/15 17:38:23  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 4.24  2003/01/29 15:51:54  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 4.23  2003/01/24 15:57:37  gap
#H  replaced several fusions by ones that are compatible with Brauer tables
#H      TB
#H
#H  Revision 4.22  2003/01/14 17:28:50  gap
#H  changed `InfoText' values (for a better programmatic access)
#H  and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H  there is only one factor (again better programmatic handling)
#H      TB
#H
#H  Revision 4.21  2002/11/19 10:31:42  gap
#H  added comment for determining fusion 2.HS.2 -> HN
#H  (this took me several evenings, until I realized that the problem cannot
#H  be decided alone with character tables)
#H      TB
#H
#H  Revision 4.20  2002/10/22 12:44:14  gap
#H  added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H  (they make it possible to construct <p>-modular Brauer tables
#H  for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H  of <fact> is in the library)
#H      TB
#H
#H  Revision 4.19  2002/09/23 15:04:47  gap
#H  removed trailing blanks
#H      TB
#H
#H  Revision 4.18  2002/09/18 15:22:01  gap
#H  changed the `text' components of many fusions,
#H  in order to use them as a status information (for evaluation)
#H      TB
#H
#H  Revision 4.17  2002/08/21 13:53:51  gap
#H  removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H      TB
#H
#H  Revision 4.16  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 4.15  2002/07/12 06:45:57  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.14  2002/07/08 16:06:57  gap
#H  changed `construction' component from function (call) to list of function
#H  name and arguments
#H      TB
#H
#H  Revision 4.13  2001/08/28 16:23:23  gap
#H  added a few alias names (suggested by J. McKay)
#H      TB
#H
#H  Revision 4.12  2001/05/04 16:50:03  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.12 of ctbllib coincides with Rev. 4.11 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctospora.tbl,v
#H  Working file: ctospora.tbl
#H  head: 4.11
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.8.0.6
#H   GAP4R2PRE2: 4.8.0.4
#H   GAP4R2PRE1: 4.8.0.2
#H   GAP4R1: 4.4.0.2
#H  keyword substitution: kv
#H  total revisions: 13; selected revisions: 13
#H  description:
#H  ----------------------------
#H  revision 4.11
#H  date: 2000/07/22 09:31:22;  author: gap;  state: Exp;  lines: +5 -2
#H  added tables of missing maxes of 2.HS
#H  (I should have done this a long time ago ...)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.10
#H  date: 2000/06/09 17:24:18;  author: gap;  state: Exp;  lines: +6 -2
#H  added 6.SuzM12 (now the maxes of 6.Suz are complete)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.9
#H  date: 2000/03/27 09:54:45;  author: gap;  state: Exp;  lines: +6 -2
#H  added some tables of maxes of 2.Suz and corresponding fusions,
#H  added table of 3.Fi22M5
#H  
#H      TB
#H  ----------------------------
#H  revision 4.8
#H  date: 1999/10/21 14:15:48;  author: gap;  state: Exp;  lines: +16 -2
#H  added many `tomidentifer' and `tomfusion' values, which yields a better
#H  interface between `tom' and `tbl';
#H  
#H  added maxes of McL.2,
#H  
#H  unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H  
#H      TB
#H  ----------------------------
#H  revision 4.7
#H  date: 1999/09/17 14:11:52;  author: gap;  state: Exp;  lines: +20 -4
#H  added maxes of 3.Suz.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/09/14 13:30:12;  author: gap;  state: Exp;  lines: +15 -29
#H  added maxes of 3.Suz
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/08/31 13:16:16;  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 4.4
#H  date: 1999/07/15 17:12:50;  author: gap;  state: Exp;  lines: +3 -3
#H  replaced name F3+M13 by He.2
#H  (necessary since maxes of F3+ are currently not supported)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1999/07/14 11:39:42;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/11/25 15:45:45;  author: gap;  state: Exp;  lines: +7 -3
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:47:07;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.2
#H  date: 1996/12/17 16:37:46;  author: sam;  state: Exp;  lines: +3 -3
#H  changed the name of '4.2^4:s5' to '4.2^4.S5' (the extension is non-split!)
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:01:40;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("2.HS",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[88704000,88704000,15360,15360,2880,720,720,7680,7680,256,64,1000,1000,600,
600,50,50,72,72,48,48,14,14,32,32,16,16,40,40,20,22,22,22,22,24,24,30,30,40,
40,40,40],
[,[1,1,1,1,2,6,6,4,4,4,3,12,12,14,14,16,16,7,7,6,6,22,22,10,10,11,11,12,12,15,
33,33,31,31,21,21,37,37,29,29,29,29],[1,2,3,4,5,1,2,9,8,10,11,12,13,14,15,16,
17,5,5,3,4,22,23,25,24,26,27,28,29,30,31,32,33,34,8,9,14,15,40,39,42,41],,[1,
2,3,4,5,6,7,8,9,10,11,1,2,1,2,1,2,18,19,20,21,22,23,24,25,26,27,3,4,5,31,32,
33,34,35,36,6,7,8,9,8,9],,[1,2,3,4,5,6,7,9,8,10,11,12,13,14,15,16,17,19,18,20,
21,1,2,25,24,26,27,28,29,30,33,34,31,32,36,35,37,38,40,39,42,41],,,,[1,2,3,4,
5,6,7,9,8,10,11,12,13,14,15,16,17,19,18,20,21,22,23,25,24,26,27,28,29,30,1,2,
1,2,36,35,37,38,42,41,40,39]],
0,
[(39,41)(40,42),(31,33)(32,34),(26,27),( 8, 9)(18,19)(24,25)(35,36)(39,40)
(41,42),( 8, 9)(18,19)(24,25)(35,36)(39,42)(40,41)],
["ConstructProj",[["HS",[]],["2.HS",[]]]]);
ARC("2.HS","CAS",[rec(name:="2.hs",
permchars:=(20,21),
permclasses:=(),
text:="")]);
ARC("2.HS","maxes",["2.M22","Isoclinic(U3(5).2x2)","2.HSM3",
"Isoclinic(2.L3(4).2_1)","Isoclinic(S8x2)","2.2^4.S6","2.4^3.L3(2)","2xM11",
"2.HSM9","2.HSM10","2.HSM11","5:4x2.A5"]);
ALF("2.HS","HS",[1,1,2,2,3,4,4,5,5,6,7,8,8,9,9,10,10,11,11,12,12,13,13,14,
14,15,16,17,17,18,19,19,20,20,21,21,22,22,23,23,24,24]);
ALF("2.HS","2.HS.2",[1,2,3,4,5,6,7,8,8,9,10,11,12,13,14,15,16,17,17,18,19,
20,21,22,22,23,23,24,25,26,27,28,27,28,29,29,30,31,32,33,33,32],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("2.HS",["2.HS.2M1"]);

MOT("2.HS.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[177408000,177408000,30720,30720,5760,1440,1440,7680,512,128,2000,2000,1200,
1200,100,100,72,96,96,28,28,32,16,80,80,40,22,22,24,60,60,40,40,80640,3840,
640,192,80,720,72,48,64,64,60,20,20,24,28,28,40,40,40,40,40,40,60,60],
[,[1,1,1,1,2,6,6,4,4,3,11,11,13,13,15,15,7,6,6,20,20,9,10,11,11,14,27,27,19,
30,30,25,25,1,1,4,3,5,6,6,6,9,9,13,15,15,18,20,20,26,26,25,25,25,25,30,30],[1,
2,3,4,5,1,2,8,9,10,11,12,13,14,15,16,5,3,4,20,21,22,23,24,25,26,27,28,8,13,14,
33,32,34,35,36,37,38,34,34,35,42,43,44,46,45,37,49,48,51,50,54,55,53,52,44,
44],,[1,2,3,4,5,6,7,8,9,10,1,2,1,2,1,2,17,18,19,20,21,22,23,3,4,5,27,28,29,6,
7,8,8,34,35,36,37,38,39,40,41,42,43,34,35,35,47,49,48,38,38,36,36,36,36,39,
39],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,2,22,23,24,25,26,27,
28,29,30,31,33,32,34,35,36,37,38,39,40,41,42,43,44,46,45,47,34,34,50,51,55,54,
52,53,57,56],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,1,2,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,57,56]],
0,
[(56,57),(50,51),(48,49),(45,46),(32,33)(45,46)(50,51)(52,55,53,54)(56,57),
(32,33)(52,55,53,54)],
["ConstructProj",[["HS.2",[]],["2.HS.2",[]]]]);
ALF("2.HS.2","HS.2",[1,1,2,2,3,4,4,5,6,7,8,8,9,9,10,10,11,12,12,13,13,14,
15,16,16,17,18,18,19,20,20,21,21,22,23,24,25,26,27,28,29,30,31,32,33,33,
34,35,35,36,36,37,37,38,38,39,39]);
ALF("2.HS.2","HN",[1,2,2,3,7,4,14,6,6,7,10,21,9,22,13,26,30,14,15,17,33,
19,18,21,23,41,29,45,31,34,48,39,40,2,3,6,7,18,14,14,15,19,19,22,27,28,30,
33,33,53,54,39,39,40,40,48,48],[
"determined by the fusion of 2.HS.2N5 = HNN10A into HNN5B = HNM6,\n",
"which was computed explicitly from these groups"
]);
ALF("2.HS.2","4.HS.2",[1,3,4,6,7,9,11,12,15,17,19,21,22,24,25,27,28,31,33,
34,36,37,40,42,44,45,47,49,51,54,56,57,59,61,63,65,67,69,71,73,75,77,79,
81,83,83,85,87,87,89,89,91,91,93,93,95,95],[
"fusion map is unique up to table aut."
]);
ALN("2.HS.2",["HNC2A","HNN2A"]);

MOT("Isoclinic(2.HS.2)",
[
"isoclinic group of the 2.HS.2 given in the ATLAS"
],
0,
0,
0,
[(56,57),(50,51),(48,49),(45,46),(52,53)(54,55),(32,33)(52,54,53,55)],
["ConstructIsoclinic",[["2.HS.2"]]]);
ALF("Isoclinic(2.HS.2)","HS.2",[1,1,2,2,3,4,4,5,6,7,8,8,9,9,10,10,11,12,
12,13,13,14,15,16,16,17,18,18,19,20,20,21,21,22,23,24,25,26,27,28,29,30,
31,32,33,33,34,35,35,36,36,37,37,38,38,39,39]);

MOT("HS.2x2",
0,
0,
0,
0,
[(73,75)(74,76),(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,
60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)],
["ConstructDirectProduct",[["HS.2"],["Cyclic",2]]]);

MOT("Isoclinic(2.HSx2)",
0,
0,
0,
0,
[(77,81)(78,82)(79,83)(80,84),(61,65)(62,66)(63,67)(64,68),(51,53)(52,54),(15,
17)(16,18)(35,37)(36,38)(47,49)(48,50)(69,71)(70,72)(77,79)(78,80)(81,83)(82,
84),(2,4)(6,8)(12,14)(15,17)(24,26)(28,30)(32,34)(35,37)(40,42)(44,46)(47,49)
(56,58)(62,64)(66,68)(69,71)(74,76)(77,79)(81,83)],
["ConstructIsoclinic",[["2.HS"],["Cyclic",2]]]);
ALF("Isoclinic(2.HSx2)","4.HS.2",[1,2,3,2,4,5,6,5,7,8,9,10,11,10,12,13,12,
14,15,16,17,18,19,20,21,20,22,23,24,23,25,26,27,26,28,29,28,30,31,32,33,
32,34,35,36,35,37,38,37,39,40,41,40,41,42,43,44,43,45,46,47,48,49,50,47,
50,49,48,51,52,51,53,54,55,56,55,57,58,59,60,59,58,57,60],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("Isoclinic(2.HSx2)","HS",[1,1,1,1,2,2,2,2,3,3,4,4,4,4,5,5,5,5,6,6,7,
7,8,8,8,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,
14,14,15,15,16,16,17,17,17,17,18,18,19,19,19,19,20,20,20,20,21,21,21,21,
22,22,22,22,23,23,23,23,24,24,24,24]);

MOT("4.HS.2",
[
"extension of the central product of C4 and 2.HS by an automorphism,\n",
"maximal subgroup of HN.2,\n",
],
[354816000,177408000,354816000,61440,30720,61440,11520,11520,2880,1440,2880,
15360,30720,30720,1024,1024,256,256,4000,2000,4000,2400,1200,2400,200,100,200,
144,288,288,192,96,192,56,28,56,64,128,128,32,32,160,80,160,80,80,44,44,44,44,
48,96,96,120,60,120,80,80,80,80,161280,161280,7680,7680,1280,1280,384,384,160,
160,1440,1440,144,144,96,96,128,128,128,128,120,120,20,20,48,48,28,28,40,40,40
,40,40,40,60,60],
[,[1,3,1,1,3,1,3,1,9,11,9,6,4,4,6,4,4,6,19,21,19,22,24,22,25,27,25,11,9,9,9,11
,9,34,36,34,15,15,15,17,17,19,21,19,24,22,47,49,47,49,33,31,31,54,56,54,44,42,
44,42,1,1,1,1,6,6,4,4,7,7,9,9,9,9,9,9,15,15,15,15,22,22,25,25,31,31,34,34,45,
45,44,44,44,44,54,54],[1,2,3,4,5,6,7,8,1,2,3,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,7,8,8,4,5,6,34,35,36,37,38,39,40,41,42,43,44,45,46,47,50,49,48,
12,14,13,22,23,24,59,58,57,60,61,62,63,64,65,66,67,68,69,70,61,62,61,62,63,64,
77,78,79,80,81,82,83,84,67,68,87,88,89,90,93,94,91,92,81,82],,[1,2,3,4,5,6,7,8
,9,10,11,12,13,14,15,16,17,18,1,2,3,1,2,3,1,2,3,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,4,5,6,7,8,47,48,49,50,51,52,53,9,10,11,12,13,12,14,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,61,62,63,64,85,86,87,88,69,70,65,
66,65,66,71,72],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,1,2,3,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,59,58,57,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,85,86,61,62,89,90,93,94,91,92,95,96],,,,[1,2,3,4,5,6,7
,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,1,2,3,2,51,52,53,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,
87,88,89,90,91,92,93,94,95,96]],
0,
[(57,59),(91,93)(92,94),(48,50)(91,93)(92,94),
(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)
(83,84)(85,86)(87,88)(89,90)(91,94)(92,93)(95,96),
(13,14)(29,30)(38,39)(52,53)(58,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)
(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,94)(92,93)
(95,96)],
["ConstructMGA","Isoclinic(2.HSx2)","HS.2x2",[[49,50],[51,54],[52,53],[55,
58],[56,57],[59,62],[60,61],[63,64],[65,68],[66,67],[69,70],[71,72],[73,76],
[74,75],[77,80],[78,79],[81,82],[83,84]],()]);
ALF("4.HS.2","HS.2x2",[1,2,1,3,4,3,5,6,7,8,7,9,10,10,11,12,13,14,15,16,
15,17,18,17,19,20,19,21,22,22,23,24,23,25,26,25,27,28,28,29,30,31,32,31,
33,34,35,36,35,36,37,38,38,39,40,39,41,42,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78]);
ALF("4.HS.2","HN.2",[1,46,2,2,47,3,7,45,4,58,13,6,46,47,6,47,7,48,10,62,
20,9,63,21,12,64,24,27,49,50,13,59,14,16,70,30,18,53,52,17,54,20,65,22,36,
56,26,76,39,77,28,59,58,31,78,41,34,62,35,65,2,45,3,45,6,48,7,47,17,54,13,
49,13,50,14,50,18,53,18,52,21,56,25,57,27,59,30,60,44,72,34,66,35,66,41,
71],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("4.HS.2","HS.2",[1,1,1,2,2,2,3,3,4,4,4,5,5,5,6,6,7,7,8,8,8,9,9,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,16,16,16,17,17,18,18,18,
18,19,19,19,20,20,20,21,21,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,
28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,39]);
ALN("4.HS.2",["HN.2C2A","HN.2N2A","HN.2N4D"]);

MOT("2.Ru",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,29]"
],
[291852288000,291852288000,491520,491520,116480,4320,4320,15360,15360,7680,
7680,1024,512,2000,2000,600,600,96,96,56,56,192,192,128,128,32,80,80,20,48,48,
24,24,104,104,28,28,28,30,30,32,32,32,32,40,40,40,40,40,40,48,48,48,48,52,52,
52,58,58,58,58],
[,[1,1,1,1,2,6,6,3,3,4,4,4,3,14,14,16,16,6,6,20,20,9,9,12,12,13,14,14,17,18,
18,19,19,34,34,21,21,21,39,39,25,25,24,24,27,27,28,28,28,28,31,31,31,31,35,35,
35,60,60,58,58],[1,2,3,4,5,1,2,8,9,11,10,12,13,14,15,16,17,3,4,20,21,23,22,25,
24,26,27,28,29,8,9,11,10,34,35,37,38,36,16,17,43,44,41,42,45,46,50,49,48,47,
23,22,23,22,56,57,55,60,61,58,59],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,1,2,18,
19,20,21,22,23,24,25,26,3,4,5,30,31,32,33,34,35,38,36,37,6,7,41,42,43,44,8,9,
10,11,10,11,51,52,53,54,55,56,57,58,59,60,61],,[1,2,3,4,5,6,7,8,9,11,10,12,13,
14,15,16,17,18,19,1,2,23,22,25,24,26,27,28,29,30,31,33,32,34,35,5,5,5,39,40,
43,44,41,42,45,46,50,49,48,47,54,53,52,51,57,55,56,58,59,60,61],,,,,,[1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,1,2,36,37,38,39,40,41,42,43,44,45,46,49,50,47,48,53,54,51,52,5,5,5,58,
59,60,61],,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,56,57,55,1,2,1,2]],
0,
[(58,60)(59,61),(55,56,57),(55,57,56),(51,53)(52,54),(47,49)(48,50),
(36,37,38),(10,11)(22,23)(24,25)(32,33)(41,43)(42,44)(47,48)(49,50)(51,52)
(53,54),(10,11)(22,23)(24,25)(32,33)(41,43)(42,44)(47,48)(49,50)(51,54)
(52,53),(36,38,37)],
["ConstructProj",[["Ru",[]],["2.Ru",[]]]]);
ARC("2.Ru","CAS",[rec(name:="2.ru",
permchars:=(11,12,13)(17,19)(34,35),
permclasses:=(56,57),
text:="")]);
ARC("2.Ru","maxes",["2.RuM1","2.2^6:u3(3):2","2.(2^2xSz(8)):3",
"2.2^3+8:L3(2)","2xU3(5).2","2.2.2^4+6:S5","L2(25).(2x4)","2xA8","2.L2(29)",
"2x5^2:4S5","3.A6.(2x4)","5^(1+2):(4x4):4","Isoclinic(L2(13).2x2)","A6.D8",
"5:4x2.A5"]);
ALF("2.Ru","Ru",[1,1,2,2,3,4,4,5,5,6,6,7,8,9,9,10,10,11,11,12,12,13,13,14,
14,15,16,16,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,27,28,28,
29,29,30,30,31,31,32,33,34,35,35,36,36]);

MOT("2.Suz",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
[896690995200,896690995200,6635520,6635520,161280,19595520,19595520,69984,
69984,6480,6480,92160,92160,3072,1536,288,3600,3600,600,600,6912,6912,2592,
2592,2592,2592,864,864,72,168,168,192,128,128,32,108,108,108,108,80,80,20,22,
22,576,576,144,144,48,72,72,48,48,26,26,26,26,28,90,90,90,90,30,30,36,36,36,
36,40,40,42,42,42,42,48,48],
[,[1,1,1,1,2,6,6,8,8,10,10,3,3,3,4,5,17,17,19,19,6,6,8,8,8,8,8,8,11,30,30,12,
14,14,15,38,38,36,36,17,17,20,43,43,21,21,27,27,22,29,29,27,27,56,56,54,54,31,
61,61,59,59,63,63,38,38,36,36,40,40,73,73,71,71,45,45],[1,2,3,4,5,1,2,1,2,1,2,
12,13,14,15,16,17,18,19,20,3,4,3,4,3,4,3,4,5,30,31,32,33,34,35,8,9,8,9,40,41,
42,43,44,12,13,12,13,15,16,16,14,14,54,55,56,57,58,17,18,17,18,19,20,23,24,25,
26,69,70,30,31,30,31,32,32],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,1,2,
21,22,25,26,23,24,27,28,29,30,31,32,33,34,35,38,39,36,37,3,4,5,43,44,45,46,47,
48,49,51,50,53,52,56,57,54,55,58,10,11,10,11,6,7,67,68,65,66,12,13,71,72,73,
74,76,75],,[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,
26,27,28,29,1,2,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,56,57,54,55,5,61,62,59,60,63,64,65,66,67,68,69,70,6,7,6,7,76,75],,,,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,25,26,23,24,27,28,29,
30,31,32,33,34,35,38,39,36,37,40,41,42,1,2,45,46,47,48,49,51,50,53,52,56,57,
54,55,58,59,60,61,62,63,64,67,68,65,66,69,70,73,74,71,72,75,76],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,50,52,53,1,2,1,2,58,61,62,
59,60,63,64,65,66,67,68,69,70,73,74,71,72,75,76]],
0,
[(75,76),(71,73)(72,74),(59,61)(60,62),(54,56)(55,57),(50,51),(50,51)(75,76),
(23,25)(24,26)(36,38)(37,39)(52,53)(65,67)(66,68)(71,73)(72,74)(75,76),(23,25)
(24,26)(36,38)(37,39)(52,53)(65,67)(66,68)],
["ConstructProj",[["Suz",[]],["2.Suz",[]]]]);
ARC("2.Suz","maxes",["2.G2(4)","Isoclinic(6_2.U4(3).2_3')","2xU5(2)",
"2.SuzM4","2x3^5:M11","2.J2.2","2.SuzM7","2.(A4xL3(4)).2","2.SuzM9",
"Isoclinic(2.M12.2)","2.SuzM11","(A6x2.A5).2","(3^2:4x2.A6).2","(2xL3(3)).2",
"(2xL3(3)).2","2.L2(25)","2.A7"]);
ALF("2.Suz","Suz",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,9,10,11,11,12,12,13,13,14,
14,15,15,16,16,17,18,18,19,20,20,21,22,22,23,23,24,24,25,26,26,27,27,28,
28,29,30,30,31,31,32,32,33,33,34,35,35,36,36,37,37,38,38,39,39,40,40,41,
41,42,42,43,43]);
ALF("2.Suz","2.Suz.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,23,24,25,26,27,28,29,30,31,32,33,34,35,34,35,36,37,38,39,40,
41,42,43,44,45,46,46,47,47,48,49,48,49,50,51,52,51,52,53,54,55,56,55,56,
57,58,59,60,59,60,61,61]);
ALN("2.Suz",["2.Suz.2M1"]);

MOT("2.Suz.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
[1793381990400,1793381990400,13271040,13271040,322560,39191040,39191040,
139968,139968,12960,12960,184320,184320,6144,3072,576,7200,7200,1200,1200,
13824,13824,2592,2592,1728,1728,144,336,336,384,256,256,64,108,108,160,160,40,
44,44,1152,1152,288,288,96,72,48,26,26,56,90,90,60,60,36,36,80,80,42,42,48,
2419200,380160,4608,1344,4320,216,144,144,92160,92160,3072,1536,1536,256,384,
384,1200,1200,200,200,40,288,72,24,28,32,32,44,44,576,576,96,144,144,48,48,48,
48,56,56,60,60,80,80,80,80],
[,[1,1,1,1,2,6,6,8,8,10,10,3,3,3,4,5,17,17,19,19,6,6,8,8,8,8,11,28,28,12,14,
14,15,34,34,17,17,20,39,39,21,21,25,25,22,27,25,48,48,29,51,51,53,53,34,34,36,
36,59,59,41,2,1,4,5,7,8,11,10,12,12,12,13,13,13,15,15,20,20,18,18,19,22,26,27,
29,31,31,39,39,41,41,41,43,43,44,44,45,45,50,50,54,54,57,57,57,57],[1,2,3,4,5,
1,2,1,2,1,2,12,13,14,15,16,17,18,19,20,3,4,3,4,3,4,5,28,29,30,31,32,33,8,9,36,
37,38,39,40,12,13,12,13,15,16,14,48,49,50,17,18,19,20,23,24,57,58,28,29,30,62,
63,64,65,62,63,62,63,70,71,72,73,74,75,76,77,78,79,80,81,82,64,64,65,86,87,88,
89,90,70,71,72,70,71,73,74,76,77,100,101,78,79,104,105,106,107],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,1,2,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,3,4,5,39,40,41,42,43,44,45,46,47,48,49,50,10,11,6,7,55,56,12,13,59,60,61,
62,63,64,65,66,67,68,69,71,70,72,74,73,75,77,76,62,62,62,62,63,83,84,85,86,88,
87,89,90,92,91,93,95,94,97,96,99,98,100,101,66,66,71,70,71,70],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,1,2,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,5,51,52,53,54,55,56,57,58,6,7,
61,62,63,64,65,66,67,68,69,71,70,72,74,73,75,77,76,78,79,80,81,82,83,84,85,62,
88,87,90,89,92,91,93,95,94,97,96,99,98,65,65,102,103,107,106,105,104],,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,1,2,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,79,78,81,80,82,
83,84,85,86,87,88,63,63,91,92,93,94,95,96,97,98,99,101,100,103,102,106,107,
104,105],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,1,2,50,51,
52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,71,70,72,74,73,75,77,76,
79,78,81,80,82,83,84,85,86,88,87,90,89,92,91,93,95,94,97,96,99,98,100,101,103,
102,105,104,107,106]],
0,
[(100,101),(89,90),( 78, 79)( 80, 81)(102,103)(104,106)(105,107),( 78, 79)
( 80, 81)(100,101)(102,103)(104,106)(105,107),( 70, 71)( 73, 74)( 76, 77)
( 78, 79)( 80, 81)( 87, 88)( 91, 92)( 94, 95)( 96, 97)( 98, 99)(102,103)
(104,105)(106,107),( 70, 71)( 73, 74)( 76, 77)( 87, 88)( 91, 92)( 94, 95)
( 96, 97)( 98, 99)(104,107)(105,106)],
["ConstructProj",[["Suz.2",[]],["2.Suz.2",[]]]]);
ALF("2.Suz.2","Suz.2",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,9,10,11,11,12,12,13,13,
14,14,15,15,16,17,17,18,19,19,20,21,21,22,22,23,24,24,25,25,26,26,27,28,
29,30,30,31,32,32,33,33,34,34,35,35,36,36,37,38,39,40,41,42,43,44,45,46,
46,47,48,48,49,50,50,51,51,52,52,53,54,55,56,57,58,58,59,59,60,60,61,62,
62,63,63,64,64,65,65,66,66,67,67,68,68]);

MOT("Isoclinic(2.Suz.2)",
[
"isoclinic group of the 2.Suz.2 given in the ATLAS"
],
0,
0,
0,
[(100,101),(89,90),( 78, 79)( 80, 81)(102,103)(104,106)(105,107),
( 70, 71)( 73, 74)( 76, 77)( 87, 88)( 91, 92)( 94, 95)( 96, 97)( 98, 99)
(104,107)(105,106)
],
["ConstructIsoclinic",[["2.Suz.2"]]]);
ALF("Isoclinic(2.Suz.2)","Suz.2",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,9,10,11,11,
12,12,13,13,14,14,15,15,16,17,17,18,19,19,20,21,21,22,22,23,24,24,25,25,
26,26,27,28,29,30,30,31,32,32,33,33,34,34,35,35,36,36,37,38,39,40,41,42,
43,44,45,46,46,47,48,48,49,50,50,51,51,52,52,53,54,55,56,57,58,58,59,59,
60,60,61,62,62,63,63,64,64,65,65,66,66,67,67,68,68]);

MOT("3.McL",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]\n",
"3rd power map determined only up to table automorphism (35,36)"
],
[2694384000,2694384000,2694384000,120960,120960,120960,87480,87480,87480,972,
288,288,288,2250,2250,2250,75,75,75,1080,1080,1080,108,108,108,42,42,42,42,42,
42,24,24,24,27,27,90,90,90,33,33,33,33,33,33,36,36,36,42,42,42,42,42,42,90,90,
90,90,90,90,90,90,90,90,90,90],
[,[1,3,2,1,3,2,7,9,8,10,4,6,5,14,16,15,17,19,18,7,9,8,10,10,10,26,28,27,29,31,
30,11,13,12,36,35,14,16,15,43,45,44,40,42,41,20,22,21,26,28,27,29,31,30,55,57,
56,58,60,59,55,57,56,58,60,59],[1,1,1,4,4,4,1,1,1,1,11,11,11,14,14,14,17,17,
17,4,4,4,4,4,4,29,29,29,26,26,26,32,32,32,8,9,37,37,37,40,40,40,43,43,43,11,
11,11,52,52,52,49,49,49,14,14,14,14,14,14,37,37,37,37,37,37],,[1,3,2,4,6,5,7,
9,8,10,11,13,12,1,3,2,1,3,2,20,22,21,23,25,24,29,31,30,26,28,27,32,34,33,36,
35,4,6,5,40,42,41,43,45,44,46,48,47,52,54,53,49,51,50,7,9,8,7,9,8,20,22,21,20,
22,21],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,1,
2,3,1,2,3,32,33,34,35,36,37,38,39,43,44,45,40,41,42,46,47,48,4,5,6,4,5,6,58,
59,60,55,56,57,64,65,66,61,62,63],,,,[1,3,2,4,6,5,7,9,8,10,11,13,12,14,16,15,
17,19,18,20,22,21,23,25,24,26,28,27,29,31,30,32,34,33,36,35,37,39,38,1,3,2,1,
3,2,46,48,47,49,51,50,52,54,53,58,60,59,55,57,56,64,66,65,61,63,62]],
0,
[(55,58)(56,59)(57,60)(61,64)(62,65)(63,66),(40,43)(41,44)(42,45),(26,29)
(27,30)(28,31)(49,52)(50,53)(51,54),( 2, 3)( 5, 6)( 8, 9)(12,13)(15,16)(18,19)
(21,22)(24,25)(27,28)(30,31)(33,34)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)
(53,54)(55,58)(56,60)(57,59)(61,64)(62,66)(63,65),( 2, 3)( 5, 6)( 8, 9)(12,13)
(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(35,36)(38,39)(41,42)(44,45)
(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)],
["ConstructProj",[["McL",[]],,["3.McL",[23,23,-1,-1,-13,-13,11,11,-1,-1,-1,-1,
-1,-1,-13,-13,-1,-1,11,11,-1]]]]);
ARC("3.McL","CAS",[rec(name:="3.mcl",
permchars:=(16,17)(18,19)(38,40)(62,64),
permclasses:=(),
text:="")]);
ALF("3.McL","McL",[1,1,1,2,2,2,3,3,3,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,
10,10,11,11,11,12,12,12,13,14,15,15,15,16,16,16,17,17,17,18,18,18,19,19,
19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24]);
ALF("3.McL","3.McL.2",[1,2,2,3,4,4,5,6,6,7,8,9,9,10,11,11,12,13,13,14,15,
15,16,17,17,18,19,20,18,20,19,21,22,22,23,23,24,25,25,26,27,27,28,29,29,
30,31,31,32,33,34,32,34,33,35,36,37,35,37,36,38,39,40,38,40,39],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ARC("3.McL","maxes",["3_2.U4(3)","3.M22","3.McLM3","3.U3(5)","3.3^(1+4):2S5",
"3^5:M10","3xL3(4).2_2","3x2.A8","3.2^4:a7","3.McLM10","3xM11",
"3x5^(1+2):3:8"]);

MOT("3.McL.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[5388768000,2694384000,241920,120960,174960,87480,1944,576,288,4500,2250,150,
75,2160,1080,216,108,42,42,42,48,24,27,180,90,66,33,66,33,72,36,42,42,42,90,
90,90,90,90,90,15840,1440,36,96,32,10,36,36,20,20,22,22,24,24],
[,[1,2,1,2,5,6,7,3,4,10,11,12,13,5,6,7,7,18,20,19,8,9,23,10,11,28,29,26,27,14,
15,18,20,19,35,37,36,35,37,36,1,3,7,8,8,12,14,16,24,24,28,26,30,30],[1,1,3,3,
1,1,1,8,8,10,10,12,12,3,3,3,3,18,18,18,21,21,6,24,24,26,26,28,28,8,8,32,32,32,
10,10,10,24,24,24,41,42,41,44,45,46,42,42,49,50,51,52,44,44],,[1,2,3,4,5,6,7,
8,9,1,2,1,2,14,15,16,17,18,19,20,21,22,23,3,4,26,27,28,29,30,31,32,33,34,5,6,
6,14,15,15,41,42,43,44,45,41,47,48,42,42,51,52,53,54],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,1,2,2,21,22,23,24,25,28,29,26,27,30,31,3,4,4,35,37,36,38,
40,39,41,42,43,44,45,46,47,48,49,50,52,51,53,54],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,20,19,21,22,23,24,25,1,2,1,2,30,31,32,34,33,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,50,49,41,41,53,54]],
0,
[(53,54),(49,50),(49,50)(53,54),(36,37)(39,40),(36,37)(39,40)(49,50),(26,28)
(27,29)(51,52),(19,20)(33,34),(19,20)(33,34)(53,54)],
["ConstructMGA","3.McL","McL.2",
     [ [ 25, 26 ], [ 27, 28 ], [ 29, 30 ], [ 31, 32 ], [ 33, 36 ],
        [ 34, 35 ], [ 37, 38 ], [ 39, 40 ], [ 41, 42 ], [ 43, 44 ],
        [ 45, 46 ], [ 47, 48 ], [ 49, 50 ], [ 51, 52 ], [ 53, 56 ],
        [ 54, 55 ], [ 57, 58 ], [ 59, 60 ], [ 61, 62 ], [ 63, 64 ],
        [ 65, 66 ] ], ()]);
ARC("3.McL.2","maxes",["3.McL","3_2.U4(3).2_3'","3.U3(5).2","3.3^(1+4):4S5",
"3^5:(M10x2)","(3xL3(4).2_2).2","(2.A8x3).2","M11xS3","3.McL.2N5",
"3.2^(2+4):(S3xS3)"]);
ALF("3.McL.2","McL.2",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,8,9,9,10,10,10,11,11,
12,13,13,14,14,15,15,16,16,17,17,17,18,18,18,19,19,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33]);
ALF("3.McL.2","Ly",[1,3,2,8,3,4,4,5,19,6,22,7,24,8,9,9,10,11,27,28,12,31,
14,15,36,17,43,18,44,19,20,21,49,50,22,23,23,36,37,37,2,5,10,12,13,16,19,
20,26,26,29,30,31,31],[
"fusion is unique up to table automorphisms,\n",
"the representative is compatible with the 5-modular tables"
]);
ALN("3.McL.2",["LyN3A"]);

MOT("3.ON",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19,31]"
],
[1382446517760,1382446517760,1382446517760,483840,483840,483840,3240,241920,
241920,241920,768,768,768,540,540,540,72,4116,4116,4116,147,147,147,96,96,96,
96,96,96,60,60,60,33,33,33,36,84,84,84,45,45,48,48,48,48,48,48,48,48,48,48,48,
48,57,57,57,57,57,57,57,57,57,60,60,60,60,60,60,84,84,84,84,84,84,93,93,93,93,
93,93],
[,[1,3,2,1,3,2,7,4,6,5,4,6,5,14,16,15,7,18,20,19,21,23,22,11,13,12,11,13,12,
14,16,15,33,35,34,17,18,20,19,41,40,24,26,25,24,26,25,27,29,28,27,29,28,57,59,
58,60,62,61,54,56,55,30,32,31,30,32,31,37,39,38,37,39,38,75,77,76,78,80,79],[
1,1,1,4,4,4,1,8,8,8,11,11,11,14,14,14,4,18,18,18,21,21,21,24,24,24,27,27,27,
30,30,30,33,33,33,8,37,37,37,14,14,45,45,45,42,42,42,51,51,51,48,48,48,57,57,
57,60,60,60,54,54,54,63,63,63,66,66,66,69,69,69,72,72,72,78,78,78,75,75,75],,[
1,3,2,4,6,5,7,8,10,9,11,13,12,1,3,2,17,18,20,19,21,23,22,24,26,25,27,29,28,4,
6,5,33,35,34,36,37,39,38,7,7,45,47,46,42,44,43,51,53,52,48,50,49,57,59,58,60,
62,61,54,56,55,8,10,9,8,10,9,72,74,73,69,71,70,75,77,76,78,80,79],,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,1,2,3,1,2,3,24,25,26,27,28,29,30,31,32,33,34,
35,36,4,5,6,41,40,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,8,9,10,8,9,10,75,76,77,78,79,80],,,,[1,3,2,4,6,5,7,8,10,
9,11,13,12,14,16,15,17,18,20,19,21,23,22,24,26,25,27,29,28,30,32,31,1,3,2,36,
37,39,38,40,41,45,47,46,42,44,43,51,53,52,48,50,49,54,56,55,57,59,58,60,62,61,
66,68,67,63,65,64,72,74,73,69,71,70,78,80,79,75,77,76],,,,,,,,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,45,46,47,42,43,44,51,52,53,48,49,50,1,2,3,1,2,3,1,2,3,
66,67,68,63,64,65,69,70,71,72,73,74,75,76,77,78,79,80],,,,,,,,,,,,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
59,60,61,62,66,67,68,63,64,65,69,70,71,72,73,74,1,2,3,1,2,3]],
0,
[(75,78)(76,79)(77,80),(69,72)(70,73)(71,74),(63,66)(64,67)(65,68),(63,66)
(64,67)(65,68)(69,72)(70,73)(71,74),(54,57,60)(55,58,61)(56,59,62),(42,45)
(43,46)(44,47)(48,51)(49,52)(50,53),(42,45)(43,46)(44,47)(48,51)(49,52)(50,53)
(63,66)(64,67)(65,68)(69,72)(70,73)(71,74),(40,41),(40,41)(63,66)(64,67)
(65,68),(24,27)(25,28)(26,29)(42,48)(43,49)(44,50)(45,51)(46,52)(47,53),
( 2, 3)( 5, 6)( 9,10)(12,13)(15,16)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)
(38,39)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)
(73,74)(76,77)(79,80),(54,60,57)(55,61,58)(56,62,59)],
["ConstructProj",[["ON",[]],,["3.ON",[17,17,-1,-1,-1,-1,-1,-55,-55,-1,-1,-1,
-1,-1,-1,17,17,41,41,-1,-37,-37,-37,-61,-61]]]]);
ARC("3.ON","CAS",[rec(name:="3.on",
permchars:=(26,28,27)(35,37)(36,38)(41,43)(42,44),
permclasses:=(48,51)(49,52)(50,53),
text:="")]);
ARC("3.ON","maxes",["3xL3(7).2","3xONM2","3xJ1","12_2.L3(4).2_1","3.ONM5",
"3.ONM6","3xL2(31)","3xONM8","3x4^3.L3(2)","3xM11","3xONM11","3.A7","3.A7"]);
ALF("3.ON","ON",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,8,8,8,9,9,9,10,10,10,
11,11,11,12,12,12,13,13,13,14,15,15,15,16,17,18,18,18,19,19,19,20,20,20,
21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,26,26,26,27,27,27,28,28,28,
29,29,29,30,30,30]);
ALF("3.ON","3.ON.2",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,12,13,14,14,15,16,
16,17,18,19,17,19,18,20,21,21,22,23,23,24,25,26,26,27,28,29,30,31,32,33,
34,29,31,30,32,34,33,35,36,36,37,38,38,39,40,40,41,42,43,41,43,42,44,45,
45,46,47,47,48,49,50,48,50,49],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("3.ON",["3.O'N","3.ON.2M1"]);

MOT("3.ON.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19,31]"
],
[2764893035520,1382446517760,967680,483840,6480,483840,241920,1536,768,1080,
540,144,8232,4116,294,147,96,96,96,120,60,66,33,72,168,84,90,90,48,48,48,48,
48,48,114,57,114,57,114,57,60,60,60,168,84,168,84,93,93,93,351120,60,1344,
1344,32,60,60,14,22,24,24,30,30,38,38,38,56,56,56,56],
[,[1,2,1,2,5,3,4,3,4,10,11,5,13,14,15,16,8,9,9,10,11,22,23,12,13,14,28,27,17,
19,18,17,19,18,37,38,39,40,35,36,20,21,21,25,26,25,26,48,50,49,1,5,6,6,8,10,
10,15,22,24,24,28,27,37,39,35,44,44,46,46],[1,1,3,3,1,6,6,8,8,10,10,3,13,13,
15,15,17,17,17,20,20,22,22,6,25,25,10,10,32,32,32,29,29,29,37,37,39,39,35,35,
41,41,41,44,44,46,46,48,48,48,51,51,54,53,55,57,56,58,59,54,53,57,56,65,66,64,
68,67,70,69],,[1,2,3,4,5,6,7,8,9,1,2,12,13,14,15,16,17,19,18,3,4,22,23,24,25,
26,5,5,32,34,33,29,31,30,37,38,39,40,35,36,6,7,7,46,47,44,45,48,50,49,51,52,
54,53,55,51,51,58,59,61,60,52,52,65,66,64,70,69,68,67],,[1,2,3,4,5,6,7,8,9,10,
11,12,1,2,1,2,17,18,19,20,21,22,23,24,3,4,28,27,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,6,7,6,7,48,49,50,51,52,53,54,55,57,56,51,59,60,61,63,62,64,65,
66,53,54,53,54],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,18,20,21,1,2,
24,25,26,27,28,32,34,33,29,31,30,35,36,37,38,39,40,41,42,43,46,47,44,45,48,49,
50,51,52,54,53,55,56,57,58,51,61,60,62,63,64,65,66,70,69,68,67],,,,,,,,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,32,33,34,
29,30,31,1,2,1,2,1,2,41,43,42,44,45,46,47,48,49,50,51,52,54,53,55,56,57,58,59,
61,60,62,63,51,51,51,68,67,70,69],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,43,42,44,45,46,47,1,2,2,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70]],
0,
[(49,50),(44,46)(45,47)(67,69)(68,70),(42,43),(42,43)(44,46)(45,47)(67,69)
(68,70),(35,37,39)(36,38,40)(64,65,66),(29,32)(30,33)(31,34)(42,43)(44,46)
(45,47)(53,54)(60,61)(67,70)(68,69),(27,28)(56,57)(62,63),(27,28)(42,43)
(56,57)(62,63),(18,19)(30,31)(33,34),(18,19)(30,31)(33,34)(42,43)(49,50),
(29,32)(30,33)(31,34)(53,54)(60,61)(67,68)(69,70)],
["ConstructMGA","3.ON","ON.2",
     [ [ 31, 34 ], [ 32, 33 ], [ 35, 38 ], [ 36, 37 ], [ 39, 40 ],
        [ 41, 44 ], [ 42, 43 ], [ 45, 46 ], [ 47, 48 ], [ 49, 50 ],
        [ 51, 52 ], [ 53, 54 ], [ 55, 56 ], [ 57, 58 ], [ 59, 60 ],
        [ 61, 62 ], [ 63, 64 ], [ 65, 68 ], [ 66, 67 ], [ 69, 70 ],
        [ 71, 72 ], [ 73, 74 ], [ 75, 76 ], [ 77, 80 ], [ 78, 79 ] ], ()]);
ALF("3.ON.2","ON.2",[1,1,2,2,3,4,4,5,5,6,6,7,8,8,9,9,10,10,10,11,11,12,12,
13,14,14,15,16,17,17,17,18,18,18,19,19,20,20,21,21,22,22,22,23,23,24,24,
25,25,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]);
ALN("3.ON.2",["3.O'N.2"]);

MOT("3.Suz",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
[1345036492800,1345036492800,1345036492800,9953280,9953280,9953280,483840,
483840,483840,29393280,29393280,29393280,104976,104976,104976,3240,138240,
138240,138240,9216,9216,9216,4608,4608,4608,864,864,864,5400,5400,5400,900,
900,900,10368,10368,10368,3888,3888,3888,3888,3888,3888,1296,1296,1296,72,252,
252,252,576,576,576,192,192,192,96,96,96,162,162,162,162,162,162,120,120,120,
60,60,60,33,33,33,864,864,864,216,216,216,144,144,144,36,72,72,72,39,39,39,39,
39,39,84,84,84,45,45,45,45,45,54,54,54,54,54,54,60,60,60,63,63,63,63,63,63,72,
72,72],
[,[1,3,2,1,3,2,1,3,2,10,12,11,13,15,14,16,4,6,5,4,6,5,4,6,5,7,9,8,29,31,30,32,
34,33,10,12,11,13,15,14,13,15,14,13,15,14,16,48,50,49,17,19,18,20,22,21,23,25,
24,63,65,64,60,62,61,29,31,30,32,34,33,72,74,73,35,37,36,44,46,45,35,37,36,47,
44,46,45,91,93,92,88,90,89,48,50,49,98,97,99,101,100,63,65,64,60,62,61,66,68,
67,114,116,115,111,113,112,75,77,76],[1,1,1,4,4,4,7,7,7,1,1,1,1,1,1,1,17,17,
17,20,20,20,23,23,23,26,26,26,29,29,29,32,32,32,4,4,4,4,4,4,4,4,4,4,4,4,7,48,
48,48,51,51,51,54,54,54,57,57,57,15,15,15,14,14,14,66,66,66,69,69,69,72,72,72,
17,17,17,17,17,17,23,23,23,26,20,20,20,88,88,88,91,91,91,94,94,94,29,29,32,32,
32,40,40,40,42,42,42,108,108,108,48,48,48,48,48,48,51,51,51],,[1,3,2,4,6,5,7,
9,8,10,12,11,13,15,14,16,17,19,18,20,22,21,23,25,24,26,28,27,1,3,2,1,3,2,35,
37,36,41,43,42,38,40,39,44,46,45,47,48,50,49,51,53,52,54,56,55,57,59,58,63,65,
64,60,62,61,4,6,5,7,9,8,72,74,73,75,77,76,78,80,79,81,83,82,84,85,87,86,91,93,
92,88,90,89,94,96,95,16,16,10,12,11,105,107,106,102,104,103,17,19,18,111,113,
112,114,116,115,117,119,118],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,1,2,3,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,91,92,93,88,89,90,7,8,9,98,97,
99,100,101,102,103,104,105,106,107,108,109,110,10,11,12,10,11,12,117,118,
119],,,,[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,16,17,19,18,20,22,21,23,25,24,26,
28,27,29,31,30,32,34,33,35,37,36,41,43,42,38,40,39,44,46,45,47,48,50,49,51,53,
52,54,56,55,57,59,58,63,65,64,60,62,61,66,68,67,69,71,70,1,3,2,75,77,76,78,80,
79,81,83,82,84,85,87,86,91,93,92,88,90,89,94,96,95,97,98,99,101,100,105,107,
106,102,104,103,108,110,109,114,116,115,111,113,112,117,119,118],,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,1,2,3,1,2,3,94,95,96,98,97,99,100,101,102,103,104,105,106,107,108,
109,110,114,115,116,111,112,113,117,118,119]],
0,
[(111,114)(112,115)(113,116),(97,98),(88,91)(89,92)(90,93),(  2,  3)(  5,  6)
(  8,  9)( 11, 12)( 14, 15)( 18, 19)( 21, 22)( 24, 25)( 27, 28)( 30, 31)
( 33, 34)( 36, 37)( 38, 41)( 39, 43)( 40, 42)( 45, 46)( 49, 50)( 52, 53)
( 55, 56)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 70, 71)( 73, 74)
( 76, 77)( 79, 80)( 82, 83)( 86, 87)( 89, 90)( 92, 93)( 95, 96)(100,101)
(102,105)(103,107)(104,106)(109,110)(111,114)(112,116)(113,115)(118,119),
(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 18, 19)( 21, 22)( 24, 25)
( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 38, 41)( 39, 43)( 40, 42)( 45, 46)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)
( 70, 71)( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 86, 87)( 89, 90)( 92, 93)
( 95, 96)(100,101)(102,105)(103,107)(104,106)(109,110)(112,113)(115,116)
(118,119)],
["ConstructProj",[["Suz",[]],,["3.Suz",[-1,-1,-1,-1,-1,-1,-13,-13,-1,-1,-25,
-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]]]]);
ARC("3.Suz","maxes",["3xG2(4)","3^2.U4(3).2_3'","3xU5(2)","3x2^(1+6)_-.U4(2)",
"3^6.M11","3xJ2.2","3x2^(4+6).3A6","(A4x3.L3(4)).2","3x2^(2+8):(A5xS3)",
"3xM12.2","3.3^(2+4):2(A4x2^2).2","(3.A6xA5):2","(3^(1+2):4xA6).2",
"3xL3(3).2","3xL3(3).2","3xL2(25)","3.A7"]);
ALF("3.Suz","Suz",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,7,7,7,8,8,8,9,9,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,18,18,18,
19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,26,26,26,
27,27,27,28,28,28,29,29,29,30,31,31,31,32,32,32,33,33,33,34,34,34,35,36,
37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,43,43,43]);
ALF("3.Suz","3.Suz.2",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,13,13,14,15,
15,16,17,17,18,19,19,20,21,21,22,23,23,24,25,25,26,27,28,26,28,27,29,30,
30,31,32,33,33,34,35,35,36,37,37,38,39,39,40,41,42,40,42,41,43,44,44,45,
46,46,47,48,48,49,50,50,51,52,52,53,54,54,55,56,57,57,58,59,60,58,60,59,
61,62,62,63,63,64,65,65,66,67,68,66,68,67,69,70,70,71,72,73,71,73,72,74,
75,75],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("3.Suz.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
[2690072985600,1345036492800,19906560,9953280,967680,483840,58786560,29393280,
209952,104976,6480,276480,138240,18432,9216,9216,4608,1728,864,10800,5400,
1800,900,20736,10368,3888,3888,3888,2592,1296,144,504,252,1152,576,384,192,
192,96,162,162,162,240,120,120,60,66,33,1728,864,432,216,288,144,72,144,72,39,
39,39,168,84,45,90,45,54,54,54,120,60,63,63,63,144,72,2419200,380160,4608,
1344,4320,216,144,144,46080,3072,768,256,192,600,100,40,288,72,24,28,16,22,
288,96,72,24,24,28,30,40,40],
[,[1,2,1,2,1,2,7,8,9,10,11,3,4,3,4,3,4,5,6,20,21,22,23,7,8,9,10,10,9,10,11,32,
33,12,13,14,15,16,17,40,41,42,20,21,22,23,47,48,24,25,29,30,24,25,31,29,30,58,
59,60,32,33,63,64,65,40,41,42,43,44,71,72,73,49,50,1,1,3,5,7,9,11,11,12,12,12,
12,16,22,20,22,24,29,31,32,36,47,49,49,51,51,53,61,64,69,69],[1,1,3,3,5,5,1,1,
1,1,1,12,12,14,14,16,16,18,18,20,20,22,22,3,3,3,3,3,3,3,5,32,32,34,34,36,36,
38,38,10,10,10,43,43,45,45,47,47,12,12,12,12,16,16,18,14,14,58,58,58,61,61,20,
22,22,28,28,28,69,69,32,32,32,34,34,76,77,78,79,76,77,76,77,84,85,86,87,88,89,
90,91,78,78,79,95,96,97,84,85,84,86,88,103,89,105,106],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,1,2,1,2,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,3,4,5,6,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,11,7,8,
66,67,68,12,13,71,73,72,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,76,76,77,
92,93,94,95,96,97,98,99,100,101,102,103,80,84,84],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,1,2,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,60,59,5,6,63,
64,65,66,67,68,69,70,7,8,8,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,76,96,97,98,99,100,101,102,79,104,106,105],,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,1,2,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,77,98,99,100,101,102,103,104,106,105],,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,1,
2,2,61,62,63,64,65,66,67,68,69,70,71,73,72,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106]],
0,
[(105,106),(72,73),(59,60)],
["ConstructMGA","3.Suz","Suz.2",
     [ [ 44, 45 ], [ 46, 47 ], [ 48, 49 ], [ 50, 51 ], [ 52, 53 ],
        [ 54, 55 ], [ 56, 57 ], [ 58, 59 ], [ 60, 61 ], [ 62, 63 ],
        [ 64, 67 ], [ 65, 66 ], [ 68, 69 ], [ 70, 71 ], [ 72, 73 ],
        [ 74, 75 ], [ 76, 77 ], [ 78, 79 ], [ 80, 81 ], [ 82, 83 ],
        [ 84, 85 ], [ 86, 87 ], [ 88, 89 ], [ 90, 91 ], [ 92, 93 ],
        [ 94, 95 ], [ 96, 97 ], [ 98, 99 ], [ 100, 101 ], [ 102, 103 ],
        [ 104, 105 ], [ 106, 107 ], [ 108, 109 ], [ 110, 111 ], [ 112, 113 ],
        [ 114, 115 ], [ 116, 117 ], [ 118, 119 ] ], ()]);
ARC("3.Suz.2","maxes",["3.Suz",
"(3xG2(4)).2",
"3^2.U4(3).(2^2)_{133}",
"(3xU5(2)).2",
"(3x2^(1+6)_-.U4(2)).2",
"3^6:(M11x2)",
"S3xJ2.2",
"(3x2^(4+6):3A6).2",
"(A4x3.L3(4).2_3).2",
"(3x2^(2+8):(A5xS3)).2",
"S3xM12.2",
"3.3^(2+4):2(S4xD8)",
"(3.A6.2_2xA5):2",
"(3^(1+2):8xA6).2",
"(3xL2(25)).2_2",
"3.A7.2"]);
ALF("3.Suz.2","Co1",[1,5,2,18,3,19,5,6,6,7,8,9,45,10,46,12,47,13,50,15,61,
16,62,18,22,20,21,23,22,23,25,27,74,29,80,31,81,34,83,36,37,35,38,89,40,
90,44,94,45,49,49,48,47,54,56,51,55,58,97,98,59,100,63,62,64,69,70,68,71,
101,74,75,75,80,82,3,4,12,13,19,24,25,26,29,29,30,30,34,40,39,43,47,54,56,
59,66,77,80,80,82,84,83,88,90,99,99],[
"fusion map is unique up to table automorphisms"
]);
ALF("3.Suz.2","Suz.2",[1,1,2,2,3,3,4,4,5,5,6,7,7,8,8,9,9,10,10,11,11,12,
12,13,13,14,14,14,15,15,16,17,17,18,18,19,19,20,20,21,21,21,22,22,23,23,
24,24,25,25,26,26,27,27,28,29,29,30,30,30,31,31,32,33,33,34,34,34,35,35,
36,36,36,37,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68]);
ALN("3.Suz.2",["Co1N3A"]);

MOT("6.Suz",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
[2690072985600,2690072985600,2690072985600,2690072985600,2690072985600,
2690072985600,19906560,19906560,19906560,19906560,19906560,19906560,483840,
483840,483840,58786560,58786560,58786560,58786560,58786560,58786560,209952,
209952,209952,209952,209952,209952,6480,6480,276480,276480,276480,276480,
276480,276480,9216,9216,9216,4608,4608,4608,864,864,864,10800,10800,10800,
10800,10800,10800,1800,1800,1800,1800,1800,1800,20736,20736,20736,20736,20736,
20736,7776,7776,7776,7776,7776,7776,7776,7776,7776,7776,7776,7776,2592,2592,
2592,2592,2592,2592,72,504,504,504,504,504,504,576,576,576,384,384,384,384,
384,384,96,96,96,324,324,324,324,324,324,324,324,324,324,324,324,240,240,240,
240,240,240,60,60,60,66,66,66,66,66,66,1728,1728,1728,1728,1728,1728,432,432,
432,432,432,432,144,144,144,72,72,144,144,144,144,144,144,78,78,78,78,78,78,
78,78,78,78,78,78,84,84,84,90,90,90,90,90,90,90,90,90,90,108,108,108,108,108,
108,108,108,108,108,108,108,120,120,120,120,120,120,126,126,126,126,126,126,
126,126,126,126,126,126,144,144,144,144,144,144],
[,[1,3,5,1,3,5,1,3,5,1,3,5,4,6,2,16,18,20,16,18,20,22,24,26,22,24,26,28,28,7,
9,11,7,9,11,7,9,11,10,12,8,13,15,14,45,47,49,45,47,49,51,53,55,51,53,55,16,18,
20,16,18,20,22,24,26,22,24,26,22,24,26,22,24,26,22,24,26,22,24,26,29,82,84,86,
82,84,86,30,32,34,36,38,37,36,38,37,39,41,40,106,108,110,106,108,110,100,102,
104,100,102,104,45,47,49,45,47,49,54,56,52,121,123,125,121,123,125,57,59,61,
57,59,61,75,77,79,75,77,79,60,62,58,81,81,75,77,79,75,77,79,156,158,160,156,
158,160,150,152,154,150,152,154,85,87,83,167,167,165,165,169,171,173,169,171,
173,106,108,110,106,108,110,100,102,104,100,102,104,112,114,116,112,114,116,
199,201,203,199,201,203,193,195,197,193,195,197,127,129,131,127,129,131],[1,4,
1,4,1,4,7,10,7,10,7,10,13,13,13,1,4,1,4,1,4,1,4,1,4,1,4,1,4,30,33,30,33,30,33,
36,36,36,39,39,39,42,42,42,45,48,45,48,45,48,51,54,51,54,51,54,7,10,7,10,7,10,
7,10,7,10,7,10,7,10,7,10,7,10,7,10,7,10,7,10,13,82,85,82,85,82,85,88,88,88,91,
94,91,94,91,94,97,97,97,24,27,24,27,24,27,26,23,26,23,26,23,112,115,112,115,
112,115,118,118,118,121,124,121,124,121,124,30,33,30,33,30,33,30,33,30,33,30,
33,39,39,39,42,42,36,36,36,36,36,36,150,153,150,153,150,153,156,159,156,159,
156,159,162,162,162,45,48,45,48,51,54,51,54,51,54,65,68,65,68,65,68,73,70,73,
70,73,70,187,190,187,190,187,190,82,85,82,85,82,85,82,85,82,85,82,85,88,88,88,
88,88,88],,[1,6,5,4,3,2,7,12,11,10,9,8,13,15,14,16,21,20,19,18,17,22,27,26,25,
24,23,28,29,30,35,34,33,32,31,36,38,37,39,41,40,42,44,43,1,6,5,4,3,2,1,6,5,4,
3,2,57,62,61,60,59,58,69,74,73,72,71,70,63,68,67,66,65,64,75,80,79,78,77,76,
81,82,87,86,85,84,83,88,90,89,91,96,95,94,93,92,97,99,98,106,111,110,109,108,
107,100,105,104,103,102,101,7,12,11,10,9,8,13,15,14,121,126,125,124,123,122,
127,132,131,130,129,128,133,138,137,136,135,134,139,141,140,143,142,147,146,
145,144,149,148,156,161,160,159,158,157,150,155,154,153,152,151,162,164,163,
28,29,28,29,16,21,20,19,18,17,181,186,185,184,183,182,175,180,179,178,177,176,
30,35,34,33,32,31,193,198,197,196,195,194,199,204,203,202,201,200,208,207,206,
205,210,209],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,1,2,3,4,5,6,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143,144,145,146,147,148,149,156,157,158,159,160,161,150,151,152,153,
154,155,13,14,15,167,168,165,166,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,187,188,189,190,191,192,16,17,18,19,20,21,16,17,
18,19,20,21,208,209,210,205,206,207],,,,[1,6,5,4,3,2,7,12,11,10,9,8,13,15,14,
16,21,20,19,18,17,22,27,26,25,24,23,28,29,30,35,34,33,32,31,36,38,37,39,41,40,
42,44,43,45,50,49,48,47,46,51,56,55,54,53,52,57,62,61,60,59,58,69,74,73,72,71,
70,63,68,67,66,65,64,75,80,79,78,77,76,81,82,87,86,85,84,83,88,90,89,91,96,95,
94,93,92,97,99,98,106,111,110,109,108,107,100,105,104,103,102,101,112,117,116,
115,114,113,118,120,119,1,6,5,4,3,2,127,132,131,130,129,128,133,138,137,136,
135,134,139,141,140,143,142,147,146,145,144,149,148,156,161,160,159,158,157,
150,155,154,153,152,151,162,164,163,165,166,167,168,169,174,173,172,171,170,
181,186,185,184,183,182,175,180,179,178,177,176,187,192,191,190,189,188,199,
204,203,202,201,200,193,198,197,196,195,194,205,210,209,208,207,206],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,143,142,144,
145,146,147,148,149,1,2,3,4,5,6,1,2,3,4,5,6,162,163,164,167,168,165,166,169,
170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,
189,190,191,192,199,200,201,202,203,204,193,194,195,196,197,198,205,206,207,
208,209,210]],
0,
[(205,208)(206,209)(207,210),(193,199)(194,200)(195,201)(196,202)(197,203)
(198,204),(165,167)(166,168),(150,156)(151,157)(152,158)(153,159)(154,160)
(155,161),(142,143),(142,143)(205,208)(206,209)(207,210),(  2,  6)(  3,  5)
(  8, 12)(  9, 11)( 14, 15)( 17, 21)( 18, 20)( 23, 27)( 24, 26)( 31, 35)
( 32, 34)( 37, 38)( 40, 41)( 43, 44)( 46, 50)( 47, 49)( 52, 56)( 53, 55)
( 58, 62)( 59, 61)( 63, 69)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)
( 76, 80)( 77, 79)( 83, 87)( 84, 86)( 89, 90)( 92, 96)( 93, 95)( 98, 99)
(100,106)(101,111)(102,110)(103,109)(104,108)(105,107)(113,117)(114,116)
(119,120)(122,126)(123,125)(128,132)(129,131)(134,138)(135,137)(140,141)
(144,147)(145,146)(148,149)(151,155)(152,154)(157,161)(158,160)(163,164)
(170,174)(171,173)(175,181)(176,186)(177,185)(178,184)(179,183)(180,182)
(188,192)(189,191)(193,199)(194,204)(195,203)(196,202)(197,201)(198,200)
(205,208)(206,207)(209,210),(  2,  6)(  3,  5)(  8, 12)(  9, 11)( 14, 15)
( 17, 21)( 18, 20)( 23, 27)( 24, 26)( 31, 35)( 32, 34)( 37, 38)( 40, 41)
( 43, 44)( 46, 50)( 47, 49)( 52, 56)( 53, 55)( 58, 62)( 59, 61)( 63, 69)
( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)( 76, 80)( 77, 79)( 83, 87)
( 84, 86)( 89, 90)( 92, 96)( 93, 95)( 98, 99)(100,106)(101,111)(102,110)
(103,109)(104,108)(105,107)(113,117)(114,116)(119,120)(122,126)(123,125)
(128,132)(129,131)(134,138)(135,137)(140,141)(144,147)(145,146)(148,149)
(151,155)(152,154)(157,161)(158,160)(163,164)(170,174)(171,173)(175,181)
(176,186)(177,185)(178,184)(179,183)(180,182)(188,192)(189,191)(194,198)
(195,197)(200,204)(201,203)(206,210)(207,209)],
["ConstructProj",[["Suz",[]],["2.Suz",[]],["3.Suz",[-1,-1,-1,-1,-1,-1,-13,-13,
-1,-1,-25,-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]],,,["6.Suz",[-1,-1,-1,-1,-1,-1,-7,-7,-1,-1,-1,-1,-1,-1,-13,
-13,-1,-25,-25,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ARC("6.Suz","CAS",[rec(name:="6.suz",
permchars:=(45,46)(47,48)(52,53)(54,56)(55,57)(90,92,91)(98,99)(124,125)
(159,160,162,161)(165,166,167)(170,172,173,171)(177,178,180,179)(182,184,
183)(188,189)(200,201),
permclasses:=(63,69)(64,70)(65,71)(66,72)(67,73)(68,74),
text:="")]);
ALF("6.Suz","Suz",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,
6,6,7,7,7,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,
13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,
17,18,18,18,18,18,18,19,19,19,20,20,20,20,20,20,21,21,21,22,22,22,22,22,
22,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,26,26,26,26,26,26,27,27,
27,27,27,27,28,28,28,28,28,28,29,29,29,30,30,31,31,31,31,31,31,32,32,32,
32,32,32,33,33,33,33,33,33,34,34,34,35,35,36,36,37,37,37,37,37,37,38,38,
38,38,38,38,39,39,39,39,39,39,40,40,40,40,40,40,41,41,41,41,41,41,42,42,
42,42,42,42,43,43,43,43,43,43]);
ALF("6.Suz","2.Suz",[1,2,1,2,1,2,3,4,3,4,3,4,5,5,5,6,7,6,7,6,7,8,9,8,9,8,
9,10,11,12,13,12,13,12,13,14,14,14,15,15,15,16,16,16,17,18,17,18,17,18,19,
20,19,20,19,20,21,22,21,22,21,22,23,24,23,24,23,24,25,26,25,26,25,26,27,
28,27,28,27,28,29,30,31,30,31,30,31,32,32,32,33,34,33,34,33,34,35,35,35,
36,37,36,37,36,37,38,39,38,39,38,39,40,41,40,41,40,41,42,42,42,43,44,43,
44,43,44,45,46,45,46,45,46,47,48,47,48,47,48,49,49,49,50,51,52,53,52,53,
52,53,54,55,54,55,54,55,56,57,56,57,56,57,58,58,58,59,60,61,62,63,64,63,
64,63,64,65,66,65,66,65,66,67,68,67,68,67,68,69,70,69,70,69,70,71,72,71,
72,71,72,73,74,73,74,73,74,75,76,75,76,75,76]);
ALF("6.Suz","3.Suz",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,10,11,12,10,11,12,13,
14,15,13,14,15,16,16,17,18,19,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,29,30,31,32,33,34,32,33,34,35,36,37,35,36,37,38,39,40,38,39,40,41,42,
43,41,42,43,44,45,46,44,45,46,47,48,49,50,48,49,50,51,52,53,54,55,56,54,
55,56,57,58,59,60,61,62,60,61,62,63,64,65,63,64,65,66,67,68,66,67,68,69,
70,71,72,73,74,72,73,74,75,76,77,75,76,77,78,79,80,78,79,80,81,82,83,84,
84,85,86,87,85,86,87,88,89,90,88,89,90,91,92,93,91,92,93,94,95,96,97,97,
98,98,99,100,101,99,100,101,102,103,104,102,103,104,105,106,107,105,106,
107,108,109,110,108,109,110,111,112,113,111,112,113,114,115,116,114,115,
116,117,118,119,117,118,119]);
ALF("6.Suz","6.Suz.2",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,10,11,12,13,14,13,12,
15,16,17,18,17,16,19,20,21,22,23,24,23,22,25,26,26,27,28,28,29,30,30,31,
32,33,34,33,32,35,36,37,38,37,36,39,40,41,42,41,40,43,44,45,46,47,48,43,
48,47,46,45,44,49,50,51,52,51,50,53,54,55,56,57,56,55,58,59,59,60,61,62,
63,62,61,64,65,65,66,67,68,69,70,71,66,71,70,69,68,67,72,73,74,75,74,73,
76,77,77,78,79,80,81,80,79,82,83,84,85,84,83,86,87,88,89,88,87,90,91,91,
92,92,93,94,94,93,95,95,96,97,98,99,100,101,96,101,100,99,98,97,102,103,
103,104,105,104,105,106,107,108,109,108,107,110,111,112,113,114,115,110,
115,114,113,112,111,116,117,118,119,118,117,120,121,122,123,124,125,120,
125,124,123,122,121,126,127,127,126,128,128],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ARC("6.Suz","maxes",["3x2.G2(4)","Isoclinic((3^2x2).U4(3).2_3')","6xU5(2)",
"3x2.SuzM4","2x3^6.M11","3x2.J2.2","3x2.SuzM7","6.SuzM8","3x2.SuzM9",
"3xIsoclinic(2.M12.2)","6.SuzM11","(3.A6x2.A5).2","(3^(1+2):4x2.A6).2",
"3x(2xL3(3)).2","3x(2xL3(3)).2","3x2.L2(25)","6.A7"]);
ALN("6.Suz",["6.Suz.2M1"]);

MOT("6.Suz.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
[5380145971200,2690072985600,2690072985600,5380145971200,39813120,19906560,
19906560,39813120,967680,483840,117573120,58786560,58786560,117573120,419904,
209952,209952,419904,12960,12960,552960,276480,276480,552960,18432,9216,9216,
4608,1728,864,21600,10800,10800,21600,3600,1800,1800,3600,41472,20736,20736,
41472,7776,7776,7776,7776,7776,7776,5184,2592,2592,5184,144,1008,504,504,1008,
1152,576,768,384,384,768,192,96,324,324,324,324,324,324,480,240,240,480,120,
60,132,66,66,132,3456,1728,1728,3456,864,432,432,864,288,144,72,144,144,144,
78,78,78,78,78,78,168,84,90,90,180,90,90,180,108,108,108,108,108,108,240,120,
120,240,126,126,126,126,126,126,144,144,144,2419200,380160,4608,1344,4320,216,
144,144,92160,92160,3072,1536,1536,256,384,384,1200,1200,200,200,40,288,72,24,
28,32,32,44,44,576,576,96,144,144,48,48,48,48,56,56,60,60,80,80,80,80],
[,[1,3,3,1,1,3,3,1,4,2,11,13,13,11,15,17,17,15,19,19,5,7,7,5,5,7,8,6,9,10,31,
33,33,31,35,37,37,35,11,13,13,11,15,17,17,15,17,17,15,17,17,15,20,54,56,56,54,
21,23,25,26,26,25,27,28,66,70,68,66,70,68,31,33,33,31,38,36,78,80,80,78,39,41,
41,39,49,51,51,49,42,40,53,49,51,51,96,100,98,96,100,98,57,55,104,104,106,108,
108,106,66,70,68,66,70,68,72,74,74,72,120,124,122,120,124,122,82,84,84,4,1,8,
9,14,15,20,19,21,21,21,24,24,24,27,27,38,38,34,34,35,42,52,53,57,60,60,78,78,
82,82,82,86,86,89,89,90,90,102,102,109,109,116,116,116,116],[1,4,1,4,5,8,5,8,
9,9,1,4,1,4,1,4,1,4,1,4,21,24,21,24,25,25,27,27,29,29,31,34,31,34,35,38,35,38,
5,8,5,8,5,8,5,8,5,8,5,8,5,8,9,54,57,54,57,58,58,60,63,60,63,64,64,17,16,17,16,
17,16,72,75,72,75,76,76,78,81,78,81,21,24,21,24,21,24,21,24,27,27,29,25,25,25,
96,99,96,99,96,99,102,102,31,34,35,38,35,38,45,48,45,48,45,48,116,119,116,119,
54,57,54,57,54,57,58,58,58,129,130,131,132,129,130,129,130,137,138,139,140,
141,142,143,144,145,146,147,148,149,131,131,132,153,154,155,156,157,137,138,
139,137,138,140,141,143,144,167,168,145,146,171,172,173,174],,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,2,3,4,1,
2,3,4,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,
63,64,65,66,67,68,69,70,71,5,6,7,8,9,10,78,79,80,81,82,83,84,85,86,87,88,89,
90,91,92,93,94,95,96,97,98,99,100,101,102,103,19,20,11,12,13,14,110,111,112,
113,114,115,21,22,23,24,120,125,124,123,122,121,126,127,128,129,130,131,132,
133,134,135,136,138,137,139,141,140,142,144,143,129,129,129,129,130,150,151,
152,153,155,154,156,157,159,158,160,162,161,164,163,166,165,167,168,133,133,
138,137,138,137],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,1,2,3,4,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,
76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,101,100,99,98,
97,9,10,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,11,12,
13,14,13,12,126,128,127,129,130,131,132,133,134,135,136,138,137,139,141,140,
142,144,143,145,146,147,148,149,150,151,152,129,155,154,157,156,159,158,160,
162,161,164,163,166,165,132,132,169,170,174,173,172,171],,,,[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,1,2,3,4,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,128,127,
129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,146,145,148,
147,149,150,151,152,153,154,155,130,130,158,159,160,161,162,163,164,165,166,
168,167,170,169,173,174,171,172],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,
1,2,3,4,3,2,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,
118,119,120,125,124,123,122,121,126,127,128,129,130,131,132,133,134,135,136,
138,137,139,141,140,142,144,143,146,145,148,147,149,150,151,152,153,155,154,
157,156,159,158,160,162,161,164,163,166,165,167,168,170,169,172,171,174,173]],
0,
[(167,168),(156,157),(145,146)(147,148)(169,170)(171,173)(172,174),(127,128),
(127,128)(145,146)(147,148)(167,168)(169,170)(171,173)(172,174),(127,128)
(137,138)(140,141)(143,144)(145,146)(147,148)(154,155)(158,159)(161,162)
(163,164)(165,166)(169,170)(171,172)(173,174),(121,125)(122,124),(121,125)
(122,124)(167,168),( 97,101)( 98,100),(137,138)(140,141)(143,144)(154,155)
(158,159)(161,162)(163,164)(165,166)(171,174)(172,173)],
["ConstructMGA","6.Suz","2.Suz.2",
     [ [ 77, 78 ], [ 79, 80 ], [ 81, 82 ], [ 83, 84 ], [ 85, 86 ],
        [ 87, 88 ], [ 89, 90 ], [ 91, 92 ], [ 93, 94 ], [ 95, 96 ],
        [ 97, 100 ], [ 98, 99 ], [ 101, 102 ], [ 103, 104 ], [ 105, 106 ],
        [ 107, 108 ], [ 109, 110 ], [ 111, 112 ], [ 113, 114 ], [ 115, 116 ],
        [ 117, 118 ], [ 119, 120 ], [ 121, 122 ], [ 123, 124 ], [ 125, 126 ],
        [ 127, 128 ], [ 129, 130 ], [ 131, 132 ], [ 133, 134 ], [ 135, 136 ],
        [ 137, 138 ], [ 139, 140 ], [ 141, 142 ], [ 143, 144 ], [ 145, 146 ],
        [ 147, 148 ], [ 149, 150 ], [ 151, 152 ], [ 153, 154 ], [ 155, 156 ],
        [ 157, 158 ], [ 159, 160 ], [ 161, 162 ], [ 163, 164 ], [ 165, 166 ],
        [ 167, 168 ], [ 169, 170 ], [ 171, 172 ], [ 173, 174 ], [ 175, 176 ],
        [ 177, 178 ], [ 179, 180 ], [ 181, 182 ], [ 183, 184 ], [ 185, 186 ],
        [ 187, 190 ], [ 188, 189 ], [ 191, 192 ], [ 193, 194 ], [ 195, 196 ],
        [ 197, 198 ], [ 199, 200 ], [ 201, 202 ], [ 203, 204 ], [ 205, 206 ],
        [ 207, 208 ], [ 209, 210 ] ], ()]);
ALF("6.Suz.2","Suz.2",[1,1,1,1,2,2,2,2,3,3,4,4,4,4,5,5,5,5,6,6,7,7,7,7,8,
8,9,9,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,14,15,15,
15,15,16,17,17,17,17,18,18,19,19,19,19,20,20,21,21,21,21,21,21,22,22,22,
22,23,23,24,24,24,24,25,25,25,25,26,26,26,26,27,27,28,29,29,29,30,30,30,
30,30,30,31,31,32,32,33,33,33,33,34,34,34,34,34,34,35,35,35,35,36,36,36,
36,36,36,37,37,37,38,39,40,41,42,43,44,45,46,46,47,48,48,49,50,50,51,51,
52,52,53,54,55,56,57,58,58,59,59,60,60,61,62,62,63,63,64,64,65,65,66,66,
67,67,68,68]);
ALF("6.Suz.2","2.Suz.2",[1,2,1,2,3,4,3,4,5,5,6,7,6,7,8,9,8,9,10,11,12,13,
12,13,14,14,15,15,16,16,17,18,17,18,19,20,19,20,21,22,21,22,23,24,23,24,
23,24,25,26,25,26,27,28,29,28,29,30,30,31,32,31,32,33,33,34,35,34,35,34,
35,36,37,36,37,38,38,39,40,39,40,41,42,41,42,43,44,43,44,45,45,46,47,47,
47,48,49,48,49,48,49,50,50,51,52,53,54,53,54,55,56,55,56,55,56,57,58,57,
58,59,60,59,60,59,60,61,61,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,
76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107]);
ALF("6.Suz.2","3.Suz.2",[1,2,2,1,3,4,4,3,5,6,7,8,8,7,9,10,10,9,11,11,12,
13,13,12,14,15,16,17,18,19,20,21,21,20,22,23,23,22,24,25,25,24,26,27,28,
26,27,28,29,30,30,29,31,32,33,33,32,34,35,36,37,37,36,38,39,40,41,42,40,
41,42,43,44,44,43,45,46,47,48,48,47,49,50,50,49,51,52,52,51,53,54,55,56,
57,57,58,59,60,58,59,60,61,62,63,63,64,65,65,64,66,67,68,66,67,68,69,70,
70,69,71,72,73,71,72,73,74,75,75,76,77,78,79,80,81,82,83,84,84,85,86,86,
87,88,88,89,89,90,90,91,92,93,94,95,96,96,97,97,98,98,99,100,100,101,101,
102,102,103,103,104,104,105,105,106,106]);
ALF("6.Suz.2","2.Co1",[1,8,7,2,4,29,30,3,5,31,7,10,9,8,9,12,11,10,13,14,
16,72,73,15,17,74,20,75,21,80,23,97,96,24,25,99,98,26,30,36,37,29,33,34,
39,32,35,38,37,38,39,36,41,43,121,120,44,47,132,49,134,133,50,54,136,57,
60,55,58,59,56,62,145,146,61,64,147,70,154,153,71,73,78,79,72,79,76,77,78,
75,86,89,81,87,88,91,160,161,92,159,162,93,165,100,101,98,103,102,99,112,
113,110,111,114,109,116,166,167,115,120,123,122,121,122,123,132,135,135,5,
6,20,21,31,40,41,42,47,47,47,48,48,48,54,54,64,64,63,63,69,75,86,89,93,
106,106,126,127,132,132,132,135,135,137,137,136,136,143,144,147,147,163,
164,164,163],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("6.Suz.2","3^(1+12):6.Suz.2",[1,76,18,5,8,89,85,11,54,240,26,81,31,80,
39,95,46,93,51,117,56,248,243,58,60,251,66,255,183,410,71,462,324,225,74,
465,327,227,100,108,115,103,146,140,125,132,120,136,155,162,166,152,300,
178,498,394,322,190,414,191,424,419,194,205,440,217,354,222,356,209,349,
228,468,469,231,391,519,236,523,482,404,263,267,270,261,277,282,287,276,
293,305,442,312,309,296,318,525,490,454,487,529,458,533,335,476,333,479,
343,472,376,380,371,368,359,364,384,516,511,387,396,500,401,507,398,504,
427,429,432,52,16,69,188,259,174,298,176,179,180,181,187,185,201,196,199,
382,383,388,389,234,289,317,453,459,345,347,407,408,417,413,441,435,434,
450,452,448,445,509,510,517,521,493,494,495,496],[
"fusion map is unique up to table automorphisms"
]);

MOT("Isoclinic(6.Suz.2)",
[
"isoclinic group of the 6.Suz.2 given in the ATLAS"
],
0,
0,
0,
[(167,168),(156,157),(127,128),(121,125)(122,124),( 97,101)( 98,100),
(145,146)(147,148)(169,170)(171,173)(172,174),
(137,138)(140,141)(143,144)(154,155)(158,159)(161,162)(163,164)(165,166)
(171,174)(172,173)
],
["ConstructIsoclinic",[["6.Suz.2"]]]);
ALF("Isoclinic(6.Suz.2)","Suz.2",[1,1,1,1,2,2,2,2,3,3,4,4,4,4,5,5,5,5,6,6,
7,7,7,7,8,8,9,9,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,
14,15,15,15,15,16,17,17,17,17,18,18,19,19,19,19,20,20,21,21,21,21,21,21,
22,22,22,22,23,23,24,24,24,24,25,25,25,25,26,26,26,26,27,27,28,29,29,29,
30,30,30,30,30,30,31,31,32,32,33,33,33,33,34,34,34,34,34,34,35,35,35,35,
36,36,36,36,36,36,37,37,37,38,39,40,41,42,43,44,45,46,46,47,48,48,49,50,
50,51,51,52,52,53,54,55,56,57,58,58,59,59,60,60,61,62,62,63,63,64,64,65,
65,66,66,67,67,68,68]);
ALF("Isoclinic(6.Suz.2)","3.Suz.2",[1,2,2,1,3,4,4,3,5,6,7,8,8,7,9,10,10,9,
11,11,12,13,13,12,14,15,16,17,18,19,20,21,21,20,22,23,23,22,24,25,25,24,
26,27,28,26,27,28,29,30,30,29,31,32,33,33,32,34,35,36,37,37,36,38,39,40,
41,42,40,41,42,43,44,44,43,45,46,47,48,48,47,49,50,50,49,51,52,52,51,53,
54,55,56,57,57,58,59,60,58,59,60,61,62,63,63,64,65,65,64,66,67,68,66,67,
68,69,70,70,69,71,72,73,71,72,73,74,75,75,76,77,78,79,80,81,82,83,84,84,
85,86,86,87,88,88,89,89,90,90,91,92,93,94,95,96,96,97,97,98,98,99,100,100,
101,101,102,102,103,103,104,104,105,105,106,106]);

MOT("F3+M14",
[
"14th maximal subgroup of F3+,\n",
"differs from F3+M13 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["He.2"]]);
ALF("F3+M14","F3+",[1,2,3,6,8,10,9,11,12,18,23,24,25,25,27,35,49,47,52,53,56,
58,72,71,70,87,3,10,14,21,23,26,26,26,36,49,53,57,57,67,79,79,91,105,104],[
"fusion He.2 -> F3+ mapped under F3+.2"
]);

MOT("HN",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19]"
],
[273030912000000,177408000,3686400,544320,29160,15360,5760,3840,630000,500000,
15000,15000,2500,1440,576,360,420,80,64,27,2000,1200,800,600,600,100,100,100,
22,72,48,12,28,180,30,30,19,19,80,80,40,20,20,21,22,25,25,60,30,30,35,35,40,
40],
[,[1,1,1,4,5,3,2,3,9,10,12,11,13,4,4,5,17,7,6,20,10,9,10,12,11,13,13,13,29,14,
15,16,17,34,36,35,38,37,23,23,22,25,24,44,29,47,46,34,36,35,52,51,41,41],[1,2,
3,1,1,6,7,8,9,10,12,11,13,2,3,3,17,18,19,5,21,22,23,25,24,26,28,27,29,7,6,8,
33,9,12,11,38,37,40,39,41,43,42,17,45,47,46,22,25,24,51,52,54,53],,[1,2,3,4,5,
6,7,8,1,1,1,1,1,14,15,16,17,18,19,20,2,2,3,3,3,2,3,3,29,30,31,32,33,4,5,5,37,
38,6,6,7,8,8,44,45,10,10,14,16,16,17,17,18,18],,[1,2,3,4,5,6,7,8,9,10,12,11,
13,14,15,16,1,18,19,20,21,22,23,25,24,26,28,27,29,30,31,32,2,34,36,35,37,38,
40,39,41,43,42,4,45,47,46,48,50,49,9,9,53,54],,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,2,46,47,48,49,50,51,52,53,54],,,,,,,,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
1,1,39,40,41,42,43,44,45,46,47,48,49,50,52,51,53,54]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[133,21,5,7,-2,5,1,-3,-7,8,
2*E(5)-3*E(5)^2-3*E(5)^3+2*E(5)^4,-3*E(5)+2*E(5)^2+2*E(5)^3-3*E(5)^4,3,3,-1,2,
0,-1,1,1,-4,1,0,-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,-3*E(5)-2*E(5)^2-2*E(5)^3
 -3*E(5)^4,1,E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,1,1,-1,0,0,
2,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,1,E(5)^2+E(5)^3,E(5)+E(5)^4,0,-1,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,-2,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,-1,-1],
[GALOIS,[2,2]],[760,56,-8,22,4,8,0,0,20,10,-10,-10,5,2,-2,4,4,0,0,1,6,-4,2,2,
2,1,-3,-3,1,0,2,0,0,2,-1,-1,0,0,-2,-2,0,0,0,1,1,0,0,2,-1,-1,-1,-1,0,0],[3344,
176,16,41,-4,16,8,0,14,-31,4,4,9,5,1,4,5,0,0,2,1,6,1,-4,-4,1,1,1,0,-1,1,0,1,
-4,1,1,0,0,1,1,-2,0,0,-1,0,-1,-1,0,-1,-1,0,0,0,0],[8778,154,-54,21,3,10,-10,2,
28,28,-13*E(5)-18*E(5)^2-18*E(5)^3-13*E(5)^4,-18*E(5)-13*E(5)^2-13*E(5)^3
 -18*E(5)^4,3,1,-3,3,0,0,-2,0,4,4,-4,-E(5)-6*E(5)^2-6*E(5)^3-E(5)^4,
-6*E(5)-E(5)^2-E(5)^3-6*E(5)^4,-1,1,1,0,-1,1,-1,0,1,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0],
[GALOIS,[6,2]],[8910,286,78,27,0,14,10,6,20,35,15,15,5,7,3,0,-1,0,2,0,11,-4,3,
3,3,1,3,3,0,1,-1,0,-1,2,0,0,-1,-1,-1,-1,0,1,1,-1,0,0,0,2,0,0,-1,-1,0,0],[9405,
77,61,36,9,-3,9,-11,55,30,5,5,5,-4,4,1,4,-1,1,0,2,7,6,1,1,-3,1,1,0,0,0,1,0,1,
-1,-1,0,0,2,2,-1,-1,-1,1,0,0,0,1,1,1,-1,-1,-1,-1],[16929,385,33,27,0,17,1,9,
29,54,-21,-21,4,7,3,0,-4,1,1,0,10,5,-2,3,3,0,-2,-2,0,1,-1,0,0,2,0,0,0,0,2,2,1,
-1,-1,-1,0,-1,-1,2,0,0,1,1,1,1],[35112,616,40,84,12,24,0,0,-28,-13,
18*E(5)-2*E(5)^2-2*E(5)^3+18*E(5)^4,-2*E(5)+18*E(5)^2+18*E(5)^3-2*E(5)^4,7,4,
4,4,0,0,0,0,-9,-4,-5,-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,
2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,1,E(5)-E(5)^2-E(5)^3+E(5)^4,
-E(5)+E(5)^2+E(5)^3-E(5)^4,0,0,0,0,0,-1,E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,-1,-1,0,
0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,-1,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,
-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,0,0,0,0],
[GALOIS,[11,2]],[65835,539,-85,63,-18,11,-1,3,-105,85,10*E(5)-15*E(5)^2
 -15*E(5)^3+10*E(5)^4,-15*E(5)+10*E(5)^2+10*E(5)^3-15*E(5)^4,5,-1,-1,2,0,1,-1,
0,-11,-1,5,-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,-3*E(5)-2*E(5)^2-2*E(5)^3
 -3*E(5)^4,-1,E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,0,-1,-1,0,
0,3,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,1,1,-1,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,0,
-1,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,1,1],
[GALOIS,[13,2]],[69255,-153,135,0,0,-9,-9,15,45,5,0,0,10,0,0,0,-3,-1,-1,0,-3,
-3,5,0,0,2,0,0,-1,0,0,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0,0,0,0,0,-E(35)^2-E(35)^6
 -E(35)^8-E(35)^18-E(35)^19-E(35)^22-E(35)^23-E(35)^24-E(35)^26-E(35)^31
 -E(35)^32-E(35)^34,-E(35)-E(35)^3-E(35)^4-E(35)^9-E(35)^11-E(35)^12-E(35)^13
 -E(35)^16-E(35)^17-E(35)^27-E(35)^29-E(35)^33,-1,-1],
[GALOIS,[15,2]],[214016,1408,0,104,-40,0,16,0,161,16,-24,-24,6,4,0,0,5,4,0,-1,
8,-7,0,0,0,-2,0,0,0,-2,0,0,1,-1,0,0,0,0,0,0,1,0,0,-1,0,1,1,-1,0,0,0,0,-1,-1],[
267520,1408,256,148,4,0,0,0,120,20,20,20,-5,4,4,4,1,0,0,-2,8,8,-4,-4,-4,3,1,1,
0,0,0,0,1,3,-1,-1,0,0,0,0,0,0,0,1,0,0,0,-1,-1,-1,1,1,0,0],[270864,880,-240,
189,0,16,-8,0,134,-11,24,24,4,-11,-3,0,6,0,0,0,5,-10,5,0,0,0,0,0,0,1,1,0,-2,
-1,0,0,0,0,1,1,2,0,0,0,0,-1,-1,-1,0,0,1,1,0,0],[365750,2310,310,35,35,6,10,
-10,0,125,0,0,0,15,-5,-5,0,0,2,-1,-15,0,5,0,0,0,0,0,0,1,3,-1,0,0,0,0,0,0,1,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[374528,0,-256,56,38,0,0,0,-112,28,
-18*E(5)+2*E(5)^2+2*E(5)^3-18*E(5)^4,2*E(5)-18*E(5)^2-18*E(5)^3+2*E(5)^4,-2,0,
8,2,0,0,0,-1,0,0,4,-6*E(5)-2*E(5)^2-2*E(5)^3-6*E(5)^4,-2*E(5)-6*E(5)^2
 -6*E(5)^3-2*E(5)^4,0,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,0,0,0,0,0,-4,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,
E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,0,0],
[GALOIS,[21,2]],[406296,2904,24,162,0,40,0,0,-84,-204,6,6,11,6,-6,0,-5,0,0,0,
4,4,4,-6,-6,-1,-1,-1,0,0,-2,0,-1,-3,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,0,0],[
653125,1925,325,-41,-5,5,21,5,125,0,0,0,0,-1,7,-5,4,1,-3,1,0,5,0,0,0,0,0,0,0,
3,-1,-1,0,-1,0,0,0,0,0,0,1,0,0,1,0,0,0,-1,0,0,-1,-1,1,1],[656250,-1750,250,
105,15,10,-10,10,0,0,0,0,0,5,1,-5,0,0,-2,0,0,0,0,0,0,0,0,0,1,-1,1,1,0,0,0,0,
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,
0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,2]],[718200,2520,120,0,-27,24,0,-8,0,75,-25*E(5)-25*E(5)^4,
-25*E(5)^2-25*E(5)^3,0,0,0,-3,0,0,0,0,-5,0,-5,-5*E(5)-5*E(5)^4,
-5*E(5)^2-5*E(5)^3,0,0,0,-1,0,0,1,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,-1,-1,0,
E(5)+E(5)^4,E(5)^2+E(5)^3,0,1,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0],
[GALOIS,[27,2]],[1053360,1232,-592,63,36,-16,8,0,210,235,10,10,10,-1,-1,-4,0,
0,0,0,7,2,3,-2,-2,2,-2,-2,0,-1,-1,0,0,3,1,1,0,0,-1,-1,-2,0,0,0,0,0,0,-1,1,1,0,
0,0,0],[1066527,2079,-225,0,0,15,-9,-9,-63,152,33*E(5)+3*E(5)^2+3*E(5)^3
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[(53,54),(51,52),(39,40),(37,38),(11,12)(24,25)(27,28)(35,36)(39,40)(42,43)
(46,47)(49,50)(51,52)(53,54),(11,12)(24,25)(27,28)(35,36)(42,43)(46,47)
(49,50)]);
ARC("HN","CAS",[rec(name:="ha",
permchars:=(21,22)(27,28),
permclasses:=(35,36)(42,43)(46,47),
text:=[
"names:=ha; f; f5; hacns; harada\n",
"    order: 2^14.3^6.5^6.7.11.19 = 273,030,912,000,000\n",
"    number of classes: 54\n",
"    source:private communication of compound table\n",
"           from cambridge group atlas project 1980/81\n",
"    origin:harada, k.\n",
"           the simple group f of order\n",
"           2^14.3^6.5^6.7.11.19,\n",
"           proc. of the conference on finite groups\n",
"           [1976], 119-276 \n",
""])]);
ARC("HN","isSimple",true);
ARC("HN","extInfo",["","2"]);
ARC("HN","maxes",["A12","2.HS.2","U3(8).3_1","2^(1+8).(A5xA5).2",
"(D10xU3(5)).2","5^(1+4):2^(1+4).5.4","2^6.U4(2)","(A6xA6).D8",
"2^3.2^2.2^6.(3xL3(2))","5^2.5.5^2.4A5","M12.2","HNM12","3^4:2(A4xA4).4",
"3^(1+4):4A5"]);
ALF("HN","HN.2",[1,2,3,4,5,6,7,8,9,10,11,11,12,13,14,15,16,17,18,19,20,21,
22,23,23,24,25,25,26,27,28,29,30,31,32,32,33,33,34,35,36,37,37,38,39,40,
40,41,42,42,43,43,44,44],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("HN",["F5+","ha"]);

MOT("HN.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19],\n",
"constructions: Aut(HN)"
],
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ARC("HN.2","maxes",["HN","A12.2","4.HS.2","U3(8).6","2^(1+8)_+.(A5xA5).2^2",
"5:4xU3(5):2","5^(1+4)_+:(4Y2^(1+4)_-.5.4)","2^6.U4(2).2","(S6xS6).2^2",
"2^3.2^2.2^6.(S3xL3(2))","5^2.5.5^2.4S5","3^4:2(S4xS4).2","HN.2M13"]);
ARC("HN.2","CAS",[rec(name:="ha.2",
permchars:=( 8,14,13,12,11,10, 9)(26,30,29,28,27)(31,35,47,45,43,41,39,37,34,
 32,40,38,36,33)(42,54,53,52,51,50,49,48,46,44),
permclasses:=(),
text:=[
"names:=     ha.2, ha.z2, autha\n",
"    order:     2^15.3^6.5^6.7.11.19 = 459,719,963,972,500\n",
"    number of classes:  78\n",
"    comments:  extension of ha with an outer\n",
"               automorphism of order 2\n",
"    test:      orth.1, min, sym[3]     \n",
""])]);
ALF("HN.2","B",[1,3,5,6,7,12,14,17,18,19,19,18,22,27,28,31,43,41,47,51,49,
53,53,49,52,54,66,64,72,79,81,82,98,105,105,104,108,109,111,128,140,142,
155,164,4,8,13,17,25,25,30,38,38,43,45,50,50,57,63,78,97,100,99,101,107,
108,122,127,127,134,139,164,165,165,168,169,169,180],[
"fusion map is unique"
]);
ALN("HN.2",["F5+.2","ha.2"]);

MOT("HS",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
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ARC("HS","CAS",[rec(name:="hs",
permchars:=(20,21),
permclasses:=(),
text:=[
"names:=hs; his\n",
"     order: 2^9.3^2.5^3.7.11 = 44,352,000\n",
"     number of classes: 24\n",
"     source / origin:\n",
"            frame, j.s.\n",
"            computation of characters of the\n",
"            higman-sims group and its automorphism group\n",
"            j.algebra 20\n",
"            [1972],320-349 \n",
""])]);
ARC("HS","projectives",["2.HS",[[56,8,0,2,0,0,0,6,-4,1,0,2,0,0,0,0,-2,0,1,1,0,
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[GALOIS,[4,3]],[924,4,0,6,24*E(4),0,0,-1,4,-1,0,-2,0,2*E(4),0,0,-1,0,0,0,0,1,
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[GALOIS,[6,3]],[1000,-40,0,10,0,0,0,0,0,0,0,2,-1,0,0,0,0,0,-1,-1,0,0,0,0],[
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[GALOIS,[9,3]],[1792,0,0,-8,0,0,0,-8,2,2,0,0,0,0,0,0,0,0,-1,-1,0,2,0,0],[1848,
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ARC("HS","isSimple",true);
ARC("HS","extInfo",["2","2"]);
ARC("HS","tomfusion",rec(name:="HS",map:=[1,2,3,4,5,6,7,13,14,15,19,20,21,
49,48,47,55,56,57,57,70,72,145,145],text:=[
"unique fusion map compatible with AtlasRep"
]));
ARC("HS","maxes",["M22","U3(5).2","HSM3","L3(4).2_1","A8.2","2^4.s6",
"4^3:psl(3,2)","M11","HSM9","4.2^4.S5","2xa6.2^2","5:4xa5"]);
ALF("HS","HS.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,16,17,18,18,19,20,
21,21]);
ALF("HS","Co3",[1,2,3,5,7,8,8,9,10,10,14,13,16,19,17,19,22,23,24,25,28,31,
34,33],[
"fusion is unique up to table automorphisms,\n",
"compatible with Brauer tables,\n",
"the map on the CAS table was not compatible"
]);

MOT("HS.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\n",
"constructions: Aut(HS)"
],
[88704000,15360,5760,720,7680,512,128,1000,600,50,72,48,14,32,16,40,40,11,24,
30,20,80640,3840,640,192,80,720,72,48,64,64,60,10,24,14,20,20,20,30],
[,[1,1,1,4,2,2,2,8,9,10,4,4,13,6,7,8,9,18,12,20,16,1,1,2,2,3,4,4,4,6,6,9,10,
12,13,17,16,16,20],[1,2,3,1,5,6,7,8,9,10,3,2,13,14,15,16,17,18,5,9,21,22,23,
24,25,26,22,22,23,30,31,32,33,25,35,36,38,37,32],,[1,2,3,4,5,6,7,1,1,1,11,12,
13,14,15,2,3,18,19,4,5,22,23,24,25,26,27,28,29,30,31,22,23,34,35,26,24,24,
27],,[1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
28,29,30,31,32,33,34,22,36,38,37,39],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,1,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1],[22,6,-2,4,-6,2,2,-3,2,2,-2,0,1,0,0,1,-2,0,0,-1,-1,8,
0,4,0,0,-4,2,0,2,-2,-2,0,0,1,0,-1,-1,1],
[TENSOR,[3,2]],[77,13,1,5,5,5,1,2,-3,2,1,1,0,1,-1,-2,1,0,-1,0,0,21,5,5,1,-1,3,
3,-1,1,1,1,0,1,0,-1,0,0,-2],
[TENSOR,[5,2]],[154,10,10,1,-2,6,-2,4,4,-1,1,1,0,0,0,0,0,0,1,1,-2,28,4,0,4,0,
1,1,1,-2,2,-2,-1,1,0,0,0,0,1],
[TENSOR,[7,2]],[308,20,-20,2,-20,-4,4,8,8,-2,-2,2,0,0,0,0,0,0,-2,2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[175,15,11,4,15,-1,3,0,5,0,2,0,0,-1,1,0,1,-1,0,
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[TENSOR,[10,2]],[231,7,-9,6,15,-1,-1,6,1,1,0,-2,0,-1,-1,2,1,0,0,1,0,21,-11,5,
-3,1,6,0,-2,1,1,1,-1,0,0,1,0,0,1],
[TENSOR,[12,2]],[693,21,9,0,21,5,1,-7,3,-2,0,0,0,1,-1,1,-1,0,0,0,1,63,15,-1,3,
1,0,0,0,-1,-1,3,0,0,0,1,-1,-1,0],
[TENSOR,[14,2]],[770,34,-10,5,-14,2,-2,-5,0,0,-1,1,0,-2,0,-1,0,0,1,0,1,70,-10,
6,2,0,-5,1,-1,-2,-2,0,0,-1,0,0,1,1,0],
[TENSOR,[16,2]],[1540,-28,20,10,-20,-4,-4,-10,0,0,2,2,0,0,0,2,0,0,-2,0,0,0,0,
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[TENSOR,[19,2]],[1792,0,32,-8,0,0,0,-8,2,2,-4,0,0,0,0,0,2,-1,0,2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[1056,32,0,-6,0,0,0,6,-4,1,0,2,-1,0,0,2,0,0,0,-1,0,
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[TENSOR,[22,2]],[1386,-6,18,0,6,-2,-2,11,6,1,0,0,0,0,0,-1,-2,0,0,0,1,0,-24,4,
0,0,0,0,0,-2,2,0,1,0,0,0,-1,-1,0],
[TENSOR,[24,2]],[1408,0,16,4,0,0,0,8,-7,-2,-2,0,1,0,0,0,1,0,0,-1,0,64,0,0,0,4,
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[TENSOR,[26,2]],[1750,-10,10,-5,-10,6,2,0,0,0,1,-1,0,-2,0,0,0,1,-1,0,0,70,-10,
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[TENSOR,[28,2]],[1925,5,-19,-1,5,5,-3,0,5,0,-1,-1,0,1,1,0,1,0,-1,-1,0,91,-5,
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[TENSOR,[30,2]],[1925,5,1,-1,-35,-3,1,0,5,0,1,-1,0,1,-1,0,1,0,1,-1,0,21,5,5,1,
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[TENSOR,[32,2]],[2520,24,0,0,24,-8,0,-5,0,0,0,0,0,0,0,-1,0,1,0,0,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,0],
[TENSOR,[34,2]],[2750,-50,-10,5,10,2,2,0,0,0,-1,1,-1,0,0,0,0,0,1,0,0,20,-20,0,
4,0,5,-1,1,2,-2,0,0,1,-1,0,0,0,0],
[TENSOR,[36,2]],[3200,0,-16,-4,0,0,0,0,-5,0,2,0,1,0,0,0,-1,-1,0,1,0,64,0,0,0,
-4,4,-2,0,0,0,-1,0,0,1,1,0,0,-1],
[TENSOR,[38,2]]],
[(37,38)]);
ARC("HS.2","CAS",[rec(name:="hs:2",
permchars:=( 9,13,12,11,10)(18,26,24,23,21,29,28,27,25,22,20,19)(30,32)
(31,33),
permclasses:=(25,26),
text:=[
"names:     hs.2, hs.z2, auths\n",
"order:     2^10.3^2.5^3.7.11 = 88,704,000\n",
"number of classes:  39\n",
"source:    frame,j.s.\n",
"computation of characters of the\n",
"higman-sims group and its automorphism group\n",
"j.algebra 20 [1972], 320-439\n",
"comments:  extension of hs with an outer\n",
"automorphism of order 2\n",
"test:      orth.1, min, sym[3]     \n",
""])]);
ARC("HS.2","projectives",["2.HS.2",[[56,8,0,2,0,0,0,6,-4,1,0,2,0,0,0,-2,0,1,0,
2,0,0,0,0,0,0,0,0,0,0,0,0,E(5)-E(5)^2-E(5)^3+E(5)^4,0,0,0,0,0,0],[352,32,0,10,
0,0,0,2,12,2,0,2,2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1232,
48,0,8,0,0,0,-18,-8,2,0,0,0,0,0,-2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[1848,8,0,12,0,0,0,-2,8,-2,0,-4,0,0,0,-2,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[1000,-40,0,10,0,0,0,0,0,0,0,2,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,E(7)+E(7)^2-E(7)^3+E(7)^4-E(7)^5-E(7)^6,0,0,0,0],[2464,-32,0,-2,
0,0,0,14,4,4,0,-2,0,0,0,-2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
1792,0,0,-8,0,0,0,-8,2,2,0,0,0,0,0,0,0,-1,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
E(40)^7+E(40)^13-E(40)^21+E(40)^23-E(40)^29-E(40)^31+E(40)^37-E(40)^39,0,0,
0],[1848,8,0,-6,0,0,0,-2,8,-2,0,2,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,E(15)+E(15)^2+E(15)^4-E(15)^7+E(15)^8-E(15)^11-E(15)^13-E(15)^14],[
3960,72,0,0,0,0,0,10,0,0,0,0,-2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[4608,0,0,0,0,0,0,8,-12,-2,0,0,2,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[2520,-24,0,0,0,0,0,-5,0,0,0,0,0,0,0,1,0,1,0,0,
E(5)-E(5)^2-E(5)^3+E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)-E(5)^2+E(5)^3
 -E(5)^4,-E(5)-E(5)^2+E(5)^3+E(5)^4,0],
[GALOIS,[11,2]]],]);
ARC("HS.2","maxes",["HS","M22.2","L3(4).2^2","S8x2","2^5.S6","4^3:(L3(2)x2)",
"2^(1+6)_+:S5","(2xA6.2^2).2","HS.2N5","5:4xS5"]);
ARC("HS.2","tomfusion",rec(name:="HS.2",map:=[1,2,3,4,5,6,7,13,14,15,19,
20,21,46,45,52,53,54,67,69,135,534,535,536,540,544,549,547,551,561,560,
600,602,621,627,785,781,781,836],text:=[
"fusion map is unique"
],perm:=(1,2,3,4,5,6,7,8,9,10)));
ALF("HS.2","Co2",[1,3,4,6,8,9,11,14,15,15,21,20,22,27,28,30,32,33,39,45,
51,2,4,8,12,13,18,19,21,24,27,31,32,41,42,52,51,51,58],[
"fusion map is unique, equal to that on the CAS table"
]);
ALN("HS.2",["hs:2"]);

MOT("He",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,17]"
],
[4030387200,161280,21504,7560,504,672,384,128,300,72,24,1176,1176,1029,98,98,
16,20,12,12,56,56,14,14,15,17,17,21,21,21,21,28,28],
[,[1,1,1,4,5,2,3,3,9,4,5,12,13,14,15,16,8,9,10,11,12,13,15,16,25,26,27,29,28,
30,31,21,22],[1,2,3,1,1,6,7,8,9,2,3,13,12,14,16,15,17,18,6,7,22,21,24,23,9,27,
26,14,14,13,12,33,32],,[1,2,3,4,5,6,7,8,1,10,11,13,12,14,16,15,17,2,19,20,22,
21,24,23,4,27,26,28,29,31,30,33,32],,[1,2,3,4,5,6,7,8,9,10,11,1,1,1,1,1,17,18,
19,20,2,2,3,3,25,27,26,4,4,5,5,6,6],,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,13,12,
14,16,15,17,18,19,20,22,21,24,23,25,1,1,28,29,31,30,33,32]],
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0,1,-1,1,1,0,0,0,0,0,0,0,-1,-1,1,1],[21504,0,0,-24,0,0,0,0,4,0,0,0,0,-7,0,0,0,
0,0,0,0,0,0,0,1,-1,-1,E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19,
E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,0,0,0,0],
[GALOIS,[30,2]],[22050,90,-14,0,-6,6,-6,-2,0,0,-2,7,7,0,0,0,0,0,0,0,-1,-1,0,0,
0,1,1,0,0,1,1,-1,-1],[23324,-196,28,14,-7,0,4,-4,-1,2,1,0,0,0,0,0,0,-1,0,1,0,
0,0,0,-1,0,0,0,0,0,0,0,0]],
[(28,29),(26,27),(12,13)(15,16)(21,22)(23,24)(28,29)(30,31)(32,33),(12,13)
(15,16)(21,22)(23,24)(30,31)(32,33)]);
ARC("He","CAS",[rec(name:="he",
permchars:=( 7, 8)(30,31),
permclasses:=(15,16)(19,20)(21,22)(28,30)(29,31),
text:=[
"names:=he; hhm\n",
"    order: 2^10.3^3.5^2.7^3.17 = 4,030,387,200\n",
"    number of classes: 33\n",
"    source:private communication\n",
"           by olsson, j.b.\n",
"           univ. of dortmund [1980]\n",
"    origin:thompson, j. - guy, m.\n",
"           -unpublished-\n",
"           [c.f.: hurley, j.f. and rudvalis, a.\n",
"           finite simple groups,\n",
"           math. monthly 84, [1977], 693-714,\n",
"           c.f. also: cambridge group atlas project ] \n",
""])]);
ARC("He","isSimple",true);
ARC("He","extInfo",["","2"]);
ARC("He","maxes",["S4(4).2","2^2.psl(3,4).s3","2^6:3.s6","2^6:3.s6",
"2^1+6.psl(3,2)","7^2:2psl(2,7)","3.A7.2","7^(1+2):(S3x3)","s4xpsl(3,2)",
"7:3xpsl(3,2)","5^2:4A4"]);
ARC("He","tomfusion",rec(name:="He",map:=[1,2,3,4,5,14,15,16,17,22,23,25,25,
24,26,26,71,76,100,99,102,102,103,103,104,229,229,248,248,247,247,305,305],
text:=[
"fusion map is unique"
]));
ALF("He","He.2",[1,2,3,4,5,6,7,8,9,10,11,12,12,13,14,14,15,16,17,18,19,19,
20,20,21,22,22,23,24,25,25,26,26],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("He.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,17],\n",
"constructions: Aut(He)"
],
[8060774400,322560,43008,15120,1008,1344,768,256,600,144,48,1176,2058,98,32,
40,24,24,56,14,30,17,42,42,21,28,30240,480,15120,144,36,192,192,32,60,24,42,
16,16,20,24,24,30,42,42],
[,[1,1,1,4,5,2,3,3,9,4,5,12,13,14,8,9,10,11,12,14,21,22,24,23,25,19,1,2,4,4,5,
7,7,7,9,10,13,15,15,16,18,18,21,24,23],[1,2,3,1,1,6,7,8,9,2,3,12,13,14,15,16,
6,7,19,20,9,22,13,13,12,26,27,28,27,27,27,33,32,34,35,28,37,39,38,40,33,32,35,
37,37],,[1,2,3,4,5,6,7,8,1,10,11,12,13,14,15,2,17,18,19,20,4,22,23,24,25,26,
27,28,29,30,31,33,32,34,27,36,37,39,38,28,42,41,29,44,45],,[1,2,3,4,5,6,7,8,9,
10,11,1,1,1,15,16,17,18,2,3,21,22,4,4,5,6,27,28,29,30,31,32,33,34,35,36,27,38,
39,40,41,42,43,29,29],,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,1,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[102,22,6,12,0,6,6,-2,2,4,0,
-3,4,-3,2,2,0,0,1,-1,2,0,-2,-2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
306,18,-14,0,6,-6,2,2,6,0,-2,5,12,-2,2,-2,0,2,-3,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[680,56,8,14,-1,0,8,0,5,2,-1,8,-6,1,0,1,0,-1,0,1,-1,
0,0,0,-1,0,14,6,14,2,-1,2,2,2,-1,0,0,0,0,1,-1,-1,-1,0,0],
[TENSOR,[5,2]],[2058,-70,42,42,0,-14,-6,2,8,2,0,0,0,0,-2,0,-2,0,0,0,2,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1275,75,27,15,0,7,3,3,0,3,0,-6,1,1,
-1,0,1,0,-2,-1,0,0,1,1,0,0,15,-5,15,3,0,3,3,-1,0,1,1,-1,-1,0,0,0,0,1,1],
[TENSOR,[8,2]],[2550,70,-42,30,0,-2,6,-2,0,-2,0,-12,2,2,2,0,-2,0,0,0,0,0,2,2,
0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1920,64,0,21,0,8,0,0,-5,1,0,9,9,
2,0,-1,-1,0,1,0,1,-1,0,0,0,1,36,4,-9,3,0,0,0,0,1,1,1,0,0,-1,0,0,1,-2,-2],
[TENSOR,[11,2]],[4080,16,48,-6,0,0,0,0,5,-2,0,6,13,-1,0,1,0,0,2,-1,-1,0,1,1,0,
0,36,4,36,0,0,0,0,0,1,-2,1,0,0,-1,0,0,1,1,1],
[TENSOR,[13,2]],[4352,128,0,14,8,0,0,0,2,2,0,-2,-9,-2,0,-2,0,0,2,0,-1,0,0,0,1,
0,32,0,14,2,2,0,0,0,2,0,-3,0,0,0,0,0,-1,0,0],
[TENSOR,[15,2]],[6272,-64,0,35,8,-8,0,0,-3,-1,0,7,0,0,0,1,1,0,-1,0,0,-1,0,0,1,
-1,28,-4,-35,1,-2,0,0,0,3,-1,0,0,0,1,0,0,0,0,0],
[TENSOR,[17,2]],[6528,64,0,-15,0,-8,0,0,3,1,0,-3,11,4,0,-1,1,0,1,0,0,0,-1,-1,
0,-1,36,4,-27,-3,0,0,0,0,1,1,1,0,0,-1,0,0,-2,1,1],
[TENSOR,[19,2]],[14994,162,-14,0,6,-6,2,-6,-6,0,-2,-7,0,0,-2,2,0,2,1,0,0,0,0,
0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[7650,90,50,0,6,6,-6,-2,0,0,2,
-1,6,-1,0,0,0,0,-1,1,0,0,0,0,-1,-1,0,0,0,0,0,2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,
0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0],
[TENSOR,[22,2]],[15300,180,-28,0,-6,-12,4,-4,0,0,2,-2,12,-2,0,0,0,-2,-2,0,0,0,
0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10880,-64,0,-1,8,8,0,0,5,-1,0,
-5,2,2,0,1,-1,0,-1,0,-1,0,-1,-1,1,1,44,-4,-1,-1,2,0,0,0,-1,-1,2,0,0,1,0,0,-1,
-1,-1],
[TENSOR,[25,2]],[22950,-90,-90,0,0,6,6,6,0,0,0,-3,18,-3,-2,0,0,0,1,1,0,0,0,0,
0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[11900,140,28,20,-7,0,4,4,0,-4,1,
0,-7,0,0,0,0,1,0,0,0,0,-1,-1,0,0,20,0,20,-4,-1,4,4,0,0,0,-1,0,0,0,1,1,0,-1,
-1],
[TENSOR,[28,2]],[13720,-56,56,-14,7,0,8,0,-5,-2,-1,0,0,0,0,-1,0,-1,0,0,1,1,0,
0,0,0,14,6,14,2,-1,-2,-2,-2,-1,0,0,0,0,1,1,1,-1,0,0],
[TENSOR,[30,2]],[14400,0,-64,0,6,0,0,0,0,0,2,8,-6,1,0,0,0,0,0,-1,0,1,0,0,-1,0,
0,0,0,0,0,4*E(8)-4*E(8)^3,-4*E(8)+4*E(8)^3,0,0,0,0,0,0,0,E(8)-E(8)^3,
-E(8)+E(8)^3,0,0,0],
[TENSOR,[32,2]],[17493,21,21,-21,0,-7,-3,5,-7,3,0,0,0,0,1,1,-1,0,0,0,-1,0,0,0,
0,0,21,1,21,-3,0,-3,-3,1,1,1,0,-1,-1,1,0,0,1,0,0],
[TENSOR,[34,2]],[20825,-55,-7,35,-1,1,-7,1,0,-1,-1,-7,0,0,1,0,1,-1,1,0,0,0,0,
0,-1,1,35,-5,35,-1,-1,-1,-1,-1,0,1,0,1,1,0,-1,-1,0,0,0],
[TENSOR,[36,2]],[21504,0,0,-24,0,0,0,0,4,0,0,0,-7,0,0,0,0,0,0,0,1,-1,
E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19,E(21)+E(21)^4+E(21)^5
 +E(21)^16+E(21)^17+E(21)^20,0,0,48,0,-24,0,0,0,0,0,-2,0,-1,0,0,0,0,0,1,
E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19,E(21)+E(21)^4+E(21)^5
 +E(21)^16+E(21)^17+E(21)^20],
[TENSOR,[38,2]],
[GALOIS,[38,2]],
[TENSOR,[40,2]],[22050,90,-14,0,-6,6,-6,-2,0,0,-2,7,0,0,0,0,0,0,-1,0,0,1,0,0,
1,-1,0,0,0,0,0,2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,0,0,0,0,-E(8)+E(8)^3,
E(8)-E(8)^3,0,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0],
[TENSOR,[42,2]],[23324,-196,28,14,-7,0,4,-4,-1,2,1,0,0,0,0,-1,0,1,0,0,-1,0,0,
0,0,0,14,-6,14,2,-1,-2,-2,2,-1,0,0,0,0,-1,1,1,-1,0,0],
[TENSOR,[44,2]]],
[(32,33)(38,39)(41,42),(23,24)(44,45)]);
ARC("He.2","maxes",["He","S4(4).4","2^2.L3(4).D12","2^(1+6)_+.L3(2).2",
"7^2:2.L2(7).2","3.s7x2","s5wrs2","2^(4+4).(S3xS3).2","7^(1+2):(S3x6)",
"S4xL3(2).2","7:6xL3(2)","Fi22N5"]);
ARC("He.2","CAS",[rec(name:="he.2",
permchars:=( 7,11, 9, 8)(10,12)(21,31,28,25,23,22)(24,32,29,26)
(27,43,42,41,38,39,40,37,36,35,34,33,30),
permclasses:=(12,13)(17,18)(41,42),
text:=[
"names:=     he.2, he.z2, authe\n",
"    order:     2^11.3^3.5^2.7^3.17 = 8,060,774,400\n",
"    number of classes:  45\n",
"    comments:  extension of he with an outer\n",
"               automorphism of order 2\n",
"    test:      orth.1, min, sym[3]     \n",
""])]);
ARC("He.2","tomfusion",rec(name:="He.2",map:=[1,2,3,4,5,12,13,14,15,20,21,
23,22,24,54,59,78,77,80,81,82,157,176,176,175,216,1067,1069,1072,1075,
1077,1090,1090,1088,1093,1107,1114,1154,1154,1167,1208,1208,1220,1332,
1332],text:=[
"fusion map is unique"
],perm:=(1,2,3,4,5,6,7,8,9,10,11,12)));
ALF("He.2","F3+",[1,2,3,6,8,10,9,11,12,18,23,24,25,25,27,35,49,46,52,53,
56,58,71,72,70,87,3,10,14,21,23,26,26,26,36,49,53,57,57,67,78,78,91,104,
105],[
"fusion map is unique up to table automorphisms"
]);

MOT("Ly",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,31,37,67]"
],
[51765179004000000,39916800,2694384000,174960,20160,2250000,3750,120960,2160,
324,168,480,96,54,3600,50,66,66,288,72,168,2250,90,75,18,40,42,42,22,22,24,24,
24,25,28,90,90,31,31,31,31,31,33,33,37,37,40,40,42,42,67,67,67],
[,[1,1,3,4,2,6,7,3,4,4,11,5,5,14,6,7,18,17,8,9,11,22,23,24,14,15,28,27,18,17,
19,20,20,34,21,22,23,39,40,41,42,38,44,43,46,45,26,26,28,27,52,53,51],[1,2,1,
1,5,6,7,2,2,2,11,12,13,4,15,16,17,18,5,5,21,6,6,7,10,26,11,11,29,30,12,13,13,
34,35,15,15,42,38,39,40,41,17,18,45,46,47,48,21,21,51,52,53],,[1,2,3,4,5,1,1,
8,9,10,11,12,13,14,2,2,17,18,19,20,21,3,4,3,25,5,27,28,29,30,31,32,33,6,35,8,
9,38,39,40,41,42,43,44,46,45,12,12,49,50,51,52,53],,[1,2,3,4,5,6,7,8,9,10,1,
12,13,14,15,16,18,17,19,20,2,22,23,24,25,26,3,3,30,29,31,33,32,34,5,36,37,40,
41,42,38,39,44,43,45,46,48,47,8,8,53,51,52],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,1,1,19,20,21,22,23,24,25,26,28,27,2,2,31,33,32,34,35,36,37,40,41,42,
38,39,3,3,45,46,48,47,50,49,53,51,52],,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,27,29,30,31,33,32,34,35,
36,37,1,1,1,1,1,43,44,46,45,47,48,50,49,53,51,52],,,,,,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,33,32,34,35,36,
37,38,39,40,41,42,43,44,1,1,47,48,49,50,52,53,
51],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[2480,-16,104,-4,0,-20,5,8,-4,2,2,0,0,-1,4,-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
 ,0,0,-2,4,1,-1,-1,0,-1,-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)^10,0,0,0,0,0,-2,1,0,0,0,0,0,
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
 ,1,1,0,0,1,1,1,1,1],
[GALOIS,[2,2]],[45694,110,253,10,26,69,-6,29,2,2,-2,4,0,1,5,0,0,0,5,2,-2,3,0,
3,-1,1,1,1,0,0,1,0,0,-1,-2,-1,2,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,0,0,0],[48174,
126,357,6,-14,49,-1,21,6,0,0,-4,0,0,1,1,E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,
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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
 ,-1,0,0,-1,0,1,1,0,0,0,0,0,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)^10,0,0,1,1,0,0,1,1,1],
[GALOIS,[5,2]],[120064,0,-896,-32,0,64,14,0,0,0,0,0,0,-2,0,0,2*E(11)+2*E(11)^3
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 -E(11)^10,-1,-1,0,0,0,0,0,0,0],
[GALOIS,[7,2]],[381766,-154,-770,67,14,-109,-9,14,11,-1,0,-6,2,1,11,1,0,0,2,
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0],[1152735,-417,2751,51,-1,235,10,63,3,-3,3,-1,-1,0,3,-2,1,1,-1,-1,3,1,1,1,0,
-1,0,0,1,1,-1,-1,-1,0,-1,3,3,0,0,0,0,0,1,1,0,0,-1,-1,0,0,0,0,0],[1534500,660,
1980,117,16,125,0,-36,-3,3,2,6,2,0,5,0,0,0,4,1,2,5,2,0,0,1,-1,-1,0,0,0,-1,-1,
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ARC("Ly","CAS",[rec(name:="ly",
permchars:=(21,22)(24,25)(26,27)(39,41)(40,42)(45,46),
permclasses:=(29,30)(36,37)(40,42,41)(52,53),
text:=[
"names:=ly; lys; lyons\n",
"      order: 2^8.3^7.5^6.7.11.31.37.67 = 51,765,179,004,000,000\n",
"      number of classes: 53\n",
"      source / origin:\n",
"             lyons, r.\n",
"             evidence for a new finite simple group\n",
"             j.algebra 20\n",
"             [1972],540-569 \n",
""])]);
ARC("Ly","isSimple",true);
ARC("Ly","extInfo",["",""]);
ARC("Ly","maxes",["G2(5)","3.McL.2","5^3.psl(3,5)","2.A11","5^(1+4):4S6",
"LyM6","3^(2+4):2A5.D8","67:22","37:18"]);

MOT("McL",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
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ARC("McL","CAS",[rec(name:="mcl",
permchars:=(16,17)(18,19),
permclasses:=(),
text:=[
"names:mcl; mc\n",
"order: 2^7.3^6.5^3.7.11 = 898,128,000\n",
"number of classes: 24\n",
"source:private communication\n",
"by olsson, j.b.\n",
"univ. of dortmund [1980]\n",
"origin:thompson, j.g.\n",
"-unpublished-\n",
"[cf. janko, wong\n",
"a characterization of mc laughlin's\n",
"simple group,\n",
"j.algebra 20\n",
"[1972], 203-225\n",
"maximal subgroup   index\n",
"3^1+4:2.s5         15400\n",
"3^4:m10            15400\n",
"psl[3,4]:2         22275\n",
""])]);
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0,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0],
[GALOIS,[15,3]],[8064,0,72,0,0,14,-1,0,0,0,0,0,0,0,0,1,1,0,0,0,2,2,0,0],[
10395,-21,-54,0,-1,-5,0,-6,0,0,0,1,0,0,-1,0,0,2,0,0,1,1,-1,-1],[10395,-21,27,
0,-1,-5,0,3,0,0,0,1,0,0,-1,0,0,-1,0,0,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,E(15)^7+E(15)^11+E(15)^13+E(15)^14,
E(15)+E(15)^2+E(15)^4+E(15)^8],
[GALOIS,[19,7]],[12375,55,-45,0,-1,0,0,-5,-2,-1,-1,-1,0,0,0,0,0,-1,-1,-1,0,0,
0,0]],]);
ARC("McL","isSimple",true);
ARC("McL","extInfo",["3","2"]);
ARC("McL","tomfusion",rec(name:="McL",map:=[1,2,3,4,6,7,8,9,10,12,12,19,24,24,
25,27,27,35,36,36,37,37,83,83],text:=[
"fusion map is unique"
]));
ALF("McL","McL.2",[1,2,3,4,5,6,7,8,9,10,10,11,12,12,13,14,15,16,17,17,18,
18,19,19]);
ALF("McL","Co3",[1,2,4,5,8,9,10,11,13,16,16,19,21,21,22,24,25,27,29,29,30,
30,42,42],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("McL","Co2",[1,3,5,6,11,14,15,16,20,22,22,28,29,29,30,33,33,40,43,44,
47,46,60,59],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ARC("McL","maxes",["U4(3)","M22","McLM3","U3(5)","3^(1+4):2S5","3^4:m10",
"L3(4).2_2","2.A8","2^4:a7","McLM10","M11","5^(1+2):3:8"]);

MOT("McL.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\n",
"constructions: Aut(McL)"
],
[1796256000,80640,58320,1944,192,1500,50,720,72,14,16,27,60,22,22,24,14,30,30,
15840,1440,36,96,32,10,36,36,20,20,22,22,24,24],
[,[1,1,3,4,2,6,7,3,4,10,5,12,6,15,14,8,10,18,18,1,2,4,5,5,7,8,9,13,13,15,14,
16,16],[1,2,1,1,5,6,7,2,2,10,11,3,13,14,15,5,17,6,13,20,21,20,23,24,25,21,21,
28,29,30,31,23,23],,[1,2,3,4,5,1,1,8,9,10,11,12,2,14,15,16,17,3,8,20,21,22,23,
24,20,26,27,21,21,30,31,32,33],,[1,2,3,4,5,6,7,8,9,1,11,12,13,15,14,16,2,18,
19,20,21,22,23,24,25,26,27,28,29,31,30,32,33],,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,1,1,16,17,18,19,20,21,22,23,24,25,26,27,29,28,20,20,32,33]],
[[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],[22,
6,-5,4,2,-3,2,3,0,1,0,1,1,0,0,-1,-1,0,-2,0,4,0,-2,2,0,1,-2,-1,-1,0,0,1,1],
[TENSOR,[3,2]],[231,7,15,6,-1,6,1,7,-2,0,-1,0,2,0,0,-1,0,0,2,11,-5,2,-1,-1,1,
1,-2,0,0,0,0,-1,-1],
[TENSOR,[5,2]],[252,28,9,9,4,2,2,1,1,0,0,0,-2,-1,-1,1,0,-1,1,10,10,1,2,2,0,1,
1,0,0,-1,-1,-1,-1],
[TENSOR,[7,2]],[1540,-28,-26,10,-4,-10,0,14,2,0,0,-2,2,0,0,2,0,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[896,0,32,-4,0,-4,1,0,0,0,0,-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)^10,0,0,2,0,16,0,-2,0,
0,1,0,0,0,0,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)^10,0,0],
[TENSOR,[10,2]],
[GALOIS,[10,2]],
[TENSOR,[12,2]],[1750,70,-5,13,2,0,0,-5,1,0,0,-2,0,1,1,-1,0,0,0,10,-10,1,4,0,
0,-1,-1,0,0,-1,-1,1,1],
[TENSOR,[14,2]],[3520,64,-44,10,0,-5,0,4,-2,-1,0,1,-1,0,0,0,1,1,-1,0,16,0,0,0,
0,-2,-2,1,1,0,0,0,0],
[TENSOR,[16,2]],[3520,-64,-44,10,0,-5,0,-4,2,-1,0,1,1,0,0,0,-1,1,1,0,0,0,0,0,
0,0,0,E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,
0],
[TENSOR,[18,2]],[4500,20,45,-9,4,0,0,5,-1,-1,0,0,0,1,1,1,-1,0,0,10,10,1,-2,-2,
0,1,1,0,0,-1,-1,1,1],
[TENSOR,[20,2]],[4752,-48,54,0,0,2,2,-6,0,-1,0,0,2,0,0,0,1,-1,-1,0,0,0,0,0,0,
0,0,0,0,0,0,E(24)+E(24)^11-E(24)^17-E(24)^19,-E(24)-E(24)^11+E(24)^17+E(24)^19
 ],
[TENSOR,[22,2]],[5103,63,0,0,3,3,-2,0,0,0,1,0,3,-1,-1,0,0,0,0,45,9,0,3,-1,0,0,
0,-1,-1,1,1,0,0],
[TENSOR,[24,2]],[5544,-56,36,9,0,19,-1,4,1,0,0,0,-1,0,0,0,0,1,-1,44,-4,-1,0,0,
-1,2,-1,1,1,0,0,0,0],
[TENSOR,[26,2]],[16038,-90,0,0,6,-12,-2,0,0,1,-2,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[16500,20,30,12,-4,0,0,-10,-4,1,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[9625,105,40,-5,-3,0,0,0,3,0,-1,1,0,0,0,0,0,0,0,55,-5,1,-3,
1,0,-2,1,0,0,0,0,0,0],
[TENSOR,[30,2]],[19712,0,-160,-16,0,12,2,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[20790,-42,54,0,-2,-10,0,6,0,0,2,0,-2,0,0,-2,0,-1,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0]],
[(32,33),(28,29),(28,29)(32,33),(14,15)(30,31)]);
ARC("McL.2","CAS",[rec(name:="mcl.2",
permchars:=( 9,13,12,11,10)(28,30)(29,31),
permclasses:=(),
text:=[
"names:=     mcl.2, mcl.z2, autmcl\n",
"     order:     2^8.3^6.5^3.7.11 = 1,796,256,000\n",
"     number of classes:  33\n",
"     comments:  extension of mcl with an outer\n",
"                automorphism of order 2\n",
"     test:      orth.1, min, sym[3]     \n",
""])]);
ARC("McL.2","maxes",["McL","U4(3).2_3","U3(5).2","3^(1+4):4S5","3^4:(M10x2)",
"L3(4).2^2","Isoclinic(2.A8.2)","2xM11","5^(1+2):(24:2)","2^(2+4):(S3xS3)"]);
ARC("McL.2","tomfusion",rec(name:="McL.2",map:=[1,2,4,5,7,10,11,12,13,19,
26,38,39,44,44,58,63,64,153,3,6,14,25,27,40,56,57,114,114,116,116,131,131],
text:=[
"fusion map is unique"
],
perm:=(4,5)(6,7)));
ALF("McL.2","Co3",[1,2,4,5,8,9,10,11,13,16,19,21,22,24,25,27,29,30,42,3,7,
14,17,18,23,26,28,34,33,36,37,40,40],[
"fusion map is unique up to table automorphisms,\n",
"compatible with Brauer tables,\n",
"the fusion map on the CAS table was not compatible"
]);

MOT("ON",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19,31]"
],
[460815505920,161280,3240,80640,256,180,72,1372,49,32,32,20,11,36,28,45,45,16,
16,16,16,19,19,19,20,20,28,28,31,31],
[,[1,1,3,2,2,6,3,8,9,5,5,6,13,7,8,17,16,10,10,11,11,23,24,22,12,12,15,15,29,
30],[1,2,1,4,5,6,2,8,9,10,11,12,13,4,15,6,6,19,18,21,20,23,24,22,25,26,27,28,
30,29],,[1,2,3,4,5,1,7,8,9,10,11,2,13,14,15,3,3,19,18,21,20,23,24,22,4,4,28,
27,29,30],,[1,2,3,4,5,6,7,1,1,10,11,12,13,14,2,17,16,18,19,20,21,22,23,24,25,
26,4,4,29,30],,,,[1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,16,17,19,18,21,20,22,23,
24,26,25,28,27,30,29],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,18,
21,20,1,1,1,26,25,27,28,29,30],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,26,25,27,28,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[10944,64,9,64,
0,-1,1,17,3,0,0,-1,-1,1,1,-1,-1,0,0,0,0,0,0,0,-1,-1,1,1,1,1],[13376,-64,11,64,
0,1,-1,-1,-1,0,0,1,0,1,-1,1,1,0,0,0,0,0,0,0,-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,[3,3]],[25916,-36,-4,20,4,1,0,-5,2,0,0,-1,0,2,-1,1,1,0,0,0,0,0,0,0,
E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,-1,-1,0,0],
[GALOIS,[5,11]],[26752,128,22,0,0,2,2,-2,-2,0,0,-2,0,0,2,2,2,0,0,0,0,0,0,0,0,
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0,0,0,0,0],[32395,75,-5,35,3,0,3,6,-1,-1,3,0,0,-1,-2,0,0,-1,-1,1,1,0,0,0,0,0,
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-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,0,0,0,0,0,0],
[GALOIS,[16,3]],[85064,-56,14,-56,8,-1,-2,0,0,0,0,-1,1,-2,0,-1,-1,0,0,0,0,1,1,
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[GALOIS,[26,4]],
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[GALOIS,[29,5]]],
[(29,30),(27,28),(25,26),(25,26)(27,28),(22,23,24),(18,19)(20,21),(18,19)
(20,21)(25,26)(27,28),(16,17),(16,17)(25,26),(10,11)(18,20)(19,21),
(22,24,23)]);
ARC("ON","CAS",[rec(name:="on",
permchars:=(26,28,27),
permclasses:=(20,21),
text:=[
"names:=on; onan; ons\n",
"    order: 2^9.3^4.5.7^3.11.19.31 = 460,815,505,920\n",
"    number of classes: 30\n",
"    source / origin:\n",
"           o'nan, m.e.\n",
"           some evidence for the existence\n",
"           of a new finite simple group\n",
"           proc. london math. soc. [3] 32\n",
"           [1976],421-479 \n",
""])]);
ARC("ON","projectives",["3.ON",[[342,6,0,-6,2,-3,0,-1,-1,0,0,1,1,0,-1,0,0,
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[GALOIS,[21,4]],
[GALOIS,[21,2]],[253440,0,0,0,0,0,0,12,-2,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,
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[GALOIS,[24,3]]],]);
ARC("ON","isSimple",true);
ARC("ON","extInfo",["3","2"]);
ALF("ON","ON.2",[1,2,3,4,5,6,7,8,9,10,10,11,12,13,14,15,16,17,18,17,18,19,
20,21,22,22,23,24,25,25],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ARC("ON","maxes",["L3(7).2","ONM2","J1","4_2.L3(4).2_1","ONM5",
"3^4:2^(1+4)D10","L2(31)","ONM8","4^3.L3(2)","M11","ONM11","A7","A7"]);
ALN("ON",["O'N"]);

MOT("ON.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19,31],\n",
"constructions: Aut(ON)"
],
[921631011840,322560,6480,161280,512,360,144,2744,98,32,40,22,72,56,90,90,16,
16,38,38,38,20,56,56,31,351120,60,1344,1344,32,60,60,14,22,24,24,30,30,38,38,
38,56,56,56,56],
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42,45,44],,[1,2,3,4,5,1,7,8,9,10,2,12,13,14,3,3,18,17,20,21,19,4,24,23,25,26,
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19,20,21,22,24,23,25,26,27,29,28,30,31,32,33,26,36,35,37,38,39,40,41,45,44,43,
42],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,17,1,1,1,22,23,24,25,26,
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[TENSOR,[20,2]],[116963,35,-1,35,3,8,-1,0,0,-1,0,0,-1,0,-1,-1,1,1,-1,-1,-1,0,
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[TENSOR,[22,2]],[143374,14,4,126,-2,-1,-4,0,0,2,-1,0,0,0,-1,-1,0,0,0,0,0,1,0,
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[TENSOR,[24,2]],[169290,90,0,-90,-2,0,0,-5,2,0,0,0,0,-1,0,0,E(8)-E(8)^3,
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[TENSOR,[26,2]],
[GALOIS,[26,3]],
[TENSOR,[28,2]],[175616,0,8,0,0,-4,0,0,0,0,0,1,0,0,E(5)-2*E(5)^2-2*E(5)^3
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[TENSOR,[30,2]],
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[TENSOR,[32,2]],[175770,90,0,90,-6,0,0,7,0,-2,0,1,0,-1,0,0,0,0,1,1,1,0,-1,-1,
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[TENSOR,[36,2]],
[GALOIS,[36,4]],
[TENSOR,[38,2]],
[GALOIS,[36,2]],
[TENSOR,[40,2]],[234080,-160,-10,0,0,0,2,7,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
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[TENSOR,[42,2]],
[GALOIS,[42,15]],
[TENSOR,[44,2]]],
[(23,24)(42,44)(43,45),(19,20,21)(39,40,41),(19,21,20)(39,41,40),(17,18)
(23,24)(28,29)(35,36)(42,45)(43,44),(15,16)(31,32)(37,38),(17,18)(28,29)
(35,36)(42,43)(44,45)]);
ARC("ON.2","CAS",[rec(name:="on.2",
permchars:=( 6,10, 8, 7)( 9,17,15,14,13,12,11)(16,20,18)(19,23,22,21)
(36,40,38)(37,41,39)(42,44)(43,45),
permclasses:=(35,36)(39,41)(43,44),
text:=[
"names:=     on.2, on.z2, auton\n",
"    order:     2^10.3^4.5.7^3.11.19.31 = 921,631,011,840\n",
"    number of classes:  45\n",
"    comments:  extension of on with an outer\n",
"               automorphism of order 2\n",
"    test:      orth.1, min, sym[3]     \n",
""])]);
ARC("ON.2","maxes",["ON","J1x2","4_2.L3(4).(2^2)_{12*3}","(3^2:4xA6).2^2",
"3^4:2^(1+4).(5:4)","4^3.(L3(2)x2)","7^(1+2)_+:(3xD16)","31:30","A6.2_2",
"L3(2).2"]);
ALN("ON.2",["O'N.2"]);

MOT("Ru",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,29]"
],
[145926144000,245760,116480,2160,7680,3840,1024,512,1000,300,48,28,96,64,32,
40,20,24,12,52,28,28,28,15,16,16,20,20,20,24,24,52,52,52,29,29],
[,[1,1,1,4,2,2,2,2,9,10,4,12,5,7,8,9,10,11,11,20,12,12,12,24,14,14,16,16,16,
18,18,20,20,20,36,35],[1,2,3,1,5,6,7,8,9,10,2,12,13,14,15,16,17,5,6,20,22,23,
21,10,26,25,27,29,28,13,13,33,34,32,36,35],,[1,2,3,4,5,6,7,8,1,1,11,12,13,14,
15,2,3,18,19,20,23,21,22,4,25,26,5,6,6,30,31,32,33,34,35,36],,[1,2,3,4,5,6,7,
8,9,10,11,1,13,14,15,16,17,18,19,20,3,3,3,24,26,25,27,29,28,31,30,34,32,33,35,
36],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,21,22,23,24,25,26,
27,29,28,31,30,3,3,3,35,36],,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,33,34,32,1,1]],
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1],
[GALOIS,[11,2]],
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(21,22,23)]);
ARC("Ru","CAS",[rec(name:="ru",
permchars:=(11,12,13)(17,19)(34,35),
permclasses:=(33,34),
text:=[
"names:=ru; ruv; rud\n",
"    order: 2^14.3^3.5^3.7.13.29 = 145,926,144,000\n",
"    number of classes: 36\n",
"    source:private communication\n",
"           by olsson, j.b.\n",
"           univ. of dortmund [1980]\n",
"    origin:frame, j.s.\n",
"           may,18th 1972\n",
"           -unpublished-\n",
"maximal subgroup   index\n",
" 2^6:u3[3]:2        188500\n",
""])]);
ARC("Ru","projectives",["2.Ru",[[28,4,0,1,4,4*E(4),0,0,3,-2,1,0,2*E(4),2*E(4),
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ARC("Ru","isSimple",true);
ARC("Ru","extInfo",["2",""]);
ARC("Ru","maxes",["2F4(2)'.2","2^6:u3(3):2","(2^2xSz(8)):3","2^3+8:L3(2)",
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"5^1+2:(2^5)","L2(13).2","A6.2^2","5:4xa5"]);

MOT("Suz",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
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[(41,42),(35,36),(32,33),(14,15)(22,23)(38,39)(41,42),(14,15)(22,23)(38,39)]);
ARC("Suz","CAS",[rec(name:="suz",
permchars:=( 7, 8)(13,14)(18,19)(21,22)(25,26)(31,32),
permclasses:=(38,39),
text:=[
"names:=suz; suzuki\n",
"    order: 2^13.3^7.5^2.7.11.13 = 448,345,497,600\n",
"    number of classes: 43\n",
"    source / origin:\n",
"           wright, d.\n",
"           the irreducible characters of\n",
"           the simple group of m.suzuki\n",
"           j.algebra 29\n",
"           [1974],303-323\n",
" maximal subgroup   index\n",
" 3.u4[3]:2          22880\n",
" 3^5:m11            232960\n",
""])]);
ARC("Suz","projectives",["2.Suz",[[220,12,0,-50,4,4,-20,0,0,0,-10,0,6,-6,-6,0,
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ARC("Suz","isSimple",true);
ARC("Suz","extInfo",["6","2"]);
ALF("Suz","Suz.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,14,15,16,17,18,19,20,
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"A7"]);

MOT("Suz.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13],\n",
"constructions: Aut(Suz)"
],
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[TENSOR,[59,2]],[197120,512,0,560,20,-16,0,0,0,0,-10,0,-16,8,-4,0,0,0,0,0,-1,
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 -E(40)^39],
[TENSOR,[61,2]],[208494,-594,90,-729,0,0,6,-18,2,0,9,4,-9,0,0,0,-1,-2,-2,0,0,
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[TENSOR,[63,2]],[243243,-405,-161,0,0,9,-45,27,-9,1,8,3,0,0,0,1,0,3,-1,1,0,0,
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[TENSOR,[65,2]],[248832,0,-64,0,0,-9,0,0,0,8,-8,-3,0,0,0,-1,3,0,0,0,0,0,1,1,0,
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[TENSOR,[67,2]]],
[(67,68)]);
ARC("Suz.2","CAS",[rec(name:="suz.2",
permchars:=(13,15,14)(22,28,27,26,25,24,23)(29,31,30)(32,46,56,55,54,52,51,50,
 49,48,45,43,41,39,37,47,44,42,40,38,36,35,34,33),
permclasses:=(),
text:=[
"names:=     suz.2, suz.z2, autsuz\n",
"    order:     2^14.3^7.5^2.7.11.13 = 896,690,995,200\n",
"    number of classes:  68\n",
"    comments:  extension of suz with an outer\n",
"               automorphism of order 2\n",
"    test:      orth.1, min, sym[3]     \n",
""])]);
ARC("Suz.2","projectives",["2.Suz.2",[[220,12,0,-50,4,4,-20,0,0,0,-10,0,6,-6,
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0]],]);
ARC("Suz.2","maxes",["Suz","G2(4).2","3_2.U4(3).(2^2)_{133}","U5(2).2",
"2^(1+6)_-.U4(2).2","3^5:(M11x2)","J2.2x2","2^(4+6):3S6","(A4xL3(4):2_3):2",
"2^(2+8):(S5xS3)","M12.2x2","3^(2+4):2(S4xD8)","(A6:2_2xA5).2","(3^2:8xA6).2",
"L2(25).2_2","A7.2"]);

MOT("Th",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,19,31]"
],
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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
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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)^30,0,0,0,0,0],
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-1,1,1,0,0,0,0,0],
[GALOIS,[17,13]],[2450240,832,260,71,44,64,0,-10,4,4,-5,-5,0,0,17,-10,-1,2,4,
4,1,0,0,-1,-1,-1,1,1,0,0,1,0,0,0,0,-1,-1,-1,1,-1,-1,0,0,1,1,1,0,0],[2572752,
-1072,624,111,84,48,0,2,-4,-16,-1,7,0,0,30,3,3,-2,0,0,3,0,0,-1,-1,-1,2,-1,0,0,
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[GALOIS,[29,2]],[10822875,-805,924,141,-75,91,-5,0,5,-4,5,0,3,-1,-21,6,-3,0,4,
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351,135,0,-120,24,9,0,15,3,7,-8,0,0,0,0,-3,3,3,-3,0,0,-1,0,0,0,0,0,-1,1,1,1,0,
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0,0],
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0]],
[(47,48),(42,43),(37,38),(34,35),(25,26)(40,41),(19,20)(25,26)(32,33)(34,35)
(37,38)(40,41)(45,46)(47,48),(19,20)(32,33)(45,46)]);
ARC("Th","CAS",[rec(name:="th",
permchars:=(),
permclasses:=(32,33)(40,41),
text:=[
"names:=th; e; f3; thompson\n",
"     order: 2^15.3^10.5^3.7^2.13.19.31 = 90,745,943,887,872,000\n",
"     number of classes: 48\n",
"     source / origin:\n",
"            smith, p.e.\n",
"            a simple subgroup of m and e8[3]\n",
"            bull.london math.soc. 8\n",
"            [1976],161-165 \n",
""])]);
ARC("Th","isSimple",true);
ARC("Th","extInfo",["",""]);
ALF("Th","B",[1,5,6,7,7,12,17,19,28,27,29,31,41,45,46,46,47,53,64,64,68,
72,75,80,82,82,96,95,98,108,109,123,123,127,127,131,131,131,136,142,142,
145,146,158,158,158,160,160],[
"fusion map is unique up to table automorphisms"
]);
ARC("Th","maxes",["3D4(2).3","2^5.psl(5,2)","2^1+8.a9","U3(8).6",
"(3xG2(3)):2","ThN3B","ThM7","3^5:2S6","5^(1+2):4S4","5^2:4s5",
"7^2:(3x2S4)","L2(19).2","L3(3)","A6.2_3","31:15","A5.2"]);
ALN("Th",["F3"]);

LIBTABLE.LOADSTATUS.ctospora:="userloaded";

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