Quelle  ctotwis1.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctotwis1.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables related to the twisted
##  groups $^2F_4(2)$, $^3D_4(2)$, $^3D_4(3)$, and $^3D_4(4)$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctotwis1.tbl,v $
#H  Revision 4.16  2012/01/30 08:32:03  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.15  2011/09/28 14:15:56  gap
#H  - fixed the maxes entry for 2F4(2)'.2,
#H  - added fusion from 2F4(2)'.2 to the table of marks
#H      TB
#H
#H  Revision 4.14  2009/07/29 14:01:10  gap
#H  added maxes of 2F4(2)'.2
#H      TB
#H
#H  Revision 4.13  2009/01/12 17:33:58  gap
#H  added missing maxes of Fi22.2 and their fusions
#H      TB
#H
#H  Revision 4.12  2008/06/24 16:23:06  gap
#H  added several fusions and names
#H      TB
#H
#H  Revision 4.11  2005/04/27 07:51:48  gap
#H  added fusion 2F4(2)'.2 -> Fi22.2
#H      TB
#H
#H  Revision 4.10  2003/05/15 17:38:26  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 4.9  2003/01/29 15:51:55  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 4.8  2003/01/21 16:25:33  gap
#H  further standardizations of `InfoText' strings,
#H  added and corrected `Maxes' infos,
#H  added some fusions
#H      TB
#H
#H  Revision 4.7  2002/07/12 06:45:57  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.6  2001/05/04 16:50:21  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.6 of ctbllib coincides with Rev. 4.5 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctotwis1.tbl,v
#H  Working file: ctotwis1.tbl
#H  head: 4.5
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.5.0.6
#H   GAP4R2PRE2: 4.5.0.4
#H   GAP4R2PRE1: 4.5.0.2
#H   GAP4R1: 4.3.0.2
#H  keyword substitution: kv
#H  total revisions: 6; selected revisions: 6
#H  description:
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/10/21 14:15:49;  author: gap;  state: Exp;  lines: +9 -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 4.4
#H  date: 1999/10/04 15:57:15;  author: gap;  state: Exp;  lines: +3 -3
#H  added and corrected several fusions from character tables
#H  to their tables of marks,
#H  unified two instances of the table of (A6xA6):2^2,
#H  corrected the name of the table of marks of 2F4(2).
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1999/07/14 11:39:43;  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 15:45:59;  author: gap;  state: Exp;  lines: +3 -2
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:47:45;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:01:53;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("2F4(2)'",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[17971200,10240,1536,108,192,128,64,50,12,32,32,16,16,10,12,12,13,13,16,16,16,
16],
[,[1,1,1,4,3,2,3,8,4,6,6,7,7,8,9,9,18,17,10,11,10,11],[1,2,3,1,5,6,7,8,3,11,
10,12,13,14,5,5,17,18,22,21,20,19],,[1,2,3,4,5,6,7,1,9,10,11,12,13,2,16,15,18,
17,21,22,19,20],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,1,21,22,19,
20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[26,-6,2,-1,-2,-2,2,1,-1,0,0,0,
0,-1,1,1,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3],
[GALOIS,[2,5]],[27,-5,3,0,3,-1,-1,2,0,-1+2*E(4),-1-2*E(4),-1,-1,0,0,0,1,1,
-E(4),E(4),-E(4),E(4)],
[GALOIS,[4,3]],[78,14,-2,-3,2,-2,2,3,1,2,2,0,0,-1,-1,-1,0,0,0,0,0,0],[300,-20,
-4,3,-4,4,4,0,-1,0,0,0,0,0,-1,-1,1,1,0,0,0,0],[325,5,-11,1,1,5,1,0,1,1,1,-1,
-1,0,1,1,0,0,-1,-1,-1,-1],[351,31,15,0,3,-1,3,1,0,-1,-1,1,1,1,0,0,0,0,-1,-1,
-1,-1],[351,-1,-9,0,3,3,-1,1,0,-1+2*E(4),-1-2*E(4),1,1,-1,0,0,0,0,E(4),-E(4),
E(4),-E(4)],
[GALOIS,[10,3]],[624,-16,16,3,0,0,0,-1,1,0,0,0,0,-1,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,0,0,0,0,0,0],
[GALOIS,[12,5]],[650,10,10,2,6,2,-2,0,-2,2,2,0,0,0,0,0,0,0,0,0,0,0],[675,35,3,
0,3,3,3,0,0,-1,-1,-1,-1,0,0,0,-1,-1,1,1,1,1],[702,30,6,0,-6,2,-2,2,0,0,0,0,0,
0,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3],
[GALOIS,[16,3]],[1300,20,-12,4,0,-4,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0],[1300,
20,-12,4,0,-4,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0],[1728,-64,0,0,0,0,0,3,0,0,0,0,
0,1,0,0,-1,-1,0,0,0,0],[2048,0,0,-4,0,0,0,-2,0,0,0,0,0,0,0,0,
-E(13)-E(13)^3-E(13)^4-E(13)^9-E(13)^10-E(13)^12,-E(13)^2-E(13)^5-E(13)^6
 -E(13)^7-E(13)^8-E(13)^11,0,0,0,0],
[GALOIS,[21,2]]],
[(19,21)(20,22),(17,18),(15,16),(12,13),(10,11)(19,20)(21,22),(10,11)(15,16)
(19,20)(21,22),(10,11)(15,16)(19,22)(20,21)]);
ARC("2F4(2)'","CAS",[rec(name:="tits",
permchars:=(21,22),
permclasses:=(21,22),
text:=[
" maximal subgroup   index\n",
" 2.2^8.f20          1755\n",
" 2^2.2^8:=s3         2925\n",
" test: 1. o.r., sym 2, 3 and restricted characters of ru decompose\n",
"       correctly\n",
""])]);
ARC("2F4(2)'","isSimple",true);
ARC("2F4(2)'","extInfo",["","2"]);
ARC("2F4(2)'","tomfusion",rec(name:="2F4(2)'",map:=[1,2,3,4,12,14,13,15,
18,48,48,49,50,55,61,61,62,62,125,125,125,125],text:=[
"unique fusion map compatible with AtlasRep"
]));
ALF("2F4(2)'","2F4(2)'.2",[1,2,3,4,5,6,7,8,9,10,11,12,12,13,14,14,15,15,
16,17,16,17]);
ALF("2F4(2)'","Fi22",[1,3,4,8,12,11,12,14,25,29,29,30,30,35,48,48,49,50,
53,54,54,53],[
"fusion map is unique up to table automorphisms"
]);
ALF("2F4(2)'","Ru",[1,2,2,4,5,7,8,9,11,14,14,15,15,16,18,18,20,20,26,25,
26,25],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("2F4(2)'",["R(2)'","Tits","r2c"]);
ARC("2F4(2)'","maxes",["L3(3).2","2F4(2)'M2","2.2^8.f20","L2(25)",
"2^2.2^8:s3","A6.2^2","2F4(2)'M7","5^2:4A4"]);

MOT("2F4(2)'.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(2F4(2)')"
],
[35942400,20480,3072,216,384,256,128,100,24,64,64,16,20,12,13,16,16,1280,1280,
192,128,32,16,12,12,16,16,20,20],
[,[1,1,1,4,3,2,3,8,4,6,6,7,8,9,15,10,11,2,2,3,2,6,5,9,9,10,11,13,13],[1,2,3,1,
5,6,7,8,3,11,10,12,13,5,15,17,16,19,18,20,21,22,23,20,20,27,26,29,28],,[1,2,3,
4,5,6,7,1,9,10,11,12,2,14,15,16,17,18,19,20,21,22,23,25,24,26,27,18,
19],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,16,17,18,19,20,21,22,23,24,25,
26,27,28,29]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[52,-12,4,-2,-4,-4,4,2,
-2,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[27,-5,3,0,3,-1,-1,2,0,-1+2*E(4),
-1-2*E(4),-1,0,0,1,-E(4),E(4),1+4*E(4),1-4*E(4),-3,1,-1,-1,0,0,E(4),-E(4),
1-E(4),1+E(4)],
[TENSOR,[4,2]],
[GALOIS,[4,3]],
[TENSOR,[6,2]],[78,14,-2,-3,2,-2,2,3,1,2,2,0,-1,-1,0,0,0,6,6,2,-2,2,0,-1,-1,0,
0,1,1],
[TENSOR,[8,2]],[300,-20,-4,3,-4,4,4,0,-1,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,
E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0],
[TENSOR,[10,2]],[325,5,-11,1,1,5,1,0,1,1,1,-1,0,1,0,-1,-1,5,5,1,-3,1,-1,1,1,
-1,-1,0,0],
[TENSOR,[12,2]],[351,31,15,0,3,-1,3,1,0,-1,-1,1,1,0,0,-1,-1,9,9,-3,1,1,-1,0,0,
1,1,-1,-1],
[TENSOR,[14,2]],[351,-1,-9,0,3,3,-1,1,0,-1+2*E(4),-1-2*E(4),1,-1,0,0,E(4),
-E(4),5+4*E(4),5-4*E(4),-3,-3,-1,1,0,0,-E(4),E(4),-E(4),E(4)],
[TENSOR,[16,2]],
[GALOIS,[16,3]],
[TENSOR,[18,2]],[1248,-32,32,6,0,0,0,-2,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[650,10,10,2,6,2,-2,0,-2,2,2,0,0,0,0,0,0,10,10,6,2,-2,0,0,0,0,0,0,0],
[TENSOR,[21,2]],[675,35,3,0,3,3,3,0,0,-1,-1,-1,0,0,-1,1,1,5,5,-3,5,1,1,0,0,-1,
-1,0,0],
[TENSOR,[23,2]],[1404,60,12,0,-12,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[2600,40,-24,8,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
1728,-64,0,0,0,0,0,3,0,0,0,0,1,0,-1,0,0,16*E(4),-16*E(4),0,0,0,0,0,0,0,0,E(4),
-E(4)],
[TENSOR,[27,2]],[4096,0,0,-8,0,0,0,-4,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0]],
[(24,25),(10,11)(16,17)(18,19)(26,27)(28,29)]);
ARC("2F4(2)'.2","CAS",[rec(name:="tits.2",
permchars:=(27,28),
permclasses:=(),
text:=[
" subgroup of ru \n",
" test:= 1. o.r., sym 2, 3 and restricted characters of ru decompose\n",
"       correctly    \n",
""])]);
ARC("2F4(2)'.2","maxes",["2F4(2)'","2.[2^9]:5:4","L2(25).2_3",
"2^2.[2^9]:S3","Fi22N5","3^(1+2):SD16","13:12"]);
ARC("2F4(2)'.2","tomfusion",rec(name:="2F4(2)",map:=[1,2,3,4,11,13,12,14,
16,42,42,43,47,51,52,102,102,351,351,353,352,363,362,364,364,401,401,404,
404],text:=[
"fusion map is unique"
],perm:=(1,2,3,4,5,6,7)));
ALF("2F4(2)'.2","Ru",[1,2,2,4,5,7,8,9,11,14,14,15,16,18,20,26,25,5,5,6,8,
14,13,19,19,25,26,27,27],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2F4(2)'.2","Fi22.2",[1,3,4,8,12,11,12,14,25,29,29,30,35,46,47,50,50,
64,64,67,66,81,82,95,95,98,98,103,103],[
"fusion map is unique"
]);
ALF("2F4(2)'.2","F4(2)",[1,4,5,8,20,17,20,24,35,46,46,47,53,68,71,78,79,
14,14,22,21,39,47,69,70,79,78,85,85],[
"fusion is unique up to table automorphisms"
]);
ALN("2F4(2)'.2",["2F4(2)","Tits.2","R(2)"]);

MOT("3D4(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[211341312,258048,3072,1512,648,3584,1536,64,72,24,1176,1176,1176,49,32,32,54,
54,54,12,13,13,13,56,56,56,18,18,18,21,21,21,28,28,28],
[,[1,1,1,4,5,2,2,3,5,4,12,13,11,14,6,7,18,19,17,9,22,23,21,12,13,11,18,19,17,
31,32,30,25,26,24],[1,2,3,1,1,6,7,8,2,3,13,11,12,14,15,16,5,5,5,7,22,23,21,26,
24,25,9,9,9,13,11,12,35,33,34],,,,[1,2,3,4,5,6,7,8,9,10,1,1,1,1,15,16,18,19,
17,20,23,21,22,2,2,2,28,29,27,4,4,4,6,6,6],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,19,17,18,20,1,1,1,24,25,26,29,27,28,30,31,32,33,34,35]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[26,
-6,2,-1,-1,6,-2,2,3,-1,5,5,5,-2,0,0,2,2,2,1,0,0,0,1,1,1,0,0,0,-1,-1,-1,-1,-1,
-1],[52,20,-4,7,-2,8,0,0,2,-1,3,3,3,3,-2,2,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,0,
0,0,1,1,1],[196,-28,-4,7,7,0,8,0,-1,-1,0,0,0,0,2,-2,1,1,1,-1,1,1,1,0,0,0,-1,
-1,-1,0,0,0,0,0,0],[273,-15,-7,-6,3,13,5,1,3,2,7,7,7,0,-1,-1,0,0,0,-1,0,0,0,
-1,-1,-1,0,0,0,1,1,1,-1,-1,-1],[324,36,12,0,0,8,0,0,0,0,9,9,9,2,2,-2,0,0,0,0,
-1,-1,-1,1,1,1,0,0,0,0,0,0,1,1,1],[351,63,7,9,0,11,3,-1,0,1,
E(7)+3*E(7)^3+3*E(7)^4+E(7)^6,3*E(7)+E(7)^2+E(7)^5+3*E(7)^6,
3*E(7)^2+E(7)^3+E(7)^4+3*E(7)^5,1,1,1,0,0,0,0,0,0,0,E(7)-E(7)^3-E(7)^4+E(7)^6,
-E(7)+E(7)^2+E(7)^5-E(7)^6,-E(7)^2+E(7)^3+E(7)^4-E(7)^5,0,0,0,E(7)+E(7)^6,
E(7)^2+E(7)^5,E(7)^3+E(7)^4,E(7)+E(7)^3+E(7)^4+E(7)^6,E(7)+E(7)^2+E(7)^5
 +E(7)^6,E(7)^2+E(7)^3+E(7)^4+E(7)^5],
[GALOIS,[7,3]],
[GALOIS,[7,2]],[468,-12,12,0,9,0,8,0,-3,0,6,6,6,-1,-2,2,0,0,0,-1,0,0,0,2,2,2,
0,0,0,0,0,0,0,0,0],[637,-35,5,7,-11,-7,17,-3,1,-1,0,0,0,0,-1,-1,1,1,1,-1,0,0,
0,0,0,0,1,1,1,0,0,0,0,0,0],[1053,-99,-3,0,0,29,-3,-3,0,0,3,3,3,-4,1,1,0,0,0,0,
0,0,0,-1,-1,-1,0,0,0,0,0,0,1,1,1],[1274,154,-14,14,5,14,-10,2,1,-2,0,0,0,0,0,
0,-1,-1,-1,-1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],[1664,128,0,8,-10,0,0,0,2,0,-2,
-2,-2,-2,0,0,-1,-1,-1,0,0,0,0,2,2,2,-1,-1,-1,1,1,1,0,0,0],[1911,119,-9,0,3,7,
7,-1,-1,0,0,0,0,0,-1,-1,E(9)^2-E(9)^4-E(9)^5+E(9)^7,E(9)^2+2*E(9)^4+2*E(9)^5
 +E(9)^7,-2*E(9)^2-E(9)^4-E(9)^5-2*E(9)^7,1,0,0,0,0,0,0,-E(9)^2-E(9)^4-E(9)^5
 -E(9)^7,E(9)^2+E(9)^7,E(9)^4+E(9)^5,0,0,0,0,0,0],
[GALOIS,[15,4]],
[GALOIS,[15,2]],[2106,90,18,0,0,-2,6,2,0,0,6*E(7)-3*E(7)^3-3*E(7)^4+6*E(7)^6,
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0,0,0,0,0,0,0,0,2*E(7)+E(7)^3+E(7)^4+2*E(7)^6,E(7)+2*E(7)^2+2*E(7)^5+E(7)^6,
E(7)^2+2*E(7)^3+2*E(7)^4+E(7)^5,0,0,0,0,0,0,-E(7)^3-E(7)^4,-E(7)-E(7)^6,
-E(7)^2-E(7)^5],
[GALOIS,[18,3]],
[GALOIS,[18,2]],[2184,-120,8,15,-3,-8,-8,0,-3,-1,7,7,7,0,0,0,0,0,0,1,0,0,0,-1,
-1,-1,0,0,0,1,1,1,-1,-1,-1],[2457,-135,1,9,0,5,-3,1,0,1,7*E(7)+7*E(7)^6,
7*E(7)^2+7*E(7)^5,7*E(7)^3+7*E(7)^4,0,-1,-1,0,0,0,0,0,0,0,-E(7)-E(7)^6,
-E(7)^2-E(7)^5,-E(7)^3-E(7)^4,0,0,0,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,
-E(7)-E(7)^6,-E(7)^2-E(7)^5,-E(7)^3-E(7)^4],
[GALOIS,[22,3]],
[GALOIS,[22,2]],[2808,-72,8,-9,0,16,0,0,0,-1,8*E(7)+3*E(7)^3+3*E(7)^4+8*E(7)^6
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0,0,0,0,0,0,0,-E(7)^3-E(7)^4,-E(7)-E(7)^6,-E(7)^2-E(7)^5,0,0,0,-E(7)-E(7)^6,
-E(7)^2-E(7)^5,-E(7)^3-E(7)^4,E(7)^3+E(7)^4,E(7)+E(7)^6,E(7)^2+E(7)^5],
[GALOIS,[25,3]],
[GALOIS,[25,2]],[3822,14,6,0,6,-14,-6,-2,2,0,0,0,0,0,0,0,-E(9)^2+E(9)^4+E(9)^5
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0,0,0,0,0,-E(9)^2-E(9)^4-E(9)^5-E(9)^7,E(9)^2+E(9)^7,E(9)^4+E(9)^5,0,0,0,0,0,
0],
[GALOIS,[28,4]],
[GALOIS,[28,2]],[3969,-63,-15,0,0,-7,9,1,0,0,0,0,0,0,1,1,0,0,0,0,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[31,4]],
[GALOIS,[31,2]],[4096,0,0,-8,-8,0,0,0,0,0,8,8,8,1,0,0,-2,-2,-2,0,1,1,1,0,0,0,
0,0,0,-1,-1,-1,0,0,0],[5096,168,-8,-7,-7,0,-16,0,-3,1,0,0,0,0,0,0,2,2,2,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(21,22,23),(21,23,22),(17,18,19)(27,28,29),(17,19,18)(27,29,28),(11,13,12)
(24,26,25)(30,32,31)(33,35,34)]);
ARC("3D4(2)","CAS",[rec(name:="st2",
permclasses:=(),
permchars:=(),
text:=[
"names:=st2; 3d4[2]\n",
"  order: 2^12.3^4.7^2.13 = 211,341,312\n",
"  number of classes: 35\n",
"  source: private communication of compound table\n",
"          from cambridge group atlas project 1980/81\n",
"  origin: conway, j. - guy, m.\n",
"          -unpublished-\n",
"  comments: - \n",
""])]);
ARC("3D4(2)","isSimple",true);
ARC("3D4(2)","extInfo",["","3"]);
ARC("3D4(2)","maxes",["2^(1+8)+:L2(8)","2^2.[2^9]:(7xS3)","U3(3).2",
"S3xL2(8)","(7xL2(7)):2","3^(1+2)+.2S4","7^2:2A4","3^2:2A4","13:4"]);
ARC("3D4(2)","tomfusion",rec(name:="3D4(2)",map:=[1,2,3,4,5,16,17,18,22,23,24,
24,24,25,86,87,90,90,90,95,102,102,102,103,103,103,449,449,449,451,451,451,
477,477,477],text:=[
"fusion map is unique"
]));
ALF("3D4(2)","3D4(2).3",[1,2,3,4,5,6,7,8,9,10,11,11,11,12,13,14,15,15,15,
16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,21]);
ALF("3D4(2)","3D4(4)",[1,2,3,5,4,6,6,8,13,14,15,16,17,18,19,19,21,22,23,
28,37,38,39,41,42,40,48,49,47,72,70,71,81,79,80],[
"fusion map is unique up to table automorphisms"
]);
ALN("3D4(2)",["st2"]);

MOT("3D4(2).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(3D4(2))"
],
[634023936,774144,9216,4536,1944,10752,4608,192,216,72,1176,147,96,96,54,36,
13,56,18,21,28,36288,36288,648,648,576,576,144,144,72,72,54,54,288,288,144,
144,96,96,12,12,18,18,21,21,24,24,24,24],
[,[1,1,1,4,5,2,2,3,5,4,11,12,6,7,15,9,17,11,15,20,18,23,22,25,24,23,22,23,22,
25,24,33,32,27,26,27,26,27,26,31,30,33,32,45,44,35,34,39,38],[1,2,3,1,1,6,7,8,
2,3,11,12,13,14,5,7,17,18,9,11,21,1,1,1,1,2,2,3,3,3,3,5,5,7,7,7,7,6,6,8,8,9,9,
12,12,14,14,13,13],,,,[1,2,3,4,5,6,7,8,9,10,1,1,13,14,15,16,17,2,19,4,6,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,46,47,48,
49],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,E(3),E(3)^2,
E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2],
[TENSOR,[2,2]],[26,-6,2,-1,-1,6,-2,2,3,-1,5,-2,0,0,2,1,0,1,0,-1,-1,8,8,-1,-1,
0,0,2,2,-1,-1,2,2,4,4,-2,-2,0,0,-1,-1,0,0,1,1,0,0,0,0],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[52,20,-4,7,-2,8,0,0,2,-1,3,3,-2,2,1,0,0,-1,-1,0,1,7,7,-2,-2,
-1,-1,-1,-1,2,2,1,1,3,3,3,3,-1,-1,0,0,-1,-1,0,0,-1,-1,1,1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],[196,-28,-4,7,7,0,8,0,-1,-1,0,0,2,-2,1,-1,1,0,-1,0,0,7,7,-2,-2,
-1,-1,-1,-1,2,2,1,1,-1,-1,-1,-1,3,3,0,0,-1,-1,0,0,1,1,-1,-1],
[TENSOR,[10,2]],
[TENSOR,[10,3]],[273,-15,-7,-6,3,13,5,1,3,2,7,0,-1,-1,0,-1,0,-1,0,1,-1,21,21,
3,3,-3,-3,-1,-1,-1,-1,0,0,5,5,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[13,2]],
[TENSOR,[13,3]],[324,36,12,0,0,8,0,0,0,0,9,2,2,-2,0,0,-1,1,0,0,1,27,27,0,0,3,
3,3,3,0,0,0,0,3,3,3,3,-1,-1,0,0,0,0,-1,-1,1,1,-1,-1],
[TENSOR,[16,2]],
[TENSOR,[16,3]],[1053,189,21,27,0,33,9,-3,0,3,-4,3,3,3,0,0,0,0,0,-1,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[468,-12,12,0,9,0,8,0,-3,0,
6,-1,-2,2,0,-1,0,2,0,0,0,27,27,0,0,3,3,3,3,0,0,0,0,-1,-1,-1,-1,3,3,0,0,0,0,-1,
-1,-1,-1,1,1],
[TENSOR,[20,2]],
[TENSOR,[20,3]],[637,-35,5,7,-11,-7,17,-3,1,-1,0,0,-1,-1,1,-1,0,0,1,0,0,7,7,
-2,-2,7,7,-1,-1,2,2,1,1,-1,-1,-1,-1,-1,-1,0,0,1,1,0,0,-1,-1,-1,-1],
[TENSOR,[23,2]],
[TENSOR,[23,3]],[1053,-99,-3,0,0,29,-3,-3,0,0,3,-4,1,1,0,0,0,-1,0,0,1,27,27,0,
0,3,3,-3,-3,0,0,0,0,3,3,-3,-3,-1,-1,0,0,0,0,-1,-1,1,1,1,1],
[TENSOR,[26,2]],
[TENSOR,[26,3]],[1274,154,-14,14,5,14,-10,2,1,-2,0,0,0,0,-1,-1,0,0,1,0,0,14,
14,5,5,-2,-2,-2,-2,1,1,-1,-1,2,2,2,2,2,2,-1,-1,1,1,0,0,0,0,0,0],
[TENSOR,[29,2]],
[TENSOR,[29,3]],[1664,128,0,8,-10,0,0,0,2,0,-2,-2,0,0,-1,0,0,2,-1,1,0,8,8,8,8,
8,8,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,-1,-1,1,1,0,0,0,0],
[TENSOR,[32,2]],
[TENSOR,[32,3]],[5733,357,-27,0,9,21,21,-3,-3,0,0,0,-3,-3,0,3,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6318,270,54,0,0,-6,18,6,0,
0,-3,-3,0,0,0,0,0,-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[2184,-120,8,15,-3,-8,-8,0,-3,-1,7,0,0,0,0,1,0,-1,0,1,-1,42,42,6,6,-6,
-6,2,2,2,2,0,0,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[37,2]],
[TENSOR,[37,3]],[7371,-405,3,27,0,15,-9,3,0,3,-7,0,-3,-3,0,0,0,1,0,-1,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8424,-216,24,-27,0,48,0,0,
0,-3,-11,3,0,0,0,0,0,1,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[11466,42,18,0,18,-42,-18,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[11907,-189,-45,0,0,-21,27,3,0,0,0,
0,3,3,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[4096,0,0,-8,-8,0,0,0,0,0,8,1,0,0,-2,0,1,0,0,-1,0,64,64,-8,-8,0,0,0,0,0,0,
-2,-2,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0],
[TENSOR,[44,2]],
[TENSOR,[44,3]],[5096,168,-8,-7,-7,0,-16,0,-3,1,0,0,0,0,2,-1,0,0,0,0,0,56,56,
2,2,0,0,-2,-2,-2,-2,2,2,-4,-4,2,2,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[47,2]],
[TENSOR,[47,3]]],
[(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)]);
ARC("3D4(2).3","CAS",[rec(name:="st.3",
permclasses:=(),
permchars:=(),
text:=[
"names:=st2a; 3d4[2].3\n",
" order: 2^12.3^5.7^2.13 = 634,023,936\n",
" number of classes: 49\n",
" source: private communication of compound table\n",
"         from cambridge group atlas project 1980/81\n",
" origin: conway, j. - guy, m.\n",
"         -unpublished-\n",
" comments: - \n",
""])]);
ARC("3D4(2).3","maxes",["3D4(2)","2^(1+8)_+:L2(8):3","2^2.[2^9]:(7:3xS3)",
"3xU3(3).2","s3xpsl(2,8).3","(7:3xL2(7)):2","3^(1+2)_+.(2S4x3)","7^2:(3x2A4)",
"3^2:2A4x3","13:12"]);
ALF("3D4(2).3","Th",[1,2,2,3,4,6,6,7,11,10,12,12,13,13,17,21,23,24,28,31,
39,3,3,5,5,10,10,10,10,9,9,17,17,19,20,19,20,20,19,22,22,28,28,31,31,33,
32,32,33],[
"fusion is unique up to table automorphisms"
]);
ALF("3D4(2).3","F4(2)",[1,2,5,6,8,11,9,22,29,33,36,37,40,42,49,56,71,72,
82,86,92,7,7,8,8,28,28,34,34,35,35,49,49,55,55,55,55,63,63,69,70,82,82,87,
87,91,91,89,89],[
"fusion map is unique up to table automorphisms"
]);
ALN("3D4(2).3",["st2.3"]);

MOT("F4(2)M10",
[
"differs from 3D4(2).3 only by fusion into F4(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["3D4(2).3"]]);
ALF("F4(2)M10","F4(2)",[1,3,5,7,8,12,10,22,30,34,37,36,41,43,50,57,71,73,
83,87,93,6,6,8,8,27,27,33,33,35,35,50,50,54,54,54,54,62,62,69,70,83,83,86,
86,90,90,88,88],[
"fusion 3D4(2).3 -> F4(2) mapped under F4(2).2"
]);

MOT("3D4(3)",
[
"computed using Magma V2.23-9     Mon Oct  1 2018 10:41:55 on schedir\n",
"[Seed = 2806849869]\n",
"Total time: 30.539 seconds, Total memory usage: 115.25MB"
],
[20560831566912,471744,386889048,472392,170586,91854,78624,672,58968,648,162,
162,42336,42336,42336,49,104,56,729,81,108,84,73008,73008,73008,73008,73008,
73008,169,169,169,169,169,672,672,672,756,756,756,63,63,63,624,624,624,624,624
,624,672,672,672,672,672,672,112,112,112,702,702,702,702,702,702,117,117,117,
117,117,117,84,84,84,104,104,104,104,104,104,56,56,56,56,56,56,73,73,73,73,73,
73,73,73,73,73,73,73,73,73,73,73,73,73,78,78,78,78,78,78,84,84,84,84,84,84,104
,104,104,104,104,104,104,104,104,104,104,104],
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36,59,60,61,62,63,58,65,66,67,68,69,64,37,38,39,43,44,45,46,47,48,49,50,51,52,
53,54,93,94,95,96,97,98,99,100,101,102,85,86,87,88,89,90,91,92,58,59,60,61,62,
63,70,71,72,70,71,72,73,78,77,76,75,74,73,78,77,76,75,74],[1,2,1,1,1,1,7,8,2,2
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,15,13,14,15,47,48,43,44,45,46,51,52,53,54,49,50,57,55,56,23,24,25,26,27,28,23
,24,25,26,27,28,34,35,36,77,78,73,74,75,76,81,82,83,84,79,80,91,92,93,94,95,96
,97,98,99,100,101,102,85,86,87,88,89,90,43,44,45,46,47,48,52,53,54,49,50,51,
123,124,125,126,115,116,117,118,119,120,121,122],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,1,1,1,1,17,18,19,20,21,22,28,23,24,25,26,27,30,29,33,31,32,2,2,2,3,3,3,6,6,
6,48,43,44,45,46,47,8,8,8,8,8,8,7,7,7,63,58,59,60,61,62,69,64,65,66,67,68,9,9,
9,78,73,74,75,76,77,18,18,18,18,18,18,100,101,102,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,108,103,104,105,106,107,22,22,22,22,22,22,116,117,118,119,
120,121,122,123,124,125,126,115],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
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9,9,112,113,114,109,110,111,17,17,17,17,17,17,17,17,17,17,17,17],,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,15,
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ARC("3D4(3)","isSimple",true);
ARC("3D4(3)","extInfo",["","3"]);

MOT("3D4(4)",
[
"computed by Eamonn O'Brien using Magma, April 2014"
],
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--> --------------------

--> maximum size reached

--> --------------------