Quelle  ctoline6.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctoline6.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of
##  $L_4(4)$, $L_4(4).2_1$, $L_4(4).2_2$, $L_4(4).2_3$, $L_4(4).2^2$,
##  $L_7(2)$, $L_7(2).2$, $L_5(3)$, $L_5(3).2$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctoline6.tbl,v $
#H  Revision 4.10  2012/01/30 08:31:44  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.9  2012/01/26 11:13:43  gap
#H  added maxes entry for L7(2)
#H      TB
#H
#H  Revision 4.8  2011/09/28 14:32:13  gap
#H  removed revision entry and SET_TABLEFILENAME call
#H      TB
#H
#H  Revision 4.7  2010/05/05 13:20:02  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 4.6  2008/06/24 16:23:05  gap
#H  added several fusions and names
#H      TB
#H
#H  Revision 4.5  2005/08/10 14:33:20  gap
#H  corrected InfoText values concerning GV4 constructions,
#H  added table of 2^2.L3(4).2_1 and related fusions
#H      TB
#H
#H  Revision 4.4  2004/08/31 12:33:33  gap
#H  added tables of 4.L2(25).2_3,
#H                  L2(49).2^2,
#H                  L2(81).2^2,
#H                  L2(81).(2x4),
#H                  3.L3(4).3.2_2,
#H                  L3(9).2^2,
#H                  L4(4).2^2,
#H                  2x2^3:L3(2)x2,
#H                  (2xA6).2^2,
#H                  2xL2(11).2,
#H                  S3xTh,
#H                  41:40,
#H                  7^(1+4):(3x2.S7),
#H                  7xL2(8),
#H                  (7xL2(8)).3,
#H                  O7(3)N3A,
#H                  O8+(3).2_1',
#H                  O8+(3).2_1'',
#H                  O8+(3).2_2',
#H                  O8+(3).(2^2)_{122},
#H                  S4(9),
#H                  S4(9).2_i,
#H                  2.U4(3).2_2',
#H                  2.U4(3).(2^2)_{133},
#H                  2.U4(3).D8,
#H                  3.U6(2).S3,
#H  added fusions 3.A6.2_i -> 3.A6.2^2,
#H                L2(49).2_i -> L2(49).2^2,
#H                L3(9).2_i -> L3(9).2^2,
#H                L4(4).2_i -> L4(4).2^2,
#H                G2(3) -> O7(3),
#H                L2(17) -> S8(2),
#H                2.L3(4).2_2 -> 2.M22.2
#H                3.L3(4).2_2 -> 3.L3(4).3.2_2
#H                3.L3(4).3 -> 3.L3(4).3.2_2
#H                2^5:S6 -> 2.M22.2
#H                O8+(3) -> O8+(3).2_1',
#H                O8+(3) -> O8+(3).2_1'',
#H                O8+(3) -> O8+(3).2_2',
#H                O8+(3) -> O8+(3).(2^2)_{122},
#H                O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H                O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H                2.U4(3) -> 2.U4(3).2_2',
#H                2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_2 -> O7(3),
#H                2.U4(3).2_2' -> U4(3).2_2,
#H                2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).4 -> 2.U4(3).D8,
#H                3.U6(2).2 -> 3.U6(2).S3,
#H                3.U6(2).3 -> 3.U6(2).S3,
#H  replaced table of psl(3,4):d12 by L3(4).D12,
#H  changed table of O8+(3).S4 to a construction table,
#H  changed encoding of the table of 12.A6.2_3,
#H  added maxes of Sz(8), Sz(8).3,
#H      TB
#H
#H  Revision 4.3  2001/05/04 16:47:49  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.3 of ctbllib coincides with Rev. 4.2 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctoline6.tbl,v
#H  Working file: ctoline6.tbl
#H  head: 4.2
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.2.0.8
#H   GAP4R2PRE2: 4.2.0.6
#H   GAP4R2PRE1: 4.2.0.4
#H   GAP4R1: 4.2.0.2
#H  keyword substitution: kv
#H  total revisions: 3; selected revisions: 3
#H  description:
#H  ----------------------------
#H  revision 4.2
#H  date: 1999/07/14 11:39:38;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:40:49;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 15:59:41;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("L4(4)",
[
"origin: constructed by T. Breuer using the perm. repr. on 85 points\n",
"and the table of the subgroup 3.L3(4).3"
],
[987033600,184320,15360,181440,181440,10800,540,768,64,20400,20400,900,900,75,
720,720,576,576,48,36,63,63,63,63,80,80,60,60,48,48,900,900,900,900,75,75,75,
75,45,45,45,45,45,45,85,85,85,85,63,63,63,63,60,60,60,60,63,63,63,63,63,63,63,
63,63,63,63,63,85,85,85,85,85,85,85,85,85,85,85,85,85,85,85,85],
[,[1,1,1,5,4,6,7,2,3,11,10,13,12,14,6,6,5,4,6,7,21,22,24,23,11,10,12,13,17,18,
32,31,34,33,35,36,38,37,40,39,44,43,42,41,46,45,48,47,51,52,49,50,33,32,31,34,
63,62,66,65,67,58,57,68,60,59,61,64,79,82,76,78,81,83,80,71,84,72,69,75,73,70,
74,77],[1,2,3,1,1,1,1,8,9,11,10,13,12,14,2,2,2,2,3,2,22,21,4,5,26,25,28,27,8,
8,12,13,12,13,14,14,11,10,12,13,13,12,13,12,48,47,45,46,21,22,21,22,27,28,27,
28,52,51,51,50,51,49,50,52,52,49,49,50,77,83,70,79,78,75,81,82,71,69,84,73,72,
74,80,76],,[1,2,3,5,4,6,7,8,9,1,1,1,1,1,16,15,18,17,19,20,22,21,24,23,3,3,2,2,
30,29,6,6,6,6,6,6,6,6,7,7,5,5,4,4,48,47,45,46,52,51,50,49,15,15,16,16,66,63,
68,58,60,57,59,67,62,64,65,61,47,46,48,45,48,48,46,47,45,46,48,45,47,45,47,
46],,[1,2,3,4,5,6,7,8,9,11,10,13,12,14,15,16,17,18,19,20,1,1,23,24,26,25,28,
27,29,30,34,33,32,31,36,35,38,37,40,39,42,41,44,43,47,48,46,45,5,5,4,4,54,53,
56,55,23,23,23,24,23,24,24,23,23,24,24,24,70,73,80,76,77,72,79,75,83,71,82,69,
84,81,78,74],,,,,,,,,,[1,2,3,5,4,6,7,8,9,11,10,13,12,14,16,15,18,17,19,20,22,
21,24,23,26,25,28,27,30,29,32,31,34,33,35,36,38,37,40,39,44,43,42,41,1,1,1,1,
52,51,50,49,56,55,54,53,66,63,68,58,60,57,59,67,62,64,65,61,11,10,11,11,11,10,
11,10,10,10,10,10,10,11,11,11]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1],[84,20,4,21,21,9,6,4,0,-1,-1,4,4,-1,5,5,5,5,1,2,0,0,0,0,-1,-1,
0,0,1,1,4,4,4,4,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[272,16,16,20,
20,17,5,0,0,17,17,-3,-3,2,1,1,4,4,1,1,-1,-1,-1,-1,1,1,1,1,0,0,-3,-3,-3,-3,2,2,
2,2,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[357,37,21,-21,-21,24,-3,5,1,17,17,2,2,2,
4,4,-5,-5,0,1,0,0,0,0,1,1,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,-1,-1,-1,-1,0,
0,0,0,0,0,0,0,-1,-1,-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],[1344,64,0,84,84,24,9,0,0,-16,-16,-1,-1,-1,4,4,4,4,0,1,0,0,0,0,0,0,-1,-1,
0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1785,121,25,84,84,-15,
-6,9,1,0,0,5,5,0,1,1,4,4,1,-2,0,0,0,0,0,0,1,1,0,0,5,5,5,5,0,0,0,0,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[2835,-45,3,0,0,0,0,3,-1,30,30,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(17)-E(17)^4-E(17)^13-E(17)^16,
-E(17)^2-E(17)^8-E(17)^9-E(17)^15,-E(17)^6-E(17)^7-E(17)^10-E(17)^11,
-E(17)^3-E(17)^5-E(17)^12-E(17)^14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(17)^2-E(17)^8-E(17)^9-E(17)^15,-E(17)^3-E(17)^5-E(17)^12-E(17)^14,
-E(17)-E(17)^4-E(17)^13-E(17)^16,-E(17)^6-E(17)^7-E(17)^10-E(17)^11,
-E(17)-E(17)^4-E(17)^13-E(17)^16,-E(17)-E(17)^4-E(17)^13-E(17)^16,
-E(17)^3-E(17)^5-E(17)^12-E(17)^14,-E(17)^2-E(17)^8-E(17)^9-E(17)^15,
-E(17)^6-E(17)^7-E(17)^10-E(17)^11,-E(17)^3-E(17)^5-E(17)^12-E(17)^14,
-E(17)-E(17)^4-E(17)^13-E(17)^16,-E(17)^6-E(17)^7-E(17)^10-E(17)^11,
-E(17)^2-E(17)^8-E(17)^9-E(17)^15,-E(17)^6-E(17)^7-E(17)^10-E(17)^11,
-E(17)^2-E(17)^8-E(17)^9-E(17)^15,-E(17)^3-E(17)^5-E(17)^12-E(17)^14],
[GALOIS,[7,2]],
[GALOIS,[7,3]],
[GALOIS,[7,6]],[3213,-51,29,0,0,18,0,-3,1,-17,-17,3,3,3,-6,-6,0,0,2,0,0,0,0,0,
-1,-1,-1,-1,0,0,3,3,3,3,3,3,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-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],[3825,-15,-15,45,45,0,0,
1,1,0,0,0,0,0,0,0,-3,-3,0,0,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,3,3,0,0,0,
0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
3825,-15,-15,45,45,0,0,1,1,0,0,0,0,0,0,0,-3,-3,0,0,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,3*E(3)^2,3*E(3),0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,0,0,0,0,E(21)^5+E(21)^17+E(21)^20,
E(21)^2+E(21)^8+E(21)^11,E(21)^2+E(21)^8+E(21)^11,E(21)^10+E(21)^13+E(21)^19,
E(21)^2+E(21)^8+E(21)^11,E(21)+E(21)^4+E(21)^16,E(21)^10+E(21)^13+E(21)^19,
E(21)^5+E(21)^17+E(21)^20,E(21)^5+E(21)^17+E(21)^20,E(21)+E(21)^4+E(21)^16,
E(21)+E(21)^4+E(21)^16,E(21)^10+E(21)^13+E(21)^19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],
[GALOIS,[13,2]],
[GALOIS,[12,3]],
[GALOIS,[13,10]],
[GALOIS,[13,5]],[3825,-15,-15,45*E(3)^2,45*E(3),0,0,1,1,0,0,0,0,0,0,0,
-3*E(3)^2,-3*E(3),0,0,3,3,0,0,0,0,0,0,E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,3*E(3),3*E(3),3*E(3)^2,3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[3825,-15,-15,45*E(3)^2,45*E(3),0,0,1,1,0,0,0,0,0,
0,0,-3*E(3)^2,-3*E(3),0,0,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,0,0,0,0,0,0,
E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(21)^10+E(21)^13+E(21)^19,
E(21)+E(21)^4+E(21)^16,E(21)^5+E(21)^17+E(21)^20,E(21)^2+E(21)^8+E(21)^11,0,0,
0,0,-E(63)^8+E(63)^23-E(63)^50+E(63)^53,-E(63)^5-E(63)^26+E(63)^59+E(63)^62,
-E(63)^17+E(63)^26+E(63)^41-E(63)^59,-E(63)^4+E(63)^22+E(63)^37-E(63)^46,
E(63)^5+E(63)^17-E(63)^41-E(63)^62,-E(63)^19+E(63)^31-E(63)^40+E(63)^55,
-E(63)-E(63)^22+E(63)^46+E(63)^58,E(63)^8-E(63)^23+E(63)^32-E(63)^44,
-E(63)^32+E(63)^44+E(63)^50-E(63)^53,-E(63)^10+E(63)^13+E(63)^19-E(63)^31,
E(63)^10-E(63)^13+E(63)^40-E(63)^55,E(63)+E(63)^4-E(63)^37-E(63)^58,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[19,43]],
[GALOIS,[19,22]],
[GALOIS,[19,13]],
[GALOIS,[19,10]],
[GALOIS,[19,31]],
[GALOIS,[18,2]],
[GALOIS,[19,2]],
[GALOIS,[19,23]],
[GALOIS,[19,11]],
[GALOIS,[19,5]],
[GALOIS,[19,26]],
[GALOIS,[19,47]],[4096,0,0,64,64,16,4,0,0,16,16,-4,-4,1,0,0,0,0,0,0,1,1,1,1,0,
0,0,0,0,0,-4,-4,-4,-4,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,1,
1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[5712,
80,16,-84,-84,9,3,0,0,17,17,-8,-8,2,5,5,-4,-4,1,-1,0,0,0,0,1,1,0,0,0,0,4,4,4,
4,-1,-1,-1,-1,-2,-2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[7140,164,20,21,21,15,-9,4,0,0,0,-5,-5,0,-1,-1,
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ARC("L4(4)","isSimple",true);
ARC("L4(4)","extInfo",["2","2^2"]);
ALF("L4(4)","L4(4).2_1",[1,2,3,4,4,5,6,7,8,9,9,10,10,11,12,12,13,13,14,15,
16,17,18,18,19,19,20,20,21,21,22,22,23,23,24,25,26,26,29,29,27,28,28,27,
30,30,31,31,33,32,33,32,34,35,35,34,36,38,41,40,37,38,36,39,40,41,37,39,
45,43,47,49,46,48,44,47,42,49,45,44,46,43,48,42],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L4(4)","L4(4).2_2",[1,3,7,4,4,8,14,12,35,5,6,10,11,32,18,18,23,23,38,
50,51,51,52,52,31,30,36,37,64,64,16,15,16,15,49,49,34,33,40,39,65,66,65,
66,26,29,28,27,53,54,54,53,61,62,61,62,55,60,58,58,56,57,56,57,59,59,55,
60,45,47,46,41,46,48,42,43,44,47,48,44,43,41,45,42],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L4(4)","L4(4).2_3",[1,2,3,4,5,6,7,8,9,10,10,11,11,12,13,14,16,15,17,
18,19,19,21,20,22,22,23,23,24,25,26,27,27,26,28,28,29,29,30,30,32,32,31,
31,33,33,34,34,36,36,35,35,37,37,38,38,39,40,41,44,39,42,43,40,41,44,43,
42,46,45,48,45,50,46,49,50,49,51,52,47,48,51,52,47],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("L4(4)",["O6+(4)"]);

MOT("L4(4).2_1",
[
"origin: constructed by T. Breuer using the perm. repr. on 85 points\n",
"and the table of the subgroup L4(4),\n",
"constructions: PSigmaL(4,4)"
],
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63,63,63,85,85,85,85,85,85,85,85,40320,384,192,360,36,32,16,30,24,12,14,14,30,
30],
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10,11,12,13,14,15,1,1,18,19,20,21,23,22,25,24,26,28,27,29,31,30,4,4,35,34,18,
18,18,18,18,18,48,46,45,43,42,44,49,47,50,51,52,53,54,55,56,57,58,59,50,50,63,
62],,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,18,19,20,21,22,23,24,
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0,0],
[TENSOR,[57,2]],
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[TENSOR,[56,2]]],
[(36,39,40)(37,38,41),(22,23)(24,25)(27,28)(34,35)(62,63),(16,17)(32,33)
(36,37)(38,39)(40,41)(60,61),(42,43,44,49)(45,47,48,46),(30,31)
(42,45,49,46,44,48,43,47)]);
ALF("L4(4).2_1","L4(4).2^2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,17,
18,19,20,21,21,22,22,23,24,24,25,26,27,28,28,29,29,30,30,31,31,32,32,33,
34,33,35,36,36,35,34,37,38,39,40,41,42,43,44,45,46,47,47,48,48],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("L4(4).2_1",["O6+(4).2_1"]);

MOT("L4(4).2_2",
[
"origin: constructed by T. Breuer using the perm. repr. on 170 points\n",
"and the table of the subgroup L4(4),\n",
"constructions: PSL(4,4) extended by transpose-inverse"
],
[1974067200,1958400,368640,181440,40800,40800,30720,21600,7680,1800,1800,1536,
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150,150,150,128,120,120,96,90,90,85,85,85,85,85,85,85,85,75,72,63,63,63,63,63,
63,63,63,63,63,60,60,50,48,45,45,40,40,40,40,34,34,34,34,32,30,30,30,30,24,
24],
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59,58,57,16,15,32,23,66,65,11,10,30,31,27,26,28,29,12,39,40,34,33,14,38],[1,2,
3,1,6,5,7,1,9,11,10,12,13,1,11,10,17,3,20,19,22,21,3,2,2,27,29,26,28,31,30,32,
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54,36,37,63,12,11,10,68,67,70,69,74,71,72,73,75,22,21,19,20,9,17],,[1,2,3,4,1,
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38,14,14,26,29,28,26,28,27,29,27,8,50,51,52,53,54,59,58,55,60,57,56,18,18,2,
64,4,4,9,9,13,13,74,71,72,73,75,24,24,25,25,80,81],,[1,2,3,4,6,5,7,8,9,11,10,
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64,66,65,68,67,70,69,2,2,2,2,75,77,76,79,78,80,81]],
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[GALOIS,[17,5]],
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[TENSOR,[32,2]],[1344,-16,64,84,-16,-16,0,24,-16,-1,-1,0,0,9,-1,-1,0,4,4,4,-1,
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[(55,57,59)(56,60,58),(53,54)(55,56)(57,60)(58,59),(26,27,29,28)(41,46,42,45)
(43,44,48,47)(71,74,73,72),( 5, 6)(10,11)(15,16)(19,20)(21,22)(30,31)(33,34)
(36,37)(39,40)(41,44)(42,47)(43,45)(46,48)(61,62)(65,66)(67,68)(69,70)(76,77)
(78,79)]);
ALF("L4(4).2_2","L4(4).2^2",[1,49,2,4,9,9,3,5,50,10,10,7,51,6,21,21,52,12,
53,53,54,54,13,55,56,26,27,27,26,18,18,11,23,23,8,19,19,14,25,25,34,33,36,
33,35,36,34,35,22,15,16,17,28,28,30,30,31,32,32,31,29,29,57,20,24,24,58,
58,59,59,60,61,60,61,62,63,63,64,64,65,66],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("L4(4).2_2",["O6+(4).2_2"]);

MOT("L4(4).2_3",
[
"origin: constructed by T. Breuer using the perm. repr. on 170 points\n",
"and the table of the subgroup L4(4),\n",
"L4(4).2_3 is the simple group L4(4) extended by the product of,\n",
"the Frobenius automorphism and ``transpose inverse''"
],
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30,32,34,35,33,36,33,36,34,35,67,68,69,70,70,71,72,73,74,75,76,76,77,77,
78,79,80,80,81,81],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("L4(4).2_3",["O6+(4).2_3"]);

MOT("L4(4).2^2",
[
"constructed using `PossibleCharacterTablesOfTypeGV4',\n",
"constructions: Aut(L4(4)), PSigmaL(4,4) extended by transpose-inverse"
],
[3948134400,737280,61440,362880,43200,2160,3072,256,40800,1800,300,1440,1152,
192,144,126,126,160,120,96,900,150,150,45,90,170,170,63,60,63,63,63,85,85,85,
85,80640,768,384,720,72,64,32,60,48,24,14,30,3916800,15360,2560,1536,600,600,
720,720,100,40,40,34,34,64,30,30,48,48,103680,2304,384,1296,432,216,192,32,20,
144,72,72,48,18,24],
[,[1,1,1,4,5,6,2,3,9,10,11,5,4,5,6,16,17,9,10,13,21,22,23,24,25,26,27,28,21,30
,31,32,33,34,35,36,1,2,3,5,6,7,8,11,14,15,16,22,1,1,3,3,9,10,6,5,11,10,18,27,
26,7,25,23,6,14,1,2,3,4,5,6,7,8,11,13,12,15,14,17,20],[1,2,3,1,1,1,7,8,9,10,11
,2,2,3,2,16,4,18,19,7,10,11,9,10,10,27,26,16,19,28,28,28,36,35,33,34,37,38,39,
37,37,42,43,44,39,38,47,44,49,50,51,52,53,54,49,49,57,58,59,61,60,62,54,53,50,
52,67,68,69,67,67,67,73,74,75,68,68,68,69,70,73],,[1,2,3,4,5,6,7,8,1,1,1,12,13
,14,15,16,17,3,2,20,5,5,5,4,6,27,26,28,12,32,30,31,26,26,27,27,37,38,39,40,41,
42,43,37,45,46,47,40,49,50,51,52,49,49,55,56,49,50,51,61,60,62,55,56,65,66,67,
68,69,70,71,72,73,74,67,76,77,78,79,80,81],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,1,17,18,19,20,21,22,23,24,25,27,26,4,29,17,17,17,35,36,34,33,37,38,39,40,41
,42,43,44,45,46,37,48,49,50,51,52,53,54,55,56,57,58,59,61,60,62,63,64,65,66,67
,68,69,70,71,72,73,74,75,76,77,78,79,80,81],,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,1,1,28,29,32,30,31,9,9,9,9,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,49,49,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1
,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1],
[TENSOR,[2,3]],[84,20,4,21,9,6,4,0,-1,4,-1,5,5,1,2,0,0,-1,0,1,4,-1,-1,1,1,-1,
-1,0,0,0,0,0,-1,-1,-1,-1,14,6,2,-1,2,2,0,-1,-1,0,0,-1,16,0,-4,4,1,-4,4,1,1,0,1
,-1,-1,0,-1,1,0,1,6,-2,2,-3,3,0,2,0,1,1,1,-2,-1,0,-1],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[272,16,16,20,17,5,0,0,17,-3,2,1,4,1,1,-1,-1,1,1,0,-3,2,2,0,0,
0,0,-1,1,-1,-1,-1,0,0,0,0,20,4,4,5,-1,0,0,0,1,1,-1,0,68,4,4,4,3,3,5,5,-2,-1,-1
,0,0,0,0,0,1,1,20,4,4,2,5,-1,0,0,0,-2,1,1,1,-1,0],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[357,37,21,-21,24,-3,5,1,17,2,2,4,-5,0,1,0,0,1,2,-1,-1,-1,-1,
-1,2,0,0,0,-1,0,0,0,0,0,0,0,7,-1,3,4,1,-1,1,2,0,-1,0,-1,85,5,1,9,5,0,-5,4,0,0,
1,0,0,1,0,-1,-1,0,15,7,3,-3,0,3,-1,1,0,1,-2,1,0,0,-1],
[TENSOR,[13,2]],
[TENSOR,[13,3]],
[TENSOR,[13,4]],[1344,64,0,84,24,9,0,0,-16,-1,-1,4,4,0,1,0,0,0,-1,0,-1,-1,-1,
-1,-1,1,1,0,-1,0,0,0,1,1,1,1,56,8,0,-4,-1,0,0,1,0,-1,0,1,-16,-16,0,0,4,-1,-1,
-4,-1,-1,0,1,1,0,-1,1,-1,0,-24,-8,0,-6,0,-3,0,0,1,-2,-2,1,0,0,0],
[TENSOR,[17,2]],
[TENSOR,[17,3]],
--> --------------------

--> maximum size reached

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