Quelle  ctoline8.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctoline8.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of $L_4(5)$ and $L_4(9)$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctoline8.tbl,v $
#H  Revision 4.7  2012/01/30 08:31:45  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.6  2011/09/28 14:32:14  gap
#H  removed revision entry and SET_TABLEFILENAME call
#H      TB
#H
#H  Revision 4.5  2009/04/22 12:39:03  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.4  2003/07/24 07:13:01  gap
#H  added the table of L4(5)
#H  (Vdovin Evgenii <vdovin@math.unipd.it> had asked for it)
#H      TB
#H
#H  Revision 4.3  2002/07/17 15:25:32  gap
#H  added missing table automorphisms
#H      TB
#H
#H  Revision 4.2  2001/05/04 16:47:55  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.2 of ctbllib coincides with Rev. 4.1 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctoline8.tbl,v
#H  Working file: ctoline8.tbl
#H  head: 1.1
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H  keyword substitution: kv
#H  total revisions: 1; selected revisions: 1
#H  description:
#H  ----------------------------
#H  revision 1.1
#H  date: 2001/03/02 18:31:15;  author: gap;  state: Exp;
#H  table of L4(9)
#H  
#H      TB
#H  ==========================================================================
##

MOT("L4(5)",
[
"origin: computed using Dixon's algorithm and character theoretic methods,\n",
"Thomas Breuer, Jun. 03rd, 2003"
],
[7254000000,28800,23400,720,480,144,375000,37500,37500,625,125,125,125,125,720
,72,24,600,100,100,36,36,24,39,39,39,75,75,30,20,24,24,30,31,31,31,31,31,31,31
,31,31,31,39,39,39,39,39,39],
[,[1,1,3,4,2,2,7,8,9,10,12,11,14,13,4,3,5,7,8,9,15,16,15,25,26,24,27,28,29,18,
23,23,29,42,43,35,34,37,36,39,38,41,40,48,49,45,44,47,46],[1,2,1,1,5,6,7,8,9,
10,12,11,14,13,2,2,17,18,19,20,6,6,5,25,26,24,8,9,7,30,17,17,18,36,37,38,39,40
,41,42,43,35,34,24,24,26,26,25,25],,[1,2,3,4,5,6,1,1,1,1,1,1,1,1,15,16,17,2,2,
2,21,22,23,24,25,26,3,3,4,5,31,32,15,34,35,36,37,38,39,40,41,42,43,44,45,46,47
,48,49],,,,,,,,[1,2,3,4,5,6,7,8,9,10,12,11,14,13,15,16,17,18,19,20,21,22,23,1,
1,1,27,28,29,30,32,31,33,36,37,38,39,40,41,42,43,35,34,3,3,3,3,3,3],,,,,,,,,,,
,,,,,,,[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,
27,28,29,30,31,32,33,1,1,1,1,1,1,1,1,1,1,45,44,47,46,49,48]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],[155,11,-1,5,7,-1,30,5,5,5,0,0,0,0,5,-1,1,6,1,1,-1,-1,1
,-1,-1,-1,-1,-1,0,2,1,1,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1],[403,19,13,1,
-5,-1,28,28,3,3,3,3,-2,-2,1,1,-1,4,4,-1,-1,-1,1,0,0,0,-2,3,1,0,-1,-1,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0],[403,19,13,1,-5,-1,28,3,28,3,-2,-2,3,3,1,1,-1,4,-1,4
,-1,-1,1,0,0,0,3,-2,1,0,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[496,16,25,4,
0,4,-4,21,21,-4,1,1,1,1,4,1,0,-4,1,1,-2,1,0,2,2,2,0,0,-1,0,0,0,-1,0,0,0,0,0,0,
0,0,0,0,-1,-1,-1,-1,-1,-1],[650,26,26,-4,6,2,25,25,25,0,0,0,0,0,-4,2,0,1,1,1,2
,2,0,0,0,0,1,1,1,1,0,0,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[3224,8,26
,5,4,-4,99,-26,-26,-1,-1,-1,-1,-1,5,2,-2,3,-2,-2,-1,2,1,0,0,0,1,1,0,-1,1,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3224,8,26,5,4,4,99,-26,-26,-1,-1,-1,-1,-1,5,2
,2,3,-2,-2,1,-2,1,0,0,0,1,1,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
3224,-8,26,-4,0,0,-26,-26,49,-1,-1,-1,-4*E(5)+E(5)^2+E(5)^3-4*E(5)^4,
E(5)-4*E(5)^2-4*E(5)^3+E(5)^4,4,-2,0,2,2,-3,0,0,0,0,0,0,1,1,1,0,0,0,-1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[9,2]],[3224,-8,26,-4,0,0,-26,49,-26,-1,
-4*E(5)+E(5)^2+E(5)^3-4*E(5)^4,E(5)-4*E(5)^2-4*E(5)^3+E(5)^4,-1,-1,4,-2,0,2,-3
,2,0,0,0,0,0,0,1,1,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,2]],[3875,35,-25,-1,11,-1,125,0,0,0,0,0,0,0,-1,-1,-1,5,0,0,-1,-1,
-1,1,1,1,0,0,-1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1],[4030,46,-26,4,-6,
2,155,5,5,5,0,0,0,0,4,-2,0,11,1,1,2,2,0,0,0,0,-1,-1,-1,-1,0,0,-1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],[4836,-60,0,6,4,0,211,36,36,11,1,1,1,1,6,0,0,-5,0,0,0,0,-2
,0,0,0,0,0,1,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6448,16,13,4,0,-4,-52,
73,-27,-2,-2,-2,3,3,4,1,0,-4,1,1,2,-1,0,0,0,0,-2,3,-1,0,0,0,-1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0],[6448,16,13,4,0,-4,-52,-27,73,-2,3,3,-2,-2,4,1,0,-4,1,1,2,-1
,0,0,0,0,3,-2,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10075,43,13,-5,-1,
-1,75,-50,75,0,0,0,0,0,-5,1,1,3,-2,3,-1,-1,-1,0,0,0,-2,3,0,-1,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[10075,43,13,-5,-1,-1,75,75,-50,0,0,0,0,0,-5,1,1,3,3,-2
,-1,-1,-1,0,0,0,3,-2,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[11904,0,48,0
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-E(13)^2-E(13)^3-E(13)^10-E(13)^11,-E(13)^4-E(13)^6-E(13)^7-E(13)^9,-2,-2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-E(13)^4-E(13)^6-E(13)^7-E(13)^9,
-E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,
-E(13)^2-E(13)^3-E(13)^10-E(13)^11,-E(13)-E(13)^5-E(13)^8-E(13)^12,
-E(13)-E(13)^5-E(13)^8-E(13)^12],
[GALOIS,[20,4]],
[GALOIS,[20,2]],[11904,0,-24,0,0,0,-96,4,4,4,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,
-E(13)^2-E(13)^3-E(13)^10-E(13)^11,-E(13)^4-E(13)^6-E(13)^7-E(13)^9,
-E(13)-E(13)^5-E(13)^8-E(13)^12,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(39)^23-E(39)^28-E(39)^29-E(39)^37,-E(39)^2-E(39)^10-E(39)^11-E(39)^16,
-E(39)-E(39)^5-E(39)^8-E(39)^25,-E(39)^14-E(39)^31-E(39)^34-E(39)^38,
-E(39)^7-E(39)^17-E(39)^19-E(39)^35,-E(39)^4-E(39)^20-E(39)^22-E(39)^32],
[GALOIS,[23,14]],
[GALOIS,[23,23]],
[GALOIS,[23,2]],
[GALOIS,[23,4]],
[GALOIS,[23,7]],[12400,16,1,4,0,4,-100,25,25,0,0,0,0,0,4,1,0,-4,1,1,-2,1,0,-2
,-2,-2,1,1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1],[12896,-32,26,8,0,0,
-104,46,46,-4,1,1,1,1,-8,-2,0,8,-2,-2,0,0,0,0,0,0,1,1,-2,0,0,0,2,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],[12896,-32,-52,-4,0,0,-104,46,46,-4,1,1,1,1,4,4,0,8,-2,-2,
0,0,0,0,0,0,-2,-2,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[14976,0,0,0,0,0
,-24,-24,-24,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
E(31)^17+E(31)^22+E(31)^23,E(31)^8+E(31)^9+E(31)^14,E(31)^4+E(31)^7+E(31)^20,
E(31)^11+E(31)^24+E(31)^27,E(31)^12+E(31)^21+E(31)^29,
E(31)^2+E(31)^10+E(31)^19,E(31)+E(31)^5+E(31)^25,E(31)^6+E(31)^26+E(31)^30,
E(31)^3+E(31)^13+E(31)^15,E(31)^16+E(31)^18+E(31)^28,0,0,0,0,0,0],
[GALOIS,[32,6]],
[GALOIS,[32,12]],
[GALOIS,[32,2]],
[GALOIS,[32,4]],
[GALOIS,[32,11]],
[GALOIS,[32,17]],
[GALOIS,[32,8]],
[GALOIS,[32,16]],
[GALOIS,[32,3]],[15625,25,25,-5,5,1,0,0,0,0,0,0,0,0,-5,1,-1,0,0,0,1,1,-1,-1,
-1,-1,0,0,0,0,-1,-1,0,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[16120,40,-26,1,4
,4,-5,20,20,-5,0,0,0,0,1,-2,-2,-5,0,0,1,-2,1,0,0,0,-1,-1,1,-1,1,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[16120,40,-26,1,4,-4,-5,20,20,-5,0,0,0,0,1,-2,2,-5,0,0,
-1,2,1,0,0,0,-1,-1,1,-1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[19344,48,0,6
,-8,0,94,-6,-6,-6,-1,-1,-1,-1,6,0,0,-2,-2,-2,0,0,-2,0,0,0,0,0,1,2,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[19344,-48,0,-12,0,0,94,-6,-6,-6,-1,-1,-1,-1,12,0,0
,2,2,2,0,0,0,0,0,0,0,0,-2,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[19344,-48,
0,6,0,0,94,-6,-6,-6,-1,-1,-1,-1,-6,0,0,2,2,2,0,0,0,0,0,0,0,0,1,0,
-E(24)-E(24)^11+E(24)^17+E(24)^19,E(24)+E(24)^11-E(24)^17-E(24)^19,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[47,13]],[24180,-12,0,-6,-4,0,305,30,30,5,0,0,0,0,-6,0,0,-7,-2,-2,0,0
,2,0,0,0,0,0,-1,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(44,45)(46,47)(48,49),(31,32),(24,25,26)(44,48,47)(45,49,46),(13,14),(11,12),
( 8, 9)(11,13)(12,14)(19,20)(27,28),(34,42,41,38,37)(35,43,40,39,36),
(34,36,38,40,42,35,37,39,41,43)]);
ARC("L4(5)","projectives",["2.L4(5)",[[156,-12,0,-6,4,0,-31,-6,-6,6,-1,-1,-1,
-1,-6,0,0,7,-2,-2,0,0,-2,0,0,0,0,0,1,-1,0,0,-1,1,-1,1,-1,1,-1,-1,1,1,-1,0,0,0,
0,0,0],[19500,-60,0,6,-4,0,-125,0,0,0,0,0,0,0,6,0,0,5,0,0,0,0,2,0,0,0,0,0,-1,1
,0,0,1,1,-1,1,-1,1,-1,-1,1,1,-1,0,0,0,0,0,0],[19344,-48,0,-6,-8,0,-94,6,6,-6,1
,1,1,1,-6,0,0,-2,2,2,0,0,-2,0,0,0,0,0,1,2,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0],[19344,48,0,-6,0,0,-94,6,6,-6,1,1,1,1,6,0,0,2,-2,-2,0,0,0,0,0,0,0,0,1,0,
E(24)-E(24)^11-E(24)^17+E(24)^19,-E(24)+E(24)^11+E(24)^17-E(24)^19,1,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[4,7]],[19344,48,0,12,0,0,-94,6,6,-6,1,1,1,1,-12,0,0,2,-2,-2,0,0,0,0,
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],[14976,0,0,0,0,0,24,24,24
,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(31)^4+E(31)^7+E(31)^20,
-E(31)^11-E(31)^24-E(31)^27,E(31)^12+E(31)^21+E(31)^29,
-E(31)^2-E(31)^10-E(31)^19,E(31)+E(31)^5+E(31)^25,-E(31)^6-E(31)^26-E(31)^30,
-E(31)^3-E(31)^13-E(31)^15,E(31)^16+E(31)^18+E(31)^28,E(31)^8+E(31)^9+E(31)^14
,-E(31)^17-E(31)^22-E(31)^23,0,0,0,0,0,0],
[GALOIS,[7,3]],
[GALOIS,[7,11]],
[GALOIS,[7,17]],
[GALOIS,[7,16]],
[GALOIS,[7,12]],
[GALOIS,[7,8]],
[GALOIS,[7,6]],
[GALOIS,[7,4]],
[GALOIS,[7,2]],[4680,-72,0,0,0,0,-180,-30,-30,5,0,0,0,0,0,0,0,12,-2,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,1,-1,-1,1,0,0,0,0,0,0],[11904,0,24,0,0,0,96
,-4,-4,4,1,1,1,1,0,0,0,0,0,0,0,0,0,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)^2+E(13)^3+E(13)^10+E(13)^11,-1,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,E(39)^4+E(39)^20+E(39)^22+E(39)^32,
-E(39)^7-E(39)^17-E(39)^19-E(39)^35,E(39)^23+E(39)^28+E(39)^29+E(39)^37,
-E(39)^2-E(39)^10-E(39)^11-E(39)^16,E(39)+E(39)^5+E(39)^8+E(39)^25,
E(39)^14+E(39)^31+E(39)^34+E(39)^38],
[GALOIS,[18,2]],
[GALOIS,[18,4]],
[GALOIS,[18,7]],
[GALOIS,[18,23]],[11904,0,-48,0,0,0,96,-4,-4,4,1,1,1,1,0,0,0,0,0,0,0,0,0,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,
E(13)+E(13)^5+E(13)^8+E(13)^12,-E(13)-E(13)^5-E(13)^8-E(13)^12,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)^4+E(13)^6+E(13)^7+E(13)^9],
[GALOIS,[23,4]],
[GALOIS,[23,2]],
[GALOIS,[18,14]],[12896,-32,-26,-8,0,0,104,-46,-46,-4,-1,-1,-1,-1,-8,2,0,-8,
-2,-2,0,0,0,0,0,0,-1,1,-2,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12896,32,
52,4,0,0,104,-46,-46,-4,-1,-1,-1,-1,-4,4,0,8,2,2,0,0,0,0,0,0,2,-2,1,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[20150,-14,-26,10,10,0,-150,-25,-25,0,0,0,0,0,
10,2,0,-6,1,1,0,0,-2,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
806,34,-26,-2,2,0,-56,-31,-31,6,-1,-1,-1,-1,-2,2,0,-4,-1,-1,0,0,2,0,0,0,-1,1,2
,2,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3224,-8,-26,-5,4,0,-99,26,26,-1,1,
1,1,1,-5,2,2*E(4),3,2,2,3*E(4),0,1,0,0,0,-1,1,0,-1,-E(4),-E(4),0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],
[GALOIS,[31,3]],[4030,26,26,-4,6,0,-155,-5,-5,5,0,0,0,0,-4,-2,-2*E(4),-1,1,1,
0,0,0,0,0,0,1,-1,-1,1,-2*E(4),-2*E(4),1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[33,3]],[16120,-40,26,-1,4,0,5,-20,-20,-5,0,0,0,0,-1,-2,2*E(4),-5,0,0
,-3*E(4),0,1,0,0,0,1,-1,1,-1,-E(4),-E(4),-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[35,3]],[12400,16,-1,-4,0,0,100,-25,-25,0,0,0,0,0,4,-1,0,4,1,1,0,-3,0
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,0,52,27,-73,-2,-3,-3,2,2,4,-1,0,4,1,1,0,3,0,0,0,0,-3,-2,-1,0,0,0,-1,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0],[6200,8,-38,4,0,0,50,50,-75,0,0,0,0,0,-4,-2,0,2,-2,3,0
,0,0,1,1,1,2,3,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,1],[496,16,-25,-4,0,0
,4,-21,-21,-4,-1,-1,-1,-1,4,-1,0,4,1,1,0,-3,0,-2,-2,-2,0,0,-1,0,0,0,-1,0,0,0,0
,0,0,0,0,0,0,1,-1,1,-1,1,1],[248,8,-14,4,0,0,2,2,-23,-2,2,2,-3,-3,-4,-2,0,2,-2
,3,0,0,0,-1,-1,-1,-4,-1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,-1],[6448,
16,-13,-4,0,0,52,-73,27,-2,2,2,-3,-3,4,-1,0,4,1,1,0,3,0,0,0,0,2,3,-1,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[248,8,-14,4,0,0,2,-23,2,-2,-3,-3,2,2,-4,-2,0
,2,3,-2,0,0,0,-1,-1,-1,1,4,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,-1],[
6200,8,-38,4,0,0,50,-75,50,0,0,0,0,0,-4,-2,0,2,3,-2,0,0,0,1,1,1,-3,-2,1,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,1],[7254,18,0,0,-6,0,-129,-54,21,4,
-E(5)+4*E(5)^2+4*E(5)^3-E(5)^4,4*E(5)-E(5)^2-E(5)^3+4*E(5)^4,1,1,0,0,0,-3,-2,3
,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[45,2]],[7254,18,0,0,-6,0,-129,21,-54,4,1,1,
-E(5)+4*E(5)^2+4*E(5)^3-E(5)^4,4*E(5)-E(5)^2-E(5)^3+4*E(5)^4,0,0,0,-3,3,-2,0,0
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[GALOIS,[47,2]]],]);
ALN("L4(5)",["O6+(5)"]);
ARC("L4(5)","isSimple",true);
ARC("L4(5)","extInfo",["4","D8"]);

MOT("2.L4(5)",
[
"computed by Thomas Breuer in December 2005,\n",
"using the character table of the factor group, Dixon's algorithm,\n",
"and character theoretic methods"
],
[14508000000,14508000000,57600,57600,46800,46800,1440,1440,960,960,144,750000,
750000,75000,75000,75000,75000,1250,1250,250,250,250,250,250,250,250,250,1440,
1440,144,144,48,48,1200,1200,200,200,200,200,72,72,72,72,48,48,78,78,78,78,78,
78,150,150,150,150,60,60,40,40,48,48,48,48,60,60,62,62,62,62,62,62,62,62,62,62
,62,62,62,62,62,62,62,62,62,62,78,78,78,78,78,78,78,78,78,78,78,78],
[,[1,1,1,1,6,6,8,8,4,4,3,13,13,15,15,17,17,18,18,23,23,21,21,27,27,25,25,8,8,6
,6,10,10,13,13,15,15,17,17,28,28,31,31,29,29,49,49,51,51,47,47,53,53,54,54,56,
56,34,34,45,45,45,45,56,56,82,82,85,85,69,69,66,66,73,73,70,70,77,77,74,74,80,
80,79,79,95,95,97,97,88,88,87,87,92,92,91,91],[1,2,3,4,2,1,2,1,9,10,11,12,13,
14,15,16,17,18,19,22,23,20,21,26,27,24,25,3,4,4,3,33,32,34,35,36,37,38,39,11,
11,11,11,9,10,48,49,50,51,46,47,14,15,17,16,13,12,58,59,33,32,33,32,35,34,70,
71,72,73,74,75,76,77,79,78,81,80,83,82,85,84,69,68,67,66,46,47,47,46,50,51,51,
50,48,49,48,49],,[1,2,3,4,5,6,7,8,9,10,11,2,1,2,1,2,1,1,2,2,1,2,1,2,1,2,1,28,
29,30,31,32,33,4,3,3,4,3,4,40,41,42,43,44,45,46,47,48,49,50,51,5,6,6,5,8,7,9,
10,60,61,62,63,28,29,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,22,23,20,21,26,27,24,25,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,2,1,2,1,2,1,52,53,54,55,56,57,58,59,62,63,60,61,64,65,70,71,
72,73,74,75,76,77,79,78,81,80,83,82,85,84,69,68,67,66,5,6,6,5,5,6,6,5,5,6,5,6]
,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23
,24,25,26,27,28,29,30,31,33,32,34,35,36,37,38,39,41,40,42,43,44,45,46,47,48,49
,50,51,52,53,54,55,56,57,58,59,61,60,63,62,64,65,1,2,2,1,1,2,2,1,1,2,2,1,2,1,1
,2,1,2,2,1,89,88,87,86,93,92,91,90,96,97,94,95]],
0,
[(86,89)(87,88)(90,93)(91,92)(94,96)(95,97),(60,62)(61,63),(46,48,50)(47,49,
51)(86,94,93)(87,95,92)(88,97,91)(89,96,90),(32,33)(40,41)(60,61)(62,63),(24,
26)(25,27),(20,22)(21,23),(14,16)(15,17)(20,24)(21,25)(22,26)(23,27)(36,38)
(37,39)(52,55)(53,54),(66,69)(67,68)(70,73)(71,72)(74,77)(75,76)(78,81)(79,80)
(82,85)(83,84),(66,70,74,79,82,69,73,77,80,85)(67,71,75,78,83,68,72,76,81,84)
],
["ConstructProj",[["L4(5)",[]],["2.L4(5)",[]]]]);
ALF("2.L4(5)","L4(5)",[1,1,2,2,3,3,4,4,5,5,6,7,7,8,8,9,9,10,10,
11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,
23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,
35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,
47,47,48,48,49,49]);

MOT("4.L4(5)",
[
"computed by Thomas Breuer in December 2005,\n",
"using the character tables of the factor groups, Dixon's algorithm,\n",
"and character theoretic methods"
],
[29016000000,29016000000,29016000000,29016000000,144,144,144,144,2880,2880,
2880,2880,2880,2880,2880,2880,57600,57600,144,144,144,144,144,144,144,93600,
93600,93600,93600,120,120,120,120,120,120,120,120,1500000,1500000,1500000,
1500000,2400,2400,2400,2400,156,156,156,156,156,156,156,156,156,156,156,156,
156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,
156,156,156,156,156,80,80,80,80,1920,1920,1920,1920,124,124,124,124,124,124,
124,124,124,124,124,124,124,124,124,124,124,124,124,124,124,124,124,124,124,
124,124,124,124,124,124,124,124,124,124,124,124,124,124,124,200,200,150000,
150000,150000,150000,200,200,150000,150000,150000,150000,96,96,96,96,96,96,96,
96,96,96,96,96,96,96,96,96,500,500,500,500,500,500,500,500,300,300,300,300,300
,300,300,300,500,500,500,500,500,500,500,500,2500,2500,2500,2500],
[,[1,1,2,2,10,10,9,9,16,16,15,15,16,16,15,15,2,1,17,25,25,25,25,29,28,28,28,29
,29,34,34,35,35,35,35,34,34,41,41,40,40,40,40,41,41,52,52,53,53,56,56,57,57,49
,49,48,48,64,64,65,65,66,66,67,67,61,61,60,60,75,75,74,74,81,81,80,80,72,72,73
,73,42,42,43,43,18,18,18,18,94,94,95,95,103,103,102,102,108,108,109,109,111,
111,110,110,121,121,120,120,125,125,124,124,129,129,128,128,117,117,116,116,91
,91,90,90,98,98,99,99,134,135,134,134,135,135,140,141,140,140,141,141,89,89,88
,88,157,157,156,156,157,157,156,156,12,12,11,11,164,164,165,165,161,161,160,
160,168,168,169,169,171,171,170,170,181,181,180,180,177,177,176,176,183,183,
182,182],[1,2,4,3,19,19,19,19,17,17,18,18,3,4,1,2,17,18,19,19,19,19,19,18,17,4
,3,2,1,44,45,42,43,41,40,39,38,39,38,40,41,42,43,45,44,50,51,53,52,55,54,56,57
,46,47,49,48,46,47,49,48,51,50,52,53,56,57,54,55,55,54,56,57,48,49,46,47,51,50
,52,53,82,83,85,84,86,87,89,88,99,98,100,101,108,109,106,107,110,111,113,112,
121,120,119,118,122,123,125,124,117,116,115,114,96,97,94,95,92,93,90,91,126,
127,129,128,105,104,103,102,130,131,133,132,134,135,136,137,139,138,140,141,
145,144,143,142,145,144,143,142,144,145,142,143,86,87,89,88,162,163,165,164,
158,159,161,160,133,132,134,135,140,141,138,139,179,178,180,181,175,174,176,
177,182,183,185,184],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,9,10,11,12,16,15,13,14,4,3,1,2,18,18,17,17,46,47,48,49
,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
,76,77,78,79,80,81,87,86,89,88,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,
101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,
120,121,122,123,124,125,126,127,128,129,17,18,3,4,2,1,17,18,3,4,2,1,142,143,
144,145,146,147,148,149,150,151,152,153,154,155,156,157,4,3,1,2,3,4,2,1,26,27,
28,29,28,29,27,26,4,3,1,2,4,3,1,2,2,1,4,3],,,,,,,,[1,2,3,4,6,5,8,7,9,10,11,12,
13,14,15,16,17,18,19,21,20,23,22,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,4,3,1,2,3,4,2,1,3,4,2,1,26,27,28,29,26,27,28,29,28,29,27,
26,26,27,28,29,29,28,26,27,26,27,28,29,82,83,84,85,86,87,88,89,99,98,101,100,
108,109,107,106,110,111,112,113,121,120,118,119,123,122,125,124,117,116,114,
115,97,96,94,95,93,92,90,91,127,126,129,128,104,105,103,102,130,131,132,133,
134,135,136,137,138,139,140,141,142,143,144,145,151,150,153,152,147,146,149,
148,154,155,156,157,163,162,165,164,159,158,161,160,166,167,168,169,170,171,
172,173,178,179,180,181,174,175,176,177,182,183,184,185],,,,,,,,,,,,,,,,,,[1,2
,4,3,7,8,5,6,10,9,11,12,14,13,15,16,17,18,19,20,21,23,22,24,25,27,26,28,29,31,
30,32,33,34,35,37,36,39,38,40,41,42,43,45,44,47,46,48,49,51,50,52,53,55,54,56,
57,77,76,75,74,79,78,80,81,72,73,70,71,68,69,66,67,61,60,59,58,63,62,64,65,82,
83,85,84,86,87,89,88,1,2,4,3,1,2,4,3,2,1,3,4,2,1,3,4,3,4,1,2,2,1,3,4,3,4,1,2,3
,4,1,2,4,3,2,1,3,4,1,2,130,131,133,132,134,135,136,137,139,138,140,141,145,144
,143,142,149,148,147,146,153,152,151,150,154,155,157,156,159,158,160,161,163,
162,164,165,167,166,168,169,170,171,173,172,175,174,176,177,179,178,180,181,
182,183,185,184]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[15625,15625,
15625,15625,1,1,1,1,-5,-5,-5,-5,-5,-5,-5,-5,25,25,1,1,1,1,1,1,1,25,25,25,25,0,
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,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,5,5,5,5,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24180,24180,24180,24180,0,
0,0,0,-6,-6,-6,-6,-6,-6,-6,-6,-12,-12,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,
-1,-1,305,305,305,305,-7,-7,-7,-7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,-2,-2,30,30,30,30,-2,-2,30,
30,30,30,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,5,5,5,5],[3875,3875,3875,3875,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
35,35,-1,-1,-1,-1,-1,-1,-1,-25,-25,-25,-25,-1,-1,-1,-1,-1,-1,-1,-1,125,125,125
,125,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
,1,1,1,1,1,1,1,11,11,11,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[4836,4836,4836,4836,0,0,0,0,6,6,6,6,6,6,6,6,-60,-60,0,0,0,0,0,0,0,0,0,0,0,
1,1,1,1,1,1,1,1,211,211,211,211,-5,-5,-5,-5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,4,4,4,4,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,36,36,36,36,0,
0,36,36,36,36,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1,1,1,1,1,1,0,0,0,0,0,0,
0,0,1,1,1,1,1,1,1,1,11,11,11,11],[155,155,155,155,-1,-1,-1,-1,5,5,5,5,5,5,5,5,
11,11,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,30,30,30,30,6,6,6,6,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,7,7,7,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0
,5,5,5,5],[403,403,403,403,-1,-1,-1,-1,1,1,1,1,1,1,1,1,19,19,-1,-1,-1,-1,-1,1,
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[GALOIS,[28,2]],
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E(31)^2+E(31)^10+E(31)^19,E(31)^2+E(31)^10+E(31)^19,E(31)^2+E(31)^10+E(31)^19,
E(31)^2+E(31)^10+E(31)^19,E(31)^4+E(31)^7+E(31)^20,E(31)^4+E(31)^7+E(31)^20,
E(31)^4+E(31)^7+E(31)^20,E(31)^4+E(31)^7+E(31)^20,E(31)^6+E(31)^26+E(31)^30,
E(31)^6+E(31)^26+E(31)^30,E(31)^6+E(31)^26+E(31)^30,E(31)^6+E(31)^26+E(31)^30,
E(31)^8+E(31)^9+E(31)^14,E(31)^8+E(31)^9+E(31)^14,E(31)^8+E(31)^9+E(31)^14,
E(31)^8+E(31)^9+E(31)^14,E(31)^12+E(31)^21+E(31)^29,E(31)^12+E(31)^21+E(31)^29
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E(31)^16+E(31)^18+E(31)^28,E(31)^16+E(31)^18+E(31)^28,
E(31)^16+E(31)^18+E(31)^28,E(31)^16+E(31)^18+E(31)^28,
E(31)^17+E(31)^22+E(31)^23,E(31)^17+E(31)^22+E(31)^23,
E(31)^17+E(31)^22+E(31)^23,E(31)^17+E(31)^22+E(31)^23,
E(31)^11+E(31)^24+E(31)^27,E(31)^11+E(31)^24+E(31)^27,
E(31)^11+E(31)^24+E(31)^27,E(31)^11+E(31)^24+E(31)^27,E(31)+E(31)^5+E(31)^25,
E(31)+E(31)^5+E(31)^25,E(31)+E(31)^5+E(31)^25,E(31)+E(31)^5+E(31)^25,
E(31)^3+E(31)^13+E(31)^15,E(31)^3+E(31)^13+E(31)^15,E(31)^3+E(31)^13+E(31)^15,
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[GALOIS,[31,12]],
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E(156)^47+E(156)^79+E(156)^83+E(156)^103,
E(156)^31+E(156)^131+E(156)^151+E(156)^155,
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E(39)^23+E(39)^28+E(39)^29+E(39)^37,-E(39)^23-E(39)^28-E(39)^29-E(39)^37,
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E(156)^23+E(156)^67+E(156)^107+E(156)^115,
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E(156)^7+E(156)^19+E(156)^35+E(156)^95,-E(156)^7-E(156)^19-E(156)^35-E(156)^95
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[GALOIS,[171,53]],
[GALOIS,[171,29]],
[GALOIS,[171,41]],
[GALOIS,[171,61]],
[GALOIS,[171,17]],
[GALOIS,[171,43]],
[GALOIS,[171,7]],
[GALOIS,[171,11]],
[GALOIS,[171,23]],
[GALOIS,[171,47]],
[GALOIS,[171,31]],
[GALOIS,[168,7]],
[GALOIS,[168,27]],
[GALOIS,[168,3]]],
[(174,178)(175,179)(176,180)(177,181),(158,163)(159,162)(160,165)(161,164),
(130,136)(131,137)(132,138)(133,139)(134,140)(135,141)(158,174)(159,175)
(160,176)(161,177)(162,179)(163,178)(164,181)(165,180)(166,173)(167,172)
(168,170)(169,171)
,
( 58, 76)( 59, 77)( 60, 75)( 61, 74)( 62, 78)( 63, 79)( 64, 80)( 65, 81)
( 66, 72)( 67, 73)( 68, 71)( 69, 70)
,
( 46, 51, 55)( 47, 50, 54)( 48, 53, 57)( 49, 52, 56)( 58, 62, 69)( 59, 63, 68)
( 60, 64, 66)( 61, 65, 67)( 70, 76, 78)( 71, 77, 79)( 72, 75, 80)( 73, 74, 81)
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( 93, 97,104,112,123)( 98,109,121,117,129)( 99,108,120,116,128)
(100,106,118,114,126)(101,107,119,115,127)
,
( 90, 99,111,116, 94,108,125,128,103,120)( 91, 98,110,117, 95,109,124,129,102,
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 126,104,118)
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(  3,  4)(  5,  7)(  6,  8)(  9, 10)( 13, 14)( 22, 23)( 26, 27)( 30, 31)
( 36, 37)( 38, 39)( 44, 45)( 46, 47)( 50, 51)( 54, 55)( 58, 59)( 62, 63)
( 68, 69)( 70, 71)( 76, 77)( 78, 79)( 84, 85)( 88, 89)( 92, 93)( 96, 97)
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(132,133)(138,139)(142,145)(143,144)(146,149)(147,148)(150,153)(151,152)
(156,157)(158,159)(162,163)(166,167)(172,173)(174,175)(178,179)(184,185)
]);

MOT("L4(9)",
[
"origin: constructed by Thomas Breuer, February 2001"
],
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205,205,205,205,205,205,205,205,205,205,205,205,205,205,205,205,205,205,205,
205,205,205,205,205,205,205,205,205,205,205],
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206],,,,,,[1,2,3,4,5,6,7,8,9,10,12,11,14,13,15,16,17,18,19,20,22,21,24,23,26,
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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)+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)+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,
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,
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ALN("L4(9)",["O6+(9)"]);
ARC("L4(9)","isSimple",true);
ARC("L4(9)","extInfo",["4","(2xD8)"]);

LIBTABLE.LOADSTATUS.ctoline8:="userloaded";

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