Quelle  ctounit5.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctounit5.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables related to the unitary
##  groups $U_4(4)$, $U_4(5)$, and $U_5(4)$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctounit5.tbl,v $
#H  Revision 4.11  2012/03/21 16:16:51  gap
#H  added fusion U5(3) -> O10-(3)
#H      TB
#H
#H  Revision 4.10  2012/01/30 08:32:05  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.9  2011/09/28 14:22:13  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added tables of U4(5).2_i, U4(5).2^2
#H      TB
#H
#H  Revision 4.8  2009/08/14 08:40:26  gap
#H  added table of U5(3)
#H      TB
#H
#H  Revision 4.7  2008/06/24 16:23:06  gap
#H  added several fusions and names
#H      TB
#H
#H  Revision 4.6  2007/07/03 08:37:56  gap
#H  added table of U4(5).2^2
#H      TB
#H
#H  Revision 4.5  2005/04/20 15:36:06  gap
#H  added tables of U5(4) and U5(4).2
#H      TB
#H
#H  Revision 4.4  2005/01/26 15:14:32  gap
#H  added the table of U4(4).4
#H      TB
#H
#H  Revision 4.3  2003/07/24 07:10:25  gap
#H  added table of U4(5) (computed for answering a question of Jan Saxl)
#H      TB
#H
#H  Revision 4.2  2001/05/04 16:50:50  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/ctounit5.tbl,v
#H  Working file: ctounit5.tbl
#H  head: 4.1
#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 4.1
#H  date: 2001/02/06 14:49:18;  author: gap;  state: Exp;
#H  added tables of S6(4) and U4(4)
#H  
#H      TB
#H  ==========================================================================
##

MOT("U4(4)",
[
"origin: computed using Dixon's algorithm and character theoretic methods,\n",
"Thomas Breuer, Sep. 04th, 1999"
],
[1018368000,307200,15360,12240,900,1280,64,312000,312000,312000,312000,18000,
18000,1500,1500,1500,1500,1500,1500,125,60,48,1600,1600,1600,1600,1200,1200,
1200,1200,100,100,100,100,100,100,80,80,65,65,65,65,900,900,900,900,75,75,75,
75,75,75,75,75,75,75,45,45,51,51,51,51,80,80,80,80,60,60,60,60,51,51,51,51,51,
51,51,51,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65],
[,[1,1,1,4,5,2,3,9,11,8,10,13,12,15,17,14,16,19,18,20,5,4,11,9,10,8,12,13,13,
12,14,16,15,17,18,19,13,12,40,41,42,39,44,45,46,43,48,49,50,47,52,53,54,51,56,
55,58,57,60,59,62,61,23,24,25,26,43,44,46,45,72,73,76,75,77,71,78,74,80,82,83,
85,88,86,79,89,91,93,94,92,90,87,81,84],[1,2,3,1,1,6,7,10,8,11,9,13,12,16,14,
17,15,19,18,20,2,3,24,26,23,25,28,30,27,29,32,34,31,33,36,35,38,37,39,40,41,42
,13,12,13,12,14,15,17,16,11,10,8,9,19,18,12,13,61,62,60,59,64,66,63,65,28,27,
30,29,61,62,61,60,59,62,60,59,81,83,86,88,89,87,93,91,85,94,90,80,79,82,84,92]
,,[1,2,3,4,5,6,7,1,1,1,1,1,1,1,1,1,1,1,1,1,21,22,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3
,3,40,41,42,39,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,61,62,60,59,6,6,6,6,21,21,21,21
,74,75,77,72,73,78,76,71,39,40,39,41,40,42,42,39,42,41,40,40,39,41,42,41],,,,,
,,,[1,2,3,4,5,6,7,10,8,11,9,13,12,16,14,17,15,19,18,20,21,22,24,26,23,25,28,30
,27,29,32,34,31,33,36,35,38,37,1,1,1,1,46,43,44,45,50,47,48,49,54,51,52,53,56,
55,58,57,59,60,61,62,64,66,63,65,69,67,70,68,73,76,71,77,78,72,74,75,8,9,10,11
,8,9,10,11,8,9,10,11,9,10,11,8],,,,[1,2,3,4,5,6,7,9,11,8,10,13,12,15,17,14,16,
19,18,20,21,22,25,23,26,24,29,27,30,28,33,31,34,32,36,35,38,37,41,42,39,40,44,
45,46,43,48,49,50,47,52,53,54,51,56,55,58,57,1,1,1,1,65,63,66,64,68,70,67,69,4
,4,4,4,4,4,4,4,88,93,94,81,84,90,83,92,80,86,87,85,82,79,89,91]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[51,-13,3,0,3,3,-1,-13*E(5)-E(5)^2,
-13*E(5)^2-E(5)^4,-E(5)-13*E(5)^3,-E(5)^3-13*E(5)^4,3*E(5)+3*E(5)^4,
3*E(5)^2+3*E(5)^3,4*E(5)^2+E(5)^3+E(5)^4,E(5)+E(5)^3+4*E(5)^4,
4*E(5)+E(5)^2+E(5)^4,E(5)+E(5)^2+4*E(5)^3,-4*E(5)-3*E(5)^2-3*E(5)^3-4*E(5)^4,
-3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4,1,-1,0,3*E(5)^2-E(5)^4,3*E(5)-E(5)^2,
-E(5)^3+3*E(5)^4,-E(5)+3*E(5)^3,3*E(5)^2-E(5)^3,3*E(5)-E(5)^4,-E(5)+3*E(5)^4,
-E(5)^2+3*E(5)^3,E(5)^2+E(5)^4,E(5)+E(5)^2,E(5)^3+E(5)^4,E(5)+E(5)^3,
E(5)+E(5)^4,E(5)^2+E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,-1,-1,-1,3*E(5),
3*E(5)^2,3*E(5)^4,3*E(5)^3,E(5)+E(5)^3+E(5)^4,E(5)+E(5)^2+E(5)^3,
E(5)+E(5)^2+E(5)^4,E(5)^2+E(5)^3+E(5)^4,-E(5)-E(5)^3,-E(5)-E(5)^2,
-E(5)^2-E(5)^4,-E(5)^3-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,
-E(5)-E(5)^2,-E(5)-E(5)^3,-E(5)^2-E(5)^4,-E(5)^3-E(5)^4,-E(5)^3,-E(5),-E(5)^4,
-E(5)^2,0,0,0,0,0,0,0,0,-E(5)^4,-E(5)^3,-E(5)^2,-E(5),-E(5)^4,-E(5)^3,-E(5)^2,
-E(5),-E(5)^4,-E(5)^3,-E(5)^2,-E(5),-E(5)^3,-E(5)^2,-E(5),-E(5)^4],
[GALOIS,[2,4]],
[GALOIS,[2,3]],
[GALOIS,[2,2]],[52,-12,4,1,4,4,0,-13,-13,-13,-13,7,7,2,2,2,2,2,2,-3,0,1,3,3,3
,3,3,3,3,3,-2,-2,-2,-2,-2,-2,-1,-1,0,0,0,0,4,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0],[221,29,13,17,2,-3,1,13*E(5)^2+13*E(5)^3,13*E(5)+13*E(5)^4,
13*E(5)+13*E(5)^4,13*E(5)^2+13*E(5)^3,-9*E(5)-8*E(5)^2-8*E(5)^3-9*E(5)^4,
-8*E(5)-9*E(5)^2-9*E(5)^3-8*E(5)^4,E(5)-3*E(5)^2-3*E(5)^3+E(5)^4,
-3*E(5)+E(5)^2+E(5)^3-3*E(5)^4,-3*E(5)+E(5)^2+E(5)^3-3*E(5)^4,
E(5)-3*E(5)^2-3*E(5)^3+E(5)^4,-5*E(5)-2*E(5)^2-2*E(5)^3-5*E(5)^4,
-2*E(5)-5*E(5)^2-5*E(5)^3-2*E(5)^4,1,2,1,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3,
-3*E(5)^2-3*E(5)^3,-3*E(5)-3*E(5)^4,4*E(5)+3*E(5)^2+3*E(5)^3+4*E(5)^4,
3*E(5)+4*E(5)^2+4*E(5)^3+3*E(5)^4,3*E(5)+4*E(5)^2+4*E(5)^3+3*E(5)^4,
4*E(5)+3*E(5)^2+3*E(5)^3+4*E(5)^4,-1,-1,-1,-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,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,
E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,
2,2,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)^2+E(5)^3,E(5)+E(5)^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],
[GALOIS,[7,2]],[272,16,16,17,5,0,0,12,12,12,12,17,17,-3,-3,-3,-3,-3,-3,2,1,1,
-4,-4,-4,-4,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,5,5,5,5,0,0,0,0,0,0,0,0,0,0,2,
2,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1],[325,5,21,16,-5,5,1,0,0,0,0,25,25,0,0,0,0,0,0,0,-1,0,0,0,0,0,5,5,
5,5,0,0,0,0,0,0,1,1,0,0,0,0,-5,-5,-5,-5,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,0,0,0,
0,-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],[612,36
,-12,0,0,4,0,39*E(5)^2-12*E(5)^4,-12*E(5)^3+39*E(5)^4,39*E(5)-12*E(5)^2,
-12*E(5)+39*E(5)^3,-9*E(5)^2-9*E(5)^3,-9*E(5)-9*E(5)^4,
-3*E(5)-3*E(5)^3+3*E(5)^4,-3*E(5)-3*E(5)^2+3*E(5)^3,3*E(5)^2-3*E(5)^3-3*E(5)^4
,3*E(5)-3*E(5)^2-3*E(5)^4,-6*E(5)-3*E(5)^2-3*E(5)^3-6*E(5)^4,
-3*E(5)-6*E(5)^2-6*E(5)^3-3*E(5)^4,2,0,0,4*E(5)^3+7*E(5)^4,7*E(5)^2+4*E(5)^4,
4*E(5)+7*E(5)^3,7*E(5)+4*E(5)^2,3*E(5)+3*E(5)^4,3*E(5)^2+3*E(5)^3,
3*E(5)^2+3*E(5)^3,3*E(5)+3*E(5)^4,-E(5)^2+E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^4,
E(5)+E(5)^3-E(5)^4,E(5)+E(5)^2-E(5)^3,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,
2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,1,1,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(5)^2,-E(5),-E(5)^4,-E(5)^3,0,0,0,0,0,0,0,0,0,0,
0,0,E(5)^3,E(5),E(5)^4,E(5)^2,E(5)^3,E(5),E(5)^4,E(5)^2,E(5)^3,E(5),E(5)^4,
E(5)^2,E(5),E(5)^4,E(5)^2,E(5)^3],
[GALOIS,[11,4]],
[GALOIS,[11,3]],
[GALOIS,[11,2]],[663,23,-9,0,3,7,-1,13*E(5)+13*E(5)^2+52*E(5)^3,
52*E(5)+13*E(5)^2+13*E(5)^4,13*E(5)+13*E(5)^3+52*E(5)^4,
52*E(5)^2+13*E(5)^3+13*E(5)^4,-9*E(5)+3*E(5)^2+3*E(5)^3-9*E(5)^4,
3*E(5)-9*E(5)^2-9*E(5)^3+3*E(5)^4,-E(5)-E(5)^2-3*E(5)^3+3*E(5)^4,
-3*E(5)-E(5)^2+3*E(5)^3-E(5)^4,-E(5)+3*E(5)^2-E(5)^3-3*E(5)^4,
3*E(5)-3*E(5)^2-E(5)^3-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-2,-1,0,
4*E(5)-3*E(5)^2-3*E(5)^4,-3*E(5)-3*E(5)^2+4*E(5)^3,4*E(5)^2-3*E(5)^3-3*E(5)^4,
-3*E(5)-3*E(5)^3+4*E(5)^4,3*E(5)+3*E(5)^2+3*E(5)^3-E(5)^4,
3*E(5)-E(5)^2+3*E(5)^3+3*E(5)^4,3*E(5)+3*E(5)^2-E(5)^3+3*E(5)^4,
-E(5)+3*E(5)^2+3*E(5)^3+3*E(5)^4,-E(5)-E(5)^2-E(5)^3+E(5)^4,
-E(5)+E(5)^2-E(5)^3-E(5)^4,-E(5)-E(5)^2+E(5)^3-E(5)^4,
E(5)-E(5)^2-E(5)^3-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,1,1,0,0,0,0,3*E(5)^3,
3*E(5),3*E(5)^2,3*E(5)^4,-E(5)^2-E(5)^4,-E(5)^3-E(5)^4,-E(5)-E(5)^3,
-E(5)-E(5)^2,E(5)+E(5)^3+E(5)^4,E(5)+E(5)^2+E(5)^3,E(5)+E(5)^2+E(5)^4,
E(5)^2+E(5)^3+E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,E(5)+E(5)^2,
E(5)+E(5)^3,E(5)^2+E(5)^4,E(5)^3+E(5)^4,-E(5)^4,-E(5)^3,-E(5)^2,-E(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],
[GALOIS,[15,4]],
[GALOIS,[15,3]],
[GALOIS,[15,2]],[663,23,-9,0,3,7,-1,-39*E(5)-52*E(5)^2-52*E(5)^3-39*E(5)^4,
-52*E(5)-39*E(5)^2-39*E(5)^3-52*E(5)^4,-52*E(5)-39*E(5)^2-39*E(5)^3-52*E(5)^4,
-39*E(5)-52*E(5)^2-52*E(5)^3-39*E(5)^4,-15*E(5)-6*E(5)^2-6*E(5)^3-15*E(5)^4,
-6*E(5)-15*E(5)^2-15*E(5)^3-6*E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-4*E(5)+3*E(5)^2+3*E(5)^3-4*E(5)^4,
3*E(5)-4*E(5)^2-4*E(5)^3+3*E(5)^4,3,-1,0,-4*E(5)-7*E(5)^2-7*E(5)^3-4*E(5)^4,
-7*E(5)-4*E(5)^2-4*E(5)^3-7*E(5)^4,-7*E(5)-4*E(5)^2-4*E(5)^3-7*E(5)^4,
-4*E(5)-7*E(5)^2-7*E(5)^3-4*E(5)^4,-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,E(5)-2*E(5)^2-2*E(5)^3+E(5)^4,
-2*E(5)+E(5)^2+E(5)^3-2*E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,
2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,0,0,0,0,3,3,3,3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(5)^2+E(5)^3,E(5)+E(5)^4,-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],
[GALOIS,[19,2]],[832,64,0,16,1,0,0,52,52,52,52,-8,-8,7,7,7,7,7,7,-3,1,0,4,4,4
,4,4,4,4,4,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1
,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
],[884,52,4,17,5,4,0,-13*E(5)^2+52*E(5)^3,52*E(5)-13*E(5)^4,-13*E(5)+52*E(5)^4
,52*E(5)^2-13*E(5)^3,9*E(5)+13*E(5)^2+13*E(5)^3+9*E(5)^4,
13*E(5)+9*E(5)^2+9*E(5)^3+13*E(5)^4,4*E(5)+3*E(5)^2+3*E(5)^3-E(5)^4,
3*E(5)+4*E(5)^2-E(5)^3+3*E(5)^4,3*E(5)-E(5)^2+4*E(5)^3+3*E(5)^4,
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4*E(5)+3*E(5)^4,3*E(5)^2+4*E(5)^3,4*E(5)^2+3*E(5)^3,3*E(5)+4*E(5)^4,
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[(59,61,60,62)(71,74,72,75,73,77,76,78),
(59,60)(61,62)(71,72,73,76)(74,75,77,78),(71,73)(72,76)(74,77)(75,78),
( 8, 9,11,10)(12,13)(14,15,17,16)(18,19)(23,25,26,24)(27,29,30,28)
(31,33,34,32)(35,36)(37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)
(51,52,53,54)(55,56)(57,58)(63,65,66,64)(67,68,70,69)(79,80,82,85)
(81,83,88,93)(84,86,89,94)(87,91,90,92),
( 8,10,11, 9)(12,13)(14,16,17,15)(18,19)(23,24,26,25)(27,28,30,29)
(31,32,34,33)(35,36)(37,38)(43,46,45,44)(47,50,49,48)(51,54,53,52)(55,56)
(57,58)(63,64,66,65)(67,69,70,68)(79,81,86,91)(80,83,89,90)(82,88,94,92)
(84,87,85,93)]);
ARC("U4(4)","isSimple",true);
ARC("U4(4)","extInfo",["","4"]);
ALF("U4(4)","U4(4).4",[1,2,3,4,5,6,7,8,8,8,8,9,9,11,11,11,11,10,10,12,13,
14,15,15,15,15,16,16,16,16,19,19,19,19,17,17,18,18,20,20,20,20,21,21,21,
21,25,25,25,25,24,24,24,24,22,22,23,23,26,26,27,27,28,28,28,28,29,29,29,
29,31,31,31,30,30,31,30,30,32,32,33,32,33,34,32,34,35,33,34,35,35,35,33,
34],[
"fusion map is unique up to table automorphisms"
]);
ALF("U4(4)","U5(4)",[1,2,3,5,4,6,8,9,10,10,9,12,11,12,11,11,12,9,10,13,14,
15,22,21,21,22,23,26,25,24,23,26,25,24,22,21,28,27,30,32,31,33,37,34,36,
35,35,37,34,36,39,38,39,38,38,39,41,40,42,43,44,45,47,46,46,47,55,52,53,
54,74,73,75,71,68,72,70,69,83,80,76,82,78,81,81,83,79,77,80,78,76,77,79,
82],[
"fusion map is unique up to table automorphisms"
]);

MOT("U4(4).4",
[
"origin: computed using Dixon's algorithm and character theoretic methods,\n",
"Thomas Breuer, Sep. 29th, 2004,\n",
"constructions: Aut(U4(4))"
],
[4073472000,1228800,61440,48960,3600,5120,256,312000,36000,3000,1500,500,240,
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3916800,15360,2560,1536,720,720,48,64,600,600,100,40,48,40,30,30,34,34,2880,
192,192,64,72,72,24,16,20,24,2880,192,192,64,72,72,24,16,20,24],
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68,69,70,71,72,73]],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[56,2]],
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E(65)+E(65)^2+E(65)^4+E(65)^8+E(65)^16+E(65)^32+E(65)^33+E(65)^49+E(65)^57
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E(65)^3+E(65)^6+E(65)^12+E(65)^17+E(65)^24+E(65)^31+E(65)^34+E(65)^41+E(65)^48
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E(65)^7+E(65)^9+E(65)^14+E(65)^18+E(65)^28+E(65)^29+E(65)^36+E(65)^37+E(65)^47
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[GALOIS,[67,11]],
[GALOIS,[67,7]],
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[GALOIS,[72,3]]],
[(54,64)(55,65)(56,66)(57,67)(58,68)(59,69)(60,70)(61,71)(62,72)(63,73),
(26,27)(30,31)(52,53),(32,33,34,35)]);
ALF("U4(4).4","O12-(2).2",[1,22,19,5,35,119,115,185,7,41,185,41,37,134,
186,140,42,136,186,200,179,43,44,188,188,47,48,187,181,194,193,201,202,
203,204,3,114,20,21,160,29,162,124,166,31,166,167,137,139,168,169,172,173,
291,293,296,296,315,337,339,302,342,321,291,293,296,296,315,337,339,302,
342,321],[
"fusion map is unique up to table automorphisms"
]);

MOT("U4(5)",
[
"origin: computed using Dixon's algorithm and character theoretic methods,\n",
"Thomas Breuer, Jul. 09th, 2003"
],
[14742000000,86400,62400,1134000,1134000,43200,2160,31200,1440,96,1125000,
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300,300,200,200,1440,1440,72,72,72,48,48,52,52,52,2250,2250,1800,1800,150,150,
90,75,75,100,100,60,63,63,63,63,72,72,72,72,72,72,72,72,52,52,52,1800,1800,150
,150,90,90,90,52,52,52,52,52,52,60,60,63,63,63,63,63,63,63,63,63,63,63,63],
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59,58,36,36,34,35,37,38,37,38,42,43,41,46,47,48,49,50,45,44,68,69,70,68,69,70,
71,72,87,88,90,91,92,95,96,94,89,97,86,93],[1,2,3,1,1,1,1,8,9,10,11,12,13,14,
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73,74,75,76,77,80,81,82,83,78,79,84,85,27,28,27,28,28,27,27,28,27,28,28,27],,,
,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,24,26,27,28
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[GALOIS,[71,2]],[14976,0,0,-144,-144,0,0,0,0,0,-24,-24,-24,1,1,1,0,0,0,0,0,0,
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0,0,0,0,0,0,E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,
E(21)^10+E(21)^13+E(21)^19,E(21)^2+E(21)^8+E(21)^11,E(21)^5+E(21)^17+E(21)^20,
E(21)+E(21)^4+E(21)^16,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)^2+E(21)^8+E(21)^11,E(21)^5+E(21)^17+E(21)^20,
E(21)+E(21)^4+E(21)^16],
[GALOIS,[75,2]],
[GALOIS,[75,5]],
[GALOIS,[75,10]],[15625,25,25,-125,-125,25,-5,25,5,1,0,0,0,0,0,0,25,-5,-5,-5,
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E(52)^29-E(52)^37-E(52)^41+E(52)^49,-E(52)^9-E(52)^17+E(52)^33+E(52)^45,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[83,33]],
[GALOIS,[83,11]],
[GALOIS,[83,5]],
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[GALOIS,[89,4]],
[GALOIS,[89,2]],[18144,0,48,0,0,0,0,-48,0,0,144,-6,-6,-6,-1,-1,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0],
[GALOIS,[92,4]],
[GALOIS,[92,2]],[18900,-36,-24,0,0,36,0,-26,0,2,150,25,25,0,0,0,-36,0,0,0,0,0
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0,0,0,0],[19656,-72,0,0,0,-36,0,-52,0,4,156,56,56,6,1,1,36,0,0,0,0,0,0,0,0,0,0
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[(60,61)(64,66)(65,67),(78,81)(79,82)(80,83),
(12,13)(15,16)(30,31)(32,33)(48,49)(53,54)(73,74),
(41,42,43)(68,69,70)(78,79,80,81,82,83),
(86,88,92)(87,90,96)(89,95,93)(91,97,94),
(24,25)(56,59)(57,58)(86,91,88,97,92,94)(87,95,90,93,96,89),
( 4, 5)(19,20)(27,28)(34,35)(37,38)(44,45)(46,47)(51,52)(56,57)(58,59)(62,63)
(64,65)(66,67)(71,72)(76,77)(84,85)(86,87,88,90,92,96)(89,91,95,97,93,94)
]);
ARC("U4(5)","isSimple",true);
ARC("U4(5)","extInfo",["2","2^2"]);
ALF("U4(5)","U4(5).2_1",[1,2,3,4,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
18,19,20,21,22,22,23,24,24,25,26,27,28,29,30,30,31,32,32,33,34,35,36,37,
38,38,39,39,40,41,42,43,43,44,45,46,47,48,47,48,49,50,51,51,52,52,53,53,
54,55,56,57,57,58,59,60,61,61,62,63,64,62,63,64,65,65,66,67,68,66,69,67,
70,70,71,68,71,69],[
"fusion map is unique up to table automorphisms"
]);
ALF("U4(5)","U4(5).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,12,13,14,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,28,29,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,44,45,46,47,48,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90],[
"fusion map is unique up to table automorphisms"
]);
ALF("U4(5)","U4(5).2_3",[1,2,3,4,4,5,6,7,8,9,10,11,11,12,13,13,14,15,16,
16,17,18,19,20,20,21,22,22,23,24,24,25,25,26,26,27,28,28,29,30,31,32,33,
34,34,35,35,36,36,37,38,38,39,39,40,41,42,41,42,43,44,45,45,46,46,47,47,
48,49,50,51,51,52,52,53,54,54,55,56,57,55,56,57,58,58,59,60,61,59,62,60,
63,63,64,61,64,62],[
"fusion map is unique up to table automorphisms"
]);
ALF("U4(5)","U4(5).2^2",[1,2,3,4,4,5,6,7,8,9,10,11,11,12,13,13,14,15,16,
16,17,18,19,20,20,21,22,22,23,24,24,25,25,26,26,27,28,28,29,30,31,32,33,
34,34,35,35,36,36,37,38,38,39,39,40,41,42,41,42,43,44,45,45,46,46,47,47,
48,49,50,51,51,52,52,53,54,54,55,56,57,55,56,57,58,58,59,60,61,59,62,60,
63,63,64,61,64,62],[
"fusion map is unique up to table automorphisms"
]);

MOT("U4(5).2_1",
[
"origin: computed using Dixon's algorithm and character theoretic methods,\n",
"Thomas Breuer, August 2005,\n",
"constructions: PSigmaU(4,5), PSU(4,5) extended by transpose-inverse"
],
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,1440,144,72,96,96,104,104,104,2250,1800,300,300,180,75,200,200,120,63,63,144,
144,72,72,72,104,104,104,1800,300,300,180,90,52,52,52,60,63,63,63,63,63,63,
18720000,18720000,28800,960,960,960,1440,1440,1440,1440,1440,1440,72,48,30000,
30000,3000,3000,2000,2000,1200,1200,50,50,50,48,48,48,40,40,40,48,48,52,52,52,
52,52,52,60,60,60,60,60,60],
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39,40,41,42,38,54,55,56,57,67,68,69,70,71,66,1,1,1,3,2,3,5,5,6,5,5,6,6,8,10,10
,11,12,11,12,11,12,13,14,15,21,17,21,29,25,28,31,31,36,37,35,36,37,35,40,40,42
,41,41,42],[1,2,3,1,1,1,7,8,9,10,11,12,13,14,15,2,2,2,2,2,3,22,23,4,25,26,27,
28,29,8,8,8,9,7,36,37,35,10,10,11,12,10,13,44,45,46,22,22,23,23,23,23,23,55,56
,54,25,26,27,25,25,63,64,62,46,47,48,47,48,47,48,72,73,74,75,76,77,74,72,73,74
,73,72,74,85,86,87,88,89,90,91,92,93,94,95,96,77,76,75,100,101,102,85,85,106,
107,105,109,110,108,92,88,86,93,89,87],,[1,2,3,4,5,6,7,8,9,1,1,1,1,1,1,16,17,
18,19,20,21,22,23,24,2,2,2,3,3,30,31,32,33,34,35,36,37,4,5,5,5,6,4,7,7,8,47,48
,49,50,51,52,53,54,55,56,16,16,16,17,18,62,63,64,30,66,67,68,69,70,71,72,73,74
,75,76,77,78,79,80,81,82,83,84,85,73,72,72,73,73,72,74,74,74,73,72,97,98,99,75
,76,77,103,104,105,106,107,108,109,110,78,79,80,81,82,83],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,1,23,24,25,26,27,28,29,30,31,32,33,34,37,
35,36,38,39,40,41,42,43,44,45,46,4,4,50,49,51,53,52,56,54,55,57,58,59,60,61,64
,62,63,65,24,24,24,24,24,24,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88
,89,90,91,92,93,94,95,96,97,98,99,100,101,102,104,103,107,105,106,110,108,109,
111,112,113,114,115,116],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,1,1,1,38,39,40,41,42,43,44,45,46
,48,47,50,49,51,53,52,3,3,3,57,58,59,60,61,7,7,7,65,67,68,69,70,71,66,72,73,74
,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,
100,101,102,104,103,73,73,73,72,72,72,111,112,113,114,115,116]],
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-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[105,9,1,-21,9,3,1,5,1,-20,5,5,5
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[TENSOR,[3,2]],[208,16,0,19,-8,10,0,8,0,-42,8,8,8,-2,-2,-8,10,-5,4,-2,0,-2,-4
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[273,-7,13,21,9,-3,-13,1,-1,23,23
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--> --------------------

--> maximum size reached

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