Quelle ctosymp2.tbl Sprache: unbekannt

#############################################################################
##
#W  ctosymp2.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables related to the
##  symplectic groups $S_4(7)$, $S_4(8)$, $S_4(9)$, $S_6(4)$, $S_6(5)$,
##  and $S_8(3)$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctosymp2.tbl,v $
#H  Revision 4.13  2012/01/30 08:32:02  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.12  2011/09/28 14:14:07  gap
#H  - reordered the tables of S4(9), S4(9).2_1, added table of S4(9).2^2
#H  - added fusions S4(4) -> U4(4), S4(5).2 -> U4(5)
#H      TB
#H
#H  Revision 4.11  2008/06/24 16:23:06  gap
#H  added several fusions and names
#H      TB
#H
#H  Revision 4.10  2007/06/05 07:51:13  gap
#H  corrected table of S4(9).2_3
#H  (the construction had introduced a nontrivial centre)
#H      TB
#H
#H  Revision 4.9  2005/06/08 07:50:33  gap
#H  added the table of S6(4).2 (one more table Bob Guralnick needed)
#H      TB
#H
#H  Revision 4.8  2005/01/26 15:10:43  gap
#H  fixed a too long info line
#H      TB
#H
#H  Revision 4.7  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 4.6  2003/10/30 09:19:53  gap
#H  added table of S8(3) (computed for answering a question of Jan Saxl)
#H      TB
#H
#H  Revision 4.5  2003/07/24 07:10:46  gap
#H  added table of S4(8) (computed for answering a question of Jan Saxl)
#H      TB
#H
#H  Revision 4.4  2001/05/04 16:50:18  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.4 of ctbllib coincides with Rev. 4.3 of tbl in GAP 4)
#H
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctosymp2.tbl,v
#H  Working file: ctosymp2.tbl
#H  head: 4.3
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H  keyword substitution: kv
#H  total revisions: 3; selected revisions: 3
#H  description:
#H  ----------------------------
#H  revision 4.3
#H  date: 2001/02/06 14:49:18;  author: gap;  state: Exp;  lines: +659 -3
#H  added tables of S6(4) and U4(4)
#H
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 2001/01/16 16:39:20;  author: gap;  state: Exp;  lines: +178 -3
#H  added table of S4(7).2
#H
#H      TB
#H  ----------------------------
#H  revision 4.1
#H  date: 2001/01/15 16:42:45;  author: gap;  state: Exp;
#H  renamed file `ctosympl.tbl' to `ctosymp1.tbl',
#H  added tables of S4(7) (a present for Gunter Malle)
#H  and S6(5) (ordered by Bob Guralnick)
#H
#H      TB
#H  ==========================================================================
##

MOT("S4(7)",
[
"origin: computed using Dixon's algorithm and character theoretic methods,\n",
"Thomas Breuer, Jan. 09th, 2001"
],
[138297600,112896,2688,1008,1008,1344,1344,64,25,1008,48,36,115248,115248,2744
,2058,49,49,1344,1344,48,48,32,24,24,2352,2352,196,196,98,56,42,42,21,24,24,24
,24,25,25,25,25,25,56,56,28,42,42,56,56,56,56],
[,[1,1,1,4,5,3,2,3,9,5,4,4,13,14,15,16,17,18,7,7,6,6,7,11,10,13,14,15,15,16,15
,32,33,34,24,24,25,25,40,41,42,43,39,26,27,31,32,33,44,45,44,45],[1,2,3,1,1,6,
7,8,9,2,3,2,14,13,15,16,18,17,20,19,22,21,23,6,7,27,26,29,28,30,31,13,14,16,21
,22,19,20,41,42,43,39,40,45,44,46,26,27,52,51,50,49],,[1,2,3,4,5,6,7,8,1,10,11
,12,14,13,15,16,18,17,20,19,22,21,23,24,25,27,26,29,28,30,31,33,32,34,36,35,38
,37,9,9,9,9,9,45,44,46,48,47,52,51,50,49],,[1,2,3,4,5,6,7,8,9,10,11,12,1,1,1,1
,1,1,19,20,21,22,23,24,25,2,2,2,2,2,3,5,5,4,35,36,37,38,39,40,41,42,43,7,7,6,
10,10,20,20,19,19]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1],[25,-7,1,1,4,1,-3,1,0,-4,1,-1,
3*E(7)+3*E(7)^2-4*E(7)^3+3*E(7)^4-4*E(7)^5-4*E(7)^6,
-4*E(7)-4*E(7)^2+3*E(7)^3-4*E(7)^4+3*E(7)^5+3*E(7)^6,-3,4,
-E(7)^3-E(7)^5-E(7)^6,-E(7)-E(7)^2-E(7)^4,3,3,-1,-1,-1,1,0,
3*E(7)+3*E(7)^2+4*E(7)^3+3*E(7)^4+4*E(7)^5+4*E(7)^6,
4*E(7)+4*E(7)^2+3*E(7)^3+4*E(7)^4+3*E(7)^5+3*E(7)^6,
-E(7)-E(7)^2+E(7)^3-E(7)^4+E(7)^5+E(7)^6,
E(7)+E(7)^2-E(7)^3+E(7)^4-E(7)^5-E(7)^6,0,1,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6,1,-1,-1,0,0,0,0,0,0,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6,1,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,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[2,3]],[126,-18,6,0,0,6,6,-2,1,0,0,0,-21,-21,7,0,0,0,6,6,0,0,-2,0,0,3
,3,3,3,-4,-1,0,0,0,0,0,0,0,1,1,1,1,1,-1,-1,-1,0,0,-1,-1,-1,-1],[150,6,6,0,3,-6
,2,2,0,3,0,0,18*E(7)+18*E(7)^2+25*E(7)^3+18*E(7)^4+25*E(7)^5+25*E(7)^6,
25*E(7)+25*E(7)^2+18*E(7)^3+25*E(7)^4+18*E(7)^5+18*E(7)^6,3,3,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,4,4,0,0,0,0,-1,
-6*E(7)-6*E(7)^2+E(7)^3-6*E(7)^4+E(7)^5+E(7)^6,
E(7)+E(7)^2-6*E(7)^3+E(7)^4-6*E(7)^5-6*E(7)^6,-1,-1,-1,-1,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,0,0,0,1,1,0,0,0,0,0,
2*E(7)+2*E(7)^2+E(7)^3+2*E(7)^4+E(7)^5+E(7)^6,
E(7)+E(7)^2+2*E(7)^3+E(7)^4+2*E(7)^5+2*E(7)^6,1,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)-E(7)^2-E(7)^4],
[GALOIS,[5,3]],[175,-17,-1,7,1,-1,7,-1,0,1,-1,1,28,28,7,0,0,0,7,7,-1,-1,-1,-1
,1,4,4,-3,-3,4,-1,1,1,0,-1,-1,1,1,0,0,0,0,0,0,0,-1,1,1,0,0,0,0],[175,31,7,1,7,
7,-1,-1,0,7,1,1,-21,-21,0,7,0,0,-1,-1,1,1,-1,1,-1,3,3,-4,-4,3,0,0,0,1,1,1,-1,
-1,0,0,0,0,0,-1,-1,0,0,0,-1,-1,-1,-1],[224,32,0,8,8,0,0,0,-1,8,0,2,28,28,0,7,0
,0,0,0,0,0,0,0,0,4,4,4,4,-3,0,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,0,0,0,1,1,0,0,0,0],
[300,12,-12,0,6,0,8,0,0,6,0,0,-43,-43,6,6,-1,-1,6,6,0,0,2,0,2,5,5,-2,-2,-2,2,
-1,-1,0,0,0,0,0,0,0,0,0,0,1,1,0,-1,-1,-1,-1,-1,-1],[300,-36,4,6,0,8,-12,0,0,0,
-2,0,6,6,13,-1,-1,-1,0,0,0,0,0,2,0,6,6,-1,-1,-1,-3,0,0,-1,0,0,0,0,0,0,0,0,0,2,
2,1,0,0,0,0,0,0],[300,36,8,6,0,6,0,2,0,0,2,0,6,6,13,-1,-1,-1,6*E(8)-6*E(8)^3,
-6*E(8)+6*E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,-6,-6,1,1,1,1,0,0,-1,
E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,-1,0,0,E(8)-E(8)^3,E(8)-E(8)^3,
-E(8)+E(8)^3,-E(8)+E(8)^3],
[GALOIS,[12,3]],[350,-50,6,8,8,6,6,-2,0,-8,0,-2,7,7,7,7,0,0,-6,-6,0,0,2,0,0,
-1,-1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,1,1,1,1],[400,16,0,-8
,7,0,8,0,0,7,0,-2,57,57,8,8,1,1,8,8,0,0,0,0,-1,9,9,2,2,2,0,0,0,-1,0,0,-1,-1,0,
0,0,0,0,1,1,0,0,0,1,1,1,1],[400,-64,8,7,-8,8,0,0,0,8,-1,-1,8,8,1,15,1,1,0,0,-2
,-2,0,-1,0,-8,-8,-1,-1,-1,1,-1,-1,0,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0],[400,
64,8,7,-8,8,0,0,0,-8,-1,1,8,8,1,15,1,1,0,0,2,2,0,-1,0,8,8,1,1,1,1,-1,-1,0,-1,
-1,0,0,0,0,0,0,0,0,0,1,-1,-1,0,0,0,0],[900,36,12,0,0,0,0,0,0,0,0,0,
3*E(7)+3*E(7)^2-39*E(7)^3+3*E(7)^4-39*E(7)^5-39*E(7)^6,
-39*E(7)-39*E(7)^2+3*E(7)^3-39*E(7)^4+3*E(7)^5+3*E(7)^6,-10,-3,
-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,6,6,0,0,2,0,0,
3*E(7)+3*E(7)^2+9*E(7)^3+3*E(7)^4+9*E(7)^5+9*E(7)^6,
9*E(7)+9*E(7)^2+3*E(7)^3+9*E(7)^4+3*E(7)^5+3*E(7)^6,
-2*E(7)^3-2*E(7)^5-2*E(7)^6,-2*E(7)-2*E(7)^2-2*E(7)^4,1,-2,0,0,0,0,0,0,0,0,0,0
,0,0,-E(7)-E(7)^2+E(7)^3-E(7)^4+E(7)^5+E(7)^6,
E(7)+E(7)^2-E(7)^3+E(7)^4-E(7)^5-E(7)^6,0,0,0,-1,-1,-1,-1],
[GALOIS,[18,3]],[1050,42,-6,0,3,6,-10,-2,0,3,0,0,
28*E(7)+28*E(7)^2-21*E(7)^3+28*E(7)^4-21*E(7)^5-21*E(7)^6,
-21*E(7)-21*E(7)^2+28*E(7)^3-21*E(7)^4+28*E(7)^5+28*E(7)^6,-7,0,0,0,4,4,0,0,0,
0,-1,4*E(7)+4*E(7)^2+3*E(7)^3+4*E(7)^4+3*E(7)^5+3*E(7)^6,
3*E(7)+3*E(7)^2+4*E(7)^3+3*E(7)^4+4*E(7)^5+4*E(7)^6,
E(7)+E(7)^2-E(7)^3+E(7)^4-E(7)^5-E(7)^6,
-E(7)-E(7)^2+E(7)^3-E(7)^4+E(7)^5+E(7)^6,0,1,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,0,0,0,1,1,0,0,0,0,0,-E(7)^3-E(7)^5-E(7)^6,
-E(7)-E(7)^2-E(7)^4,-1,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)^3-E(7)^5-E(7)^6,
-E(7)-E(7)^2-E(7)^4],
[GALOIS,[20,3]],[1200,48,0,0,-3,0,-8,0,0,-3,0,0,
-3*E(7)-3*E(7)^2+53*E(7)^3-3*E(7)^4+53*E(7)^5+53*E(7)^6,
53*E(7)+53*E(7)^2-3*E(7)^3+53*E(7)^4-3*E(7)^5-3*E(7)^6,-4,3,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,8,8,0,0,0,0,1,
-3*E(7)-3*E(7)^2+5*E(7)^3-3*E(7)^4+5*E(7)^5+5*E(7)^6,
5*E(7)+5*E(7)^2-3*E(7)^3+5*E(7)^4-3*E(7)^5-3*E(7)^6,2*E(7)^3+2*E(7)^5+2*E(7)^6
,2*E(7)+2*E(7)^2+2*E(7)^4,-1,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0,0
,-1,-1,0,0,0,0,0,-1,-1,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,1,1,1,1],
[GALOIS,[22,3]],[1200,-48,0,0,6,0,0,0,0,-6,0,0,
46*E(7)+46*E(7)^2+4*E(7)^3+46*E(7)^4+4*E(7)^5+4*E(7)^6,
4*E(7)+4*E(7)^2+46*E(7)^3+4*E(7)^4+46*E(7)^5+46*E(7)^6,-4,3,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,-4*E(8)+4*E(8)^3,4*E(8)-4*E(8)^3,0,0,0
,0,0,2*E(7)+2*E(7)^2-4*E(7)^3+2*E(7)^4-4*E(7)^5-4*E(7)^6,
-4*E(7)-4*E(7)^2+2*E(7)^3-4*E(7)^4+2*E(7)^5+2*E(7)^6,-2*E(7)-2*E(7)^2-2*E(7)^4
,-2*E(7)^3-2*E(7)^5-2*E(7)^6,1,0,-1,-1,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,0,
0,0,0,0,1,1,-E(56)^15-E(56)^23+E(56)^29+E(56)^37-E(56)^39+E(56)^53,
E(56)^5+E(56)^13-E(56)^31+E(56)^45-E(56)^47-E(56)^55,
E(56)^15+E(56)^23-E(56)^29-E(56)^37+E(56)^39-E(56)^53,
-E(56)^5-E(56)^13+E(56)^31-E(56)^45+E(56)^47+E(56)^55],
[GALOIS,[24,17]],
[GALOIS,[24,3]],
[GALOIS,[24,11]],[1225,-7,-7,7,4,-7,-3,1,0,-4,-1,-1,
-49*E(7)-49*E(7)^2-49*E(7)^4,-49*E(7)^3-49*E(7)^5-49*E(7)^6,0,0,0,0,3,3,1,1,-1
,-1,0,7*E(7)+7*E(7)^2+7*E(7)^4,7*E(7)^3+7*E(7)^5+7*E(7)^6,0,0,0,0,
-E(7)^3-E(7)^5-E(7)^6,-E(7)-E(7)^2-E(7)^4,0,1,1,0,0,0,0,0,0,0,
-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,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)^3+E(7)^5+E(7)^6],
[GALOIS,[28,3]],[1600,-64,0,-8,4,0,0,0,0,-4,0,2,
-4*E(7)-4*E(7)^2-60*E(7)^3-4*E(7)^4-60*E(7)^5-60*E(7)^6,
-60*E(7)-60*E(7)^2-4*E(7)^3-60*E(7)^4-4*E(7)^5-4*E(7)^6,4,11,
-E(7)^3-E(7)^5-E(7)^6,-E(7)-E(7)^2-E(7)^4,0,0,0,0,0,0,0,
4*E(7)+4*E(7)^2+12*E(7)^3+4*E(7)^4+12*E(7)^5+12*E(7)^6,
12*E(7)+12*E(7)^2+4*E(7)^3+12*E(7)^4+4*E(7)^5+4*E(7)^6,
2*E(7)^3+2*E(7)^5+2*E(7)^6,2*E(7)+2*E(7)^2+2*E(7)^4,-1,0,-E(7)^3-E(7)^5-E(7)^6
,-E(7)-E(7)^2-E(7)^4,-1,0,0,0,0,0,0,0,0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,0,0,0,0],
[GALOIS,[30,3]],[1800,-72,0,0,0,12,0,4,0,0,0,0,36,36,-20,-6,1,1,0,0,0,0,0,0,0
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[GALOIS,[47,3]],[2401,49,-7,7,7,-7,-7,1,1,7,-1,1,0,0,0,0,0,0,-7,-7,-1,-1,1,-1
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[(13,14)(17,18)(19,20)(21,22)(26,27)(28,29)(32,33)(35,36)(37,38)(44,45)(47,48)
(49,52)(50,51)
,(13,14)(17,18)(26,27)(28,29)(32,33)(44,45)(47,48)(49,50)(51,52),
(39,40,41,42,43)]);
ARC("S4(7)","isSimple",true);
ARC("S4(7)","extInfo",["2","2"]);
ALF("S4(7)","S4(7).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,16,16,17,18,
19,20,21,22,23,24,24,25,25,26,27,28,28,29,30,31,32,33,34,35,36,37,38,39,
39,40,41,41,42,42,43,43],[
"fusion map is unique up to table automorphisms"
]);
ALN("S4(7)",["O5(7)"]);

MOT("S4(8)",
[
"origin: computed using Dixon's algorithm and character theoretic methods,\n",
"Thomas Breuer, Jul. 10th, 2003"
],
[1056706560,258048,258048,4096,4536,4536,128,128,65,72,72,3528,3528,3528,3528,
3528,3528,49,49,49,4536,4536,4536,4536,4536,4536,81,81,81,81,81,81,65,65,65,56
,56,56,56,56,56,72,72,72,72,72,72,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63
,63,63,63,63,63,63,63,63,63,65,65,65,65,65,65,65,65,65,65,65,65],
[,[1,1,1,1,5,6,4,4,9,5,6,13,14,12,16,17,15,19,20,18,22,23,21,25,26,24,28,29,27
,31,32,30,34,35,33,14,12,13,15,16,17,21,22,23,25,26,24,49,50,48,52,53,51,55,56
,54,58,62,60,61,59,57,64,65,63,67,71,69,70,68,66,76,77,78,79,80,81,82,83,72,73
,74,75],[1,2,3,4,1,1,7,8,9,2,3,14,12,13,17,15,16,20,18,19,5,5,5,6,6,6,5,5,5,6,
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,50,50,48,49,48,51,52,53,52,53,53,51,52,51,73,74,75,76,77,78,79,80,81,82,83,72
],,[1,2,3,4,5,6,7,8,1,10,11,13,14,12,16,17,15,19,20,18,23,21,22,26,24,25,29,27
,28,32,30,31,33,34,35,37,38,36,40,41,39,44,42,43,47,45,46,49,50,48,52,53,51,57
,58,62,59,60,54,55,56,61,66,67,71,68,69,63,64,65,70,33,34,35,33,34,35,33,34,35
,33,34,35],,[1,2,3,4,5,6,7,8,9,10,11,1,1,1,1,1,1,1,1,1,22,23,21,25,26,24,28,29
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,22,23,21,22,24,25,26,26,24,25,26,24,25,74,75,76,77,78,79,80,81,82,83,72,73],,
,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,23,21,22,26,24,25,29,
27,28,32,30,31,1,1,1,36,37,38,39,40,41,44,42,43,47,45,46,48,49,50,51,52,53,60,
61,59,55,56,58,62,57,54,69,70,68,64,65,67,71,66,63,9,9,9,9,9,9,9,9,9,9,9,9]],
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1,1,1,1,1,1],[196,-28,-28,4,7,7,4,-4,1,-1,-1,0,0,0,0,0,0,0,0,0,7,7,7,7,7,7,-2,
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-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],[324,36,36,4,0,0,4,
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],[455,7,-57,7,-7,8,-1,-1,0,1,0,0,0,0,7,7,7,0,0,0,
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E(9)^2-7*E(9)^3+E(9)^4+E(9)^5-7*E(9)^6+E(9)^7,-E(9)^2-7*E(9)^3-7*E(9)^6-E(9)^7
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E(9)^2-E(9)^3+E(9)^4+E(9)^5-E(9)^6+E(9)^7,0,0,0,0,0,0,-1,-1,-1,-E(9)^4-E(9)^5,
E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^2-E(9)^7,
E(9)^2+E(9)^3+E(9)^4+E(9)^5+E(9)^6+E(9)^7,-E(9)^2+E(9)^3+E(9)^6-E(9)^7,
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E(9)^2+E(9)^4+E(9)^5+E(9)^7,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[8,4]],
[GALOIS,[8,2]],[455,-57,7,7,8,-7,-1,-1,0,0,1,7,7,7,0,0,0,0,0,0,
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E(9)^2+E(9)^3+E(9)^4+E(9)^5+E(9)^6+E(9)^7,-E(9)^2+E(9)^3+E(9)^6-E(9)^7,
-E(9)^4-E(9)^5,E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^2-E(9)^7,1,1,1,0,0,0,
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[GALOIS,[11,4]],
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[GALOIS,[17,3]],
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[GALOIS,[20,4]],
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56,65,55,64)(57,66,62,71,58,67)(59,68,61,70,60,69)]);
ALF("S4(8)","S4(8).3",[1,2,3,4,6,5,8,7,9,11,10,12,12,12,13,13,13,14,14,14,
15,15,15,16,16,16,18,18,18,17,17,17,19,19,19,20,20,20,21,21,21,22,22,22,
23,23,23,24,24,24,25,25,25,26,26,26,27,27,28,28,28,27,29,29,29,30,30,31,
31,31,30,32,33,34,35,32,33,34,35,32,33,34,35],[
"fusion map is unique up to table automorphisms"
]);
ALN("S4(8)",["O5(8)"]);
ARC("S4(8)","isSimple",true);
ARC("S4(8)","extInfo",["","6"]);

MOT("S4(8).3",
[
"computed using Magma V2.28-15    Thu Jan 16 2025 09:46:52 on schedir\n",
"[Seed = 3859373309]\n",
"Total time: 0.890 seconds, Total memory usage: 32.09MB"
],
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[(32,33,34,35),(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)
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ALF("S4(8).3","S12(2)",[1,5,7,10,13,14,49,50,52,87,90,102,103,103,140,143,
143,142,253,257,258,280,288,307,309,445,445,445,446,447,448,449,450,451,
452,16,16,95,95,100,100,101,101,143,143,144,144,251,251,252,252,268,268,
288,288,287,287],[
"fusion map is unique up to table automorphisms"
]);
ALN("S4(8).3",["O5(8).3","S12(2)M14"]);

MOT("S4(7).2",
[
"origin: Dixon's Algorithm,\n",
"constructions: Aut(S4(7))"
],
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[
(17,18)(19,20)(30,31)(32,33)(42,43)(51,52)(53,54)(55,56)(62,63)(64,65)
(67,68,70,69)(76,77)
,(67,70)(68,69),(34,35,36,37,38)(71,74,72,75,73)]);
ALN("S4(7).2",["O5(7).2"]);

MOT("S4(9)",
[
"origin: computed using Dixon's algorithm and character theoretic methods,\n",
"Thomas Breuer, Aug. 23rd, 2004"
],
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E(41)+E(41)^9+E(41)^32+E(41)^40,E(41)^6+E(41)^13+E(41)^28+E(41)^35,
E(41)^4+E(41)^5+E(41)^36+E(41)^37,E(41)^11+E(41)^17+E(41)^24+E(41)^30,
E(41)^16+E(41)^20+E(41)^21+E(41)^25,E(41)^3+E(41)^14+E(41)^27+E(41)^38,
E(41)^2+E(41)^18+E(41)^23+E(41)^39,E(41)^12+E(41)^15+E(41)^26+E(41)^29,
E(41)^8+E(41)^10+E(41)^31+E(41)^33,E(41)^7+E(41)^19+E(41)^22+E(41)^34],
[GALOIS,[47,7]],
[GALOIS,[47,8]],
[GALOIS,[47,12]],
[GALOIS,[47,2]],
[GALOIS,[47,3]],
[GALOIS,[47,16]],
[GALOIS,[47,11]],
[GALOIS,[47,4]],
[GALOIS,[47,6]],[6560,160,0,-82,-82,-10,8,-16,0,0,-10*E(5)-10*E(5)^4,
-10*E(5)^2-10*E(5)^3,0,0,0,-2,-2,-2,-2,-2,0,0,0,0,0,0,-1,-1,
-10*E(5)^2-10*E(5)^3,-10*E(5)-10*E(5)^4,0,0,0,0,0,2,2,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,2*E(5)+2*E(5)^4,
2*E(5)^2+2*E(5)^3,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[57,2]],[6560,-160,0,-82,-82,-10,8,0,0,0,-10*E(5)-10*E(5)^4,
-10*E(5)^2-10*E(5)^3,0,0,0,2,2,2,2,2,0,8*E(8)-8*E(8)^3,-8*E(8)+8*E(8)^3,0,0,0,
-1,-1,10*E(5)^2+10*E(5)^3,10*E(5)+10*E(5)^4,0,0,0,0,0,0,0,0,-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(8)+E(8)^3,
E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,
E(5)^2+E(5)^3,-E(40)^21-E(40)^29+E(40)^31+E(40)^39,
-E(40)^7+E(40)^13-E(40)^23+E(40)^37,E(40)^21+E(40)^29-E(40)^31-E(40)^39,
E(40)^7-E(40)^13+E(40)^23-E(40)^37,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[59,3]],
[GALOIS,[59,11]],
[GALOIS,[59,7]],[6560,0,16,80,80,8,-10,0,-16,0,0,0,-10*E(5)-10*E(5)^4,
-10*E(5)^2-10*E(5)^3,0,0,0,0,0,0,-2,0,0,0,0,0,-1,-1,0,0,0,0,-2*E(5)-2*E(5)^4,
-2*E(5)^2-2*E(5)^3,0,0,0,2,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,
2*E(5)^2+2*E(5)^3,2*E(5)+2*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,
0,0,0,0],
[GALOIS,[63,2]],[6560,0,-16,80,80,8,-10,0,0,0,0,0,-10*E(5)-10*E(5)^4,
-10*E(5)^2-10*E(5)^3,0,0,0,0,0,0,2,0,0,2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,0,-1,
-1,0,0,0,0,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,0,0,0,0,0,0,0,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(40)^21-E(40)^29+E(40)^31+E(40)^39,-E(40)^7+E(40)^13-E(40)^23+E(40)^37,
E(40)^21+E(40)^29-E(40)^31-E(40)^39,E(40)^7-E(40)^13+E(40)^23-E(40)^37,0,0,0,0
,0,0,0,0,0,0],
[GALOIS,[65,3]],
[GALOIS,[65,11]],
[GALOIS,[65,7]],[6561,81,9,0,0,0,0,9,9,1,-9,-9,-9,-9,1,0,0,0,0,0,0,9,9,-1,-1,
1,0,0,-9,-9,1,1,-1,-1,1,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,-1,-1,-1
,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1],[7380,180,-20,9,9,0,18,-8,0,0,-10,-10,0,0
,0,9,9,0,0,0,-2,10,10,0,0,-2,0,0,-10,-10,0,0,0,0,0,1,1,0,-1,-1,-1,-1,0,0,2,2,0
,0,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[7380,100,28,90,90
,9,9,-20,-8,0,0,0,-10,-10,0,10,10,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,-2,-2,
1,0,0,0,0,-1,-1,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
7380,-100,-8,90,90,9,9,0,10,-2,0,0,-10,-10,0,-10,-10,-1,-1,-1,1,
10*E(8)-10*E(8)^3,-10*E(8)+10*E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,0,0,0,0,2,
2,0,0,0,1,0,0,0,0,-1,-1,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,
-E(8)+E(8)^3,0,0,0,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3
,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[72,3]],[8200,-200,0,100,100,10,28,0,-20,4,0,0,0,0,0,-20,-20,-2,-2,-2
,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(22,23)(24,25)(49,50)(51,52)(57,59)(58,60)(61,63)(62,64),
(11,12)(13,14)(29,30)(31,32)(33,34)(39,40)(41,42)(43,44)(45,46)(47,48)(53,54)
(55,56)(57,60)(58,59)(61,64)(62,63)
,( 4, 5)(16,17)(18,19)(27,28)(36,37)(39,41)(40,42)(49,51)(50,52)(53,55)(54,56)
,(65,66,67,68,69,70,71,72,73,74)]);
ARC("S4(9)","isSimple",true);
ARC("S4(9)","extInfo",["2","2^2"]);
ALF("S4(9)","S4(9).2_1",[1,2,3,4,5,6,7,8,9,10,11,11,12,12,13,14,15,16,17,
18,19,20,20,21,21,22,23,24,25,25,26,26,27,27,28,29,30,31,32,32,33,33,34,
34,35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,46,47,
48,49,45,46,47,48,49],[
"fusion map is unique up to table automorphisms"
]);
ALF("S4(9)","S4(9).2_2",[1,2,3,4,4,5,6,7,8,9,10,11,12,13,14,15,15,16,16,
17,18,19,20,21,22,23,24,24,25,26,27,28,29,30,31,32,32,33,34,35,34,35,36,
37,38,39,40,41,42,43,42,43,44,45,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63],[
"fusion map is unique up to table automorphisms"
]);
ALF("S4(9)","S4(9).2_3",[1,2,3,4,4,5,6,7,8,9,10,10,11,11,12,13,13,14,14,
15,16,17,17,18,18,19,20,20,21,21,22,22,23,23,24,25,25,26,27,28,28,27,29,
29,30,30,31,31,32,33,33,32,34,35,35,34,36,36,37,37,38,38,39,39,40,41,42,
43,44,40,41,42,43,44],[
"fusion map is unique up to table automorphisms"
]);
ALN("S4(9)",["O5(9)"]);

MOT("S4(9).2_1",
[
--> --------------------

--> maximum size reached

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

Quelle ctosymp2.tbl Sprache: unbekannt

[ Dauer der Verarbeitung: 0.20 Sekunden (vorverarbeitet) ]