File: ctomaxi7.tbl

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#############################################################################
##
#W  ctomaxi7.tbl                GAP table library               Thomas Breuer
##
#H  @(#)$Id: ctomaxi7.tbl,v 4.20 2004/03/26 09:47:58 gap Exp $
##
#Y  Copyright (C)  1997,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
##
##  This file contains ordinary character tables of subgroups
##  (which are neither ATLAS tables nor tables of Ostermann) of the
##  Monster and the Babymonster.
##
Revision.ctomaxi7_tbl :=
    "@(#)$Id: ctomaxi7.tbl,v 4.20 2004/03/26 09:47:58 gap Exp $";

SET_TABLEFILENAME("ctomaxi7");
ALN:= Ignore;

MOT("3^5.U4(2)",
[
"nonsplit extension of 3^5 with U4(2),\n",
"central quotient of the derived subgroup of the 9A centralizer\n",
"in the Monster,\n",
"constructed by Simon Norton, July 1997"
],
[6298560,87480,78732,69984,1728,864,2592,432,324,216,5832,729,5832,729,324,
162,162,243,243,243,144,144,144,24,12,15,15,15,72,72,36,36,18,36,18,27,27,27,
27,27,27,36,36,36,36,36,36],
[,[1,2,3,4,1,4,1,4,3,2,13,14,11,12,15,16,17,18,19,20,5,6,6,7,10,26,27,28,13,
11,15,15,17,15,16,39,40,41,36,37,38,30,30,30,29,29,29],[1,1,1,1,5,5,7,7,7,7,1,
1,1,1,1,3,1,3,3,3,21,21,21,24,24,26,26,26,5,5,5,5,5,7,9,12,12,12,14,14,14,21,
21,21,21,21,21],,[1,2,3,4,5,6,7,8,9,10,13,14,11,12,15,16,17,18,19,20,21,23,22,
24,25,1,2,2,30,29,32,31,33,34,35,39,40,41,36,37,38,45,46,47,42,43,44]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1],[5,5,5,5,-3,-3,1,1,1,1,E(3)-2*E(3)^2,E(3)-2*E(3)^2,
-2*E(3)+E(3)^2,-2*E(3)+E(3)^2,-1,-1,2,2,2,2,1,1,1,-1,-1,0,0,0,E(3)+2*E(3)^2,
2*E(3)+E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,0,1,1,-E(3),-E(3),-E(3),-E(3)^2,
-E(3)^2,-E(3)^2,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2],
[GALOIS,[2,2]],[6,6,6,6,-2,-2,2,2,2,2,-3,-3,-3,-3,3,3,0,0,0,0,2,2,2,0,0,1,1,1,
1,1,1,1,-2,-1,-1,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1],[10,10,10,10,2,2,-2,-2,-2,-2,
5*E(3)+2*E(3)^2,5*E(3)+2*E(3)^2,2*E(3)+5*E(3)^2,2*E(3)+5*E(3)^2,1,1,1,1,1,1,2,
2,2,0,0,0,0,0,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-1,-1,-1,1,1,E(3)^2,E(3)^2,E(3)^2,
E(3),E(3),E(3),-E(3),-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3)^2],
[GALOIS,[5,2]],[15,15,15,15,-1,-1,-1,-1,-1,-1,6,6,6,6,3,3,0,0,0,0,3,3,3,-1,-1,
0,0,0,2,2,-1,-1,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[15,15,15,15,7,7,3,3,3,3,-3,
-3,-3,-3,0,0,3,3,3,3,-1,-1,-1,1,1,0,0,0,1,1,-2,-2,1,0,0,0,0,0,0,0,0,-1,-1,-1,
-1,-1,-1],[20,20,20,20,4,4,4,4,4,4,2,2,2,2,5,5,-1,-1,-1,-1,0,0,0,0,0,0,0,0,-2,
-2,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[24,24,24,24,8,8,0,0,0,0,6,6,6,6,
0,0,3,3,3,3,0,0,0,0,0,-1,-1,-1,2,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[30,30,
30,30,-10,-10,2,2,2,2,3,3,3,3,3,3,3,3,3,3,-2,-2,-2,0,0,0,0,0,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,1,1,1,1,1,1],[30,30,30,30,6,6,2,2,2,2,6*E(3)-3*E(3)^2,
6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,-3*E(3)+6*E(3)^2,-3,-3,0,0,0,0,2,2,2,0,0,0,0,
0,2*E(3)+E(3)^2,E(3)+2*E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,0,-1,-1,0,0,0,0,0,0,
-E(3)^2,-E(3)^2,-E(3)^2,-E(3),-E(3),-E(3)],
[GALOIS,[12,2]],[40,40,40,40,-8,-8,0,0,0,0,2*E(3)+8*E(3)^2,2*E(3)+8*E(3)^2,
8*E(3)+2*E(3)^2,8*E(3)+2*E(3)^2,-2,-2,1,1,1,1,0,0,0,0,0,0,0,0,-2*E(3),
-2*E(3)^2,-2*E(3),-2*E(3)^2,1,0,0,E(3)^2,E(3)^2,E(3)^2,E(3),E(3),E(3),0,0,0,0,
0,0],
[GALOIS,[14,2]],[45,45,45,45,-3,-3,-3,-3,-3,-3,-9*E(3),-9*E(3),-9*E(3)^2,
-9*E(3)^2,0,0,0,0,0,0,1,1,1,1,1,0,0,0,3*E(3),3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,
E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2],
[GALOIS,[16,2]],[60,60,60,60,-4,-4,4,4,4,4,6,6,6,6,-3,-3,-3,-3,-3,-3,0,0,0,0,
0,0,0,0,2,2,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[64,64,64,64,0,0,0,0,0,0,-8,
-8,-8,-8,4,4,-2,-2,-2,-2,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,
0,0],[81,81,81,81,9,9,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,-1,-1,1,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[216,27,-27,0,0,0,-12,0,-3,3,0,0,0,0,0,0,
0,0,0,0,0,0,0,2,-1,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[21,7]],[432,54,-54,0,0,0,24,0,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[648,81,-81,0,0,0,12,0,3,-3,0,0,
0,0,0,0,0,0,0,0,0,0,0,2,-1,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
1080,135,-135,0,0,0,-12,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,-10,-1,8,0,0,8,-4,-1,2,8,-1,8,-1,2,-1,2,5,-4,
-4,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,2,-1,-1,2,-1,-1,0,0,0,0,0,0],[80,-10,-1,8,0,
0,8,-4,-1,2,8,-1,8,-1,2,-1,2,-4,5,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,-1,2,-1,
-1,2,-1,0,0,0,0,0,0],[80,-10,-1,8,0,0,8,-4,-1,2,8,-1,8,-1,2,-1,2,-4,-4,5,0,0,
0,0,0,0,0,0,0,0,0,0,0,2,-1,-1,-1,2,-1,-1,2,0,0,0,0,0,0],[240,-30,-3,24,0,0,-8,
4,1,-2,24,-3,24,-3,6,-3,6,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,
0,0,0,0,0,0],[320,-40,-4,32,0,0,0,0,0,0,16*E(3)-8*E(3)^2,-2*E(3)+E(3)^2,
-8*E(3)+16*E(3)^2,E(3)-2*E(3)^2,-4,2,2,5,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
2*E(3)^2,-E(3)^2,-E(3)^2,2*E(3),-E(3),-E(3),0,0,0,0,0,0],[320,-40,-4,32,0,0,0,
0,0,0,16*E(3)-8*E(3)^2,-2*E(3)+E(3)^2,-8*E(3)+16*E(3)^2,E(3)-2*E(3)^2,-4,2,2,
-4,5,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(3)^2,2*E(3)^2,-E(3)^2,-E(3),2*E(3),
-E(3),0,0,0,0,0,0],[320,-40,-4,32,0,0,0,0,0,0,16*E(3)-8*E(3)^2,-2*E(3)+E(3)^2,
-8*E(3)+16*E(3)^2,E(3)-2*E(3)^2,-4,2,2,-4,-4,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(3)^2,-E(3)^2,2*E(3)^2,-E(3),-E(3),2*E(3),0,0,0,0,0,0],
[GALOIS,[30,2]],
[GALOIS,[31,2]],
[GALOIS,[32,2]],[480,-60,-6,48,0,0,-16,8,2,-4,-24,3,-24,3,6,-3,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[480,-60,-6,48,0,0,16,-8,-2,
4,-24,3,-24,3,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,
0,0],[960,-120,-12,96,0,0,0,0,0,0,24,-3,24,-3,0,0,-6,3,3,3,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[270,0,27,-27,6,-3,18,9,-9,0,0,0,0,0,0,0,
0,0,0,0,6,-3,-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],[270,0,27,
-27,6,-3,-6,-3,3,0,0,0,0,0,0,0,0,0,0,0,2,3*E(3)-E(3)^2,-E(3)+3*E(3)^2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2*E(3),2*E(3)^2,2,2*E(3)^2,2*E(3)],[270,0,27,
-27,6,-3,-6,-3,3,0,0,0,0,0,0,0,0,0,0,0,2,3*E(3)-E(3)^2,-E(3)+3*E(3)^2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3)^2,2,2*E(3),2*E(3),2,2*E(3)^2],[270,0,27,
-27,6,-3,-6,-3,3,0,0,0,0,0,0,0,0,0,0,0,2,3*E(3)-E(3)^2,-E(3)+3*E(3)^2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3),2*E(3)^2,2,2*E(3)^2,2*E(3),2],
[GALOIS,[40,2]],
[GALOIS,[41,2]],
[GALOIS,[42,2]],[810,0,81,-81,18,-9,6,3,-3,0,0,0,0,0,0,0,0,0,0,0,-6,3,3,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1080,0,108,-108,-24,12,0,0,0,0,0,
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]],
[(27,28),(19,20)(37,38)(40,41),(18,19)(36,37)(39,40),(11,13)(12,14)(22,23)(27,
28)(29,30)(31,32)(36,39)(37,40)(38,41)(42,45)(43,46)(44,47),(42,43,44)(45,46,
47),(22,23)(43,44)(46,47)]);
ARC("3^5.U4(2)","projectives",["3.3^5.U4(2)",[[27,9,0,0,3,0,7,4,-2,1,0,0,0,0,
3,-3,0,0,0,0,3,0,0,1,1,2,-1,-1,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,1,1,0,0,0,0,0,0,
0,0,0,0,0,0],[81,27,0,0,9,0,-3,0,6,3,0,0,0,0,0,0,0,0,0,0,-3,0,0,-1,-1,1,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[2,7]],[108,36,0,0,12,0,4,4,4,4,0,0,0,0,3,-3,0,0,0,0,0,0,0,0,0,-2,1,1,
0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[135,45,0,0,15,0,11,8,2,5,0,0,0,0,-3,3,0,0,0,0,3,0,0,1,1,0,0,0,
0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],
[135,45,0,0,-9,0,7,4,-2,1,0,0,0,0,6,-6,0,0,0,0,3,0,0,-1,-1,0,0,
0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0],[135,45,0,0,-9,0,7,4,-2,1,0,0,0,0,
-3,3,0,0,0,0,3,0,0,-1,-1,0,0,0,0,0,3,3,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[135,45,
0,0,-9,0,7,4,-2,1,0,0,0,0,-3,3,0,0,0,0,3,0,0,-1,-1,0,0,0,0,0,-3,-3,0,1,1,0,0,
0,0,0,0,0,0,0,0,0,0],[270,90,0,0,6,0,-14,-8,4,-2,0,0,0,0,3,-3,0,0,0,0,6,0,0,0,
0,0,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[270,90,0,0,6,0,10,4,-8,-2,0,0,0,0,3,-3,0,0,0,0,-6,0,0,0,0,0,
0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[405,135,0,0,-27,0,-3,0,6,3,0,0,0,0,0,0,0,0,0,0,-3,0,0,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,180,0,0,12,0,-4,-4,-4,-4,0,0,
0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0],
[216,-9,0,0,0,0,20,-4,2,-1,0,0,0,0,6,3,0,0,0,0,0,0,0,2,-1,1,1,
1,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[216,-9,0,0,0,0,4,4,4,-5,0,0,0,0,6,
3,0,0,0,0,0,0,0,-2,1,1,1,1,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,0,0],[864,-36,0,
0,0,0,16,-8,-2,4,0,0,0,0,6,3,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,-2,1,0,0,0,
0,0,0,0,0,0,0,0,0],[864,-36,0,0,0,0,-16,8,2,-4,0,0,0,0,6,3,0,0,0,0,0,0,0,0,0,
-1,-1,-1,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[1080,-45,0,0,0,0,4,4,4,-5,0,
0,0,0,-6,-3,0,0,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,0,0],[
1080,-45,0,0,0,0,20,-4,2,-1,0,0,0,0,-6,-3,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,
2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[1296,-54,0,0,0,0,-24,0,-6,6,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("3^5.U4(2)","U4(2)",[1,1,1,1,2,2,3,3,3,3,4,4,5,5,6,6,7,7,7,7,8,8,8,9,
9,10,10,10,11,12,13,14,15,16,16,17,17,17,18,18,18,19,19,19,20,20,20]);

MOT("3.3^5.U4(2)",
[
"derived subgroup of the 9A centralizer in the Monster,\n",
"constructed by Simon Norton, July 1997"
],
[18895680,18895680,18895680,262440,262440,262440,78732,69984,5184,5184,5184,
864,7776,7776,7776,1296,1296,1296,972,972,972,648,648,648,5832,729,5832,729,
972,972,972,486,486,486,162,243,243,243,432,432,432,144,144,72,72,72,36,36,36,
45,45,45,45,45,45,45,45,45,72,72,108,108,108,108,108,108,18,108,108,108,54,54,
54,27,27,27,27,27,27,36,36,36,36,36,36],
[,[1,3,2,4,6,5,7,8,1,3,2,8,1,3,2,8,8,8,7,7,7,4,6,5,27,28,25,26,29,31,30,32,34,
33,35,36,37,38,9,11,10,12,12,13,15,14,22,24,23,50,52,51,53,55,54,56,58,57,27,
25,29,31,30,29,31,30,35,29,31,30,32,34,33,77,78,79,74,75,76,60,60,60,59,59,
59],[1,1,1,1,1,1,1,1,9,9,9,9,13,13,13,13,13,13,13,13,13,13,13,13,3,3,2,2,1,1,
1,7,7,7,1,7,7,7,39,39,39,39,39,44,44,44,44,44,44,50,50,50,50,50,50,50,50,50,
11,10,9,9,9,9,9,9,9,13,13,13,19,19,19,26,26,26,28,28,28,41,41,41,40,40,40],,[
1,3,2,4,6,5,7,8,9,11,10,12,13,15,14,16,18,17,19,21,20,22,24,23,27,28,25,26,29,
31,30,32,34,33,35,36,37,38,39,41,40,43,42,44,46,45,47,49,48,1,3,2,4,6,5,4,6,5,
60,59,64,66,65,61,63,62,67,68,70,69,71,73,72,77,78,79,74,75,76,83,84,85,80,81,
82]],
0,
[(53,56)(54,57)(55,58),(37,38)(75,76)(78,79),(36,37)(74,75)(77,78),(2,3)(5,6)
(10,11)(14,15)(17,18)(20,21)(23,24)(25,27)(26,28)(30,31)(33,34)(40,41)(42,43)
(45,46)(48,49)(51,52)(53,56)(54,58)(55,57)(59,60)(61,64)(62,66)(63,65)(69,70)
(72,73)(74,77)(75,78)(76,79)(80,83)(81,84)(82,85),(80,81,82)(83,84,85),(42,43)
(81,82)(84,85)],
["ConstructProj",[["3^5.U4(2)",[]],,["3.3^5.U4(2)",[-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3.3^5.U4(2)","3^5.U4(2)",[1,1,1,2,2,2,3,4,5,5,5,6,7,7,7,8,8,8,9,9,9,
10,10,10,11,12,13,14,15,15,15,16,16,16,17,18,19,20,21,21,21,22,23,24,24,
24,25,25,25,26,26,26,27,27,27,28,28,28,29,30,31,31,31,32,32,32,33,34,34,
34,35,35,35,36,37,38,39,40,41,42,43,44,45,46,47]);
ALF("3.3^5.U4(2)","U4(2)",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,
3,4,4,5,5,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,
10,10,11,12,13,13,13,14,14,14,15,16,16,16,16,16,16,17,17,17,18,18,18,19,
19,19,20,20,20]);

MOT("C9Y3.3^5.U4(2)",
[
"9A centralizer in the sporadic simple Monster group M,\n",
"central product of a cyclic group of order 9 with 3.3^5.U4(2),\n",
"constructed by Simon Norton, July 1997"
],
0,
[,[1,3,2,4,6,5,7,8,1,3,2,8,1,3,2,8,8,8,7,7,7,4,6,5,27,28,25,26,29,31,30,32,34,
33,35,36,37,38,9,11,10,12,12,13,15,14,22,24,23,50,52,51,53,55,54,56,58,57,27,
25,29,31,30,29,31,30,35,29,31,30,32,34,33,77,78,79,74,75,76,60,60,60,59,59,59,
171,173,172,174,176,175,177,178,171,173,172,178,171,173,172,178,178,178,177,
177,177,174,176,175,197,198,195,196,199,201,200,202,204,203,205,206,207,208,
179,181,180,182,182,183,185,184,192,194,193,220,222,221,223,225,224,226,228,
227,197,195,199,201,200,199,201,200,205,199,201,200,202,204,203,247,248,249,
244,245,246,230,230,230,229,229,229,88,87,86,91,90,89,92,93,88,87,86,93,88,87,
86,93,93,93,92,92,92,91,90,89,112,113,110,111,116,115,114,119,118,117,120,121,
122,123,96,95,94,97,97,100,99,98,109,108,107,137,136,135,140,139,138,143,142,
141,112,110,116,115,114,116,115,114,120,116,115,114,119,118,117,162,163,164,
159,160,161,145,145,145,144,144,144],[1,1,1,1,1,1,1,1,9,9,9,9,13,13,13,13,13,
13,13,13,13,13,13,13,3,3,2,2,1,1,1,7,7,7,1,7,7,7,39,39,39,39,39,44,44,44,44,
44,44,50,50,50,50,50,50,50,50,50,11,10,9,9,9,9,9,9,9,13,13,13,19,19,19,26,26,
26,28,28,28,41,41,41,40,40,40,3,3,3,3,3,3,3,3,11,11,11,11,15,15,15,15,15,15,
15,15,15,15,15,15,2,2,1,1,3,3,3,7,7,7,3,7,7,7,41,41,41,41,41,46,46,46,46,46,
46,52,52,52,52,52,52,52,52,52,10,9,11,11,11,11,11,11,11,15,15,15,21,21,21,26,
26,26,28,28,28,40,40,40,39,39,39,2,2,2,2,2,2,2,2,10,10,10,10,14,14,14,14,14,
14,14,14,14,14,14,14,1,1,3,3,2,2,2,7,7,7,2,7,7,7,40,40,40,40,40,45,45,45,45,
45,45,51,51,51,51,51,51,51,51,51,9,11,10,10,10,10,10,10,10,14,14,14,20,20,20,
26,26,26,28,28,28,39,39,39,41,41,41],,[1,3,2,4,6,5,7,8,9,11,10,12,13,15,14,16,
18,17,19,21,20,22,24,23,27,28,25,26,29,31,30,32,34,33,35,36,37,38,39,41,40,43,
42,44,46,45,47,49,48,1,3,2,4,6,5,4,6,5,60,59,64,66,65,61,63,62,67,68,70,69,71,
73,72,77,78,79,74,75,76,83,84,85,80,81,82,173,172,171,176,175,174,177,178,181,
180,179,182,185,184,183,188,187,186,191,190,189,194,193,192,197,198,195,196,
201,200,199,204,203,202,205,206,207,208,211,210,209,213,212,216,215,214,219,
218,217,173,172,171,176,175,174,176,175,174,230,229,236,235,234,233,232,231,
237,240,239,238,243,242,241,247,248,249,244,245,246,253,254,255,250,251,252,
86,88,87,89,91,90,92,93,94,96,95,97,98,100,99,101,103,102,104,106,105,107,
109,108,112,113,110,111,114,116,115,117,119,118,120,121,122,123,124,126,125,
128,127,129,131,130,132,134,133,86,88,87,89,91,90,89,91,90,145,144,149,151,
150,146,148,147,152,153,155,154,156,158,157,162,163,164,159,160,161,168,169,
170,165,166,167]],
0,
[( 37, 38)( 75, 76)( 78, 79)(122,123)(160,161)(163,164)(207,208)(245,246)(248,
249),( 36, 38, 37)( 74, 76, 75)( 77, 79, 78)(121,123,122)(159,161,160)(162,
164,163)(206,208,207)(244,246,245)(247,249,248),( 42, 43)( 81, 82)( 84, 85)
(127,128)(166,167)(169,170)(212,213)(251,252)(254,255),( 80, 81, 82)( 83, 84,
 85)(165,166,167)(168,169,170)(250,251,252)(253,254,255),( 86, 87, 88)( 89,
 90, 91)( 94, 95, 96)( 98, 99,100)(101,102,103)(104,105,106)(107,108,109)(114,
115,116)(117,118,119)(124,125,126)(129,130,131)(132,133,134)(135,136,137)(138,
139,140)(141,142,143)(146,147,148)(149,150,151)(153,154,155)(156,157,158)(171,
173,172)(174,176,175)(179,181,180)(183,185,184)(186,188,187)(189,191,190)(192,
194,193)(199,201,200)(202,204,203)(209,211,210)(214,216,215)(217,219,218)(220,
222,221)(223,225,224)(226,228,227)(231,233,232)(234,236,235)(238,240,239)(241,
243,242),( 53, 56)( 54, 57)( 55, 58)(138,141)(139,142)(140,143)(223,226)(224,
227)(225,228),(  2,  3)(  5,  6)( 10, 11)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 25, 27)( 26, 28)( 30, 31)( 33, 34)( 40, 41)( 45, 46)( 48, 49)( 51, 52)( 54,
 55)( 57, 58)( 59, 60)( 61, 64)( 62, 66)( 63, 65)( 69, 70)( 72, 73)( 74, 77)
( 75, 78)( 76, 79)( 80, 83)( 81, 85)( 82, 84)( 86,171, 88,172, 87,173)( 89,
174, 91,175, 90,176)( 92,177)( 93,178)( 94,179, 96,180, 95,181)( 97,182)( 98,
183,100,184, 99,185)(101,186,103,187,102,188)(104,189,106,190,105,191)(107,
192,109,193,108,194)(110,197)(111,198)(112,195)(113,196)(114,199,116,200,115,
201)(117,202,119,203,118,204)(120,205)(121,206)(122,207)(123,208)(124,209,126,
210,125,211)(127,212)(128,213)(129,214,131,215,130,216)(132,217,134,218,133,
219)(135,220,137,221,136,222)(138,223,140,224,139,225)(141,226,143,227,142,
228)(144,230)(145,229)(146,234,148,235,147,236)(149,231,151,232,150,233)(152,
237)(153,238,155,239,154,240)(156,241,158,242,157,243)(159,247)(160,248)(161,
249)(162,244)(163,245)(164,246)(165,253)(166,255)(167,254)(168,250)(169,252)
(170,251)],
function( tbl )
local e, e8, e2, e7, chi, i;
ConstructDirectProduct( tbl, [["Cyclic",3],["3.3^5.U4(2)"]] );
Unbind( tbl.OrdersClassRepresentatives );
Unbind( tbl.ComputedClassFusions[ Length( tbl.ComputedClassFusions ) ] );
Unbind( tbl.ComputedClassFusions[ Length( tbl.ComputedClassFusions ) ] );
for i in [ 1 .. Length( tbl.Irr ) ] do
  tbl.Irr[i]:= ShallowCopy( tbl.Irr[i] );
od;
e:= E(9);
e8:= E(9)^8;
e2:= E(9)^2;
e7:= E(9)^7;
for chi in tbl.Irr do
  if chi[2] = chi[1] * E(3) then
    for i in [ 86 .. 170 ] do
      chi[i]:= chi[i] * e8;
    od;
    for i in [ 171 .. 255 ] do
      chi[i]:= chi[i] * e7;
    od;
  elif chi[2] = chi[1] * E(3)^2 then
    for i in [ 86 .. 170 ] do
      chi[i]:= chi[i] * e;
    od;
    for i in [ 171 .. 255 ] do
      chi[i]:= chi[i] * e2;
    od;
  fi;
od;
end);
ALF("C9Y3.3^5.U4(2)","U4(2)",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,
3,3,4,4,5,5,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,
10,10,10,11,12,13,13,13,14,14,14,15,16,16,16,16,16,16,17,17,17,18,18,18,
19,19,19,20,20,20,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,5,5,
6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,
12,13,13,13,14,14,14,15,16,16,16,16,16,16,17,17,17,18,18,18,19,19,19,20,
20,20,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,5,5,6,6,6,6,6,6,
7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,12,13,13,13,
14,14,14,15,16,16,16,16,16,16,17,17,17,18,18,18,19,19,19,20,20,20]);
ALN("C9Y3.3^5.U4(2)",["MC9A"]);

MOT("2^24.Co1",
[
"central factor group of the maximal subgroup 2^(1+24).Co1 of the Monster,\n",
"constructed by Simon Norton, Dec. 2000"
],
[69755919563168164085760000,709767191322427392000,8412055600858398720,
8317584273309696000,5844591496396800,48704929136640,43293270343680,
2705829396480,190253629440,180388626432,8244323942400,2013265920,1594506608640
,1594506608640,6039797760,2013265920,1610612736,778567680,1345036492800,
240789749760,637009920,141557760,119439360,806215680,29859840,22394880,
139345920,1161216,1032192,95126814720,792723456,704643072,301989888,100663296,
12582912,8388608,1572864,754974720,125829120,75497472,50331648,23592960,
6291456,2097152,1572864,75497472,12582912,8388608,1572864,1572864,524288,
3096576,49152,983040,983040,81920,65536,65536,49152,3024000,9216000,153600,
122880,76800,240000,48000,24000,9953280,483840,9953280,368640,276480,9953280,
368640,276480,5308416,884736,589824,147456,55296,49152,248832,82944,20736,
221184,221184,18432,12288,6912,23040,1536,9216,9216,1536,1152,17640,75264,
10752,10752,3584,2688,1474560,98304,98304,98304,16384,12288,98304,32768,8192,
32768,32768,16384,8192,4096,49152,49152,16384,16384,12288,12288,4096,4096,2048
,12288,4096,1024,1944,1944,648,7776,1296,864,9600,1200,19200,1280,9600,1920,
960,9600,1920,960,2560,2560,1280,640,320,1056,352,352,352,176,138240,9216,4608
,10368,3456,27648,4608,3072,864,9216,3072,768,4608,4608,1536,1536,576,4608,
4608,2304,768,768,4608,1536,768,768,1152,384,288,96,192,192,96,156,168,896,896
,896,896,448,448,448,448,224,5400,900,180,1440,480,480,480,240,120,120,120,120
,256,256,128,256,256,128,216,216,72,216,72,480,160,160,80,80,80,80,80,252,63,
84,84,84,84,88,88,88,88,92,92,92,92,92,92,92,92,576,192,576,192,96,192,192,96,
96,96,96,96,52,112,112,112,112,28,120,60,60,120,120,120,120,120,120,120,120,33
,35,36,39,39,40,84,60],
[,[1,1,1,1,1,1,1,3,2,3,1,3,3,1,2,3,3,4,19,20,20,20,20,24,24,24,27,27,27,5,6,7,
5,7,6,7,10,7,5,5,7,6,10,10,8,5,7,7,8,10,10,11,12,13,14,15,17,17,16,60,61,61,61
,61,65,65,65,19,19,20,22,21,24,24,24,20,20,20,22,21,22,24,24,25,22,20,21,22,23
,27,29,29,27,29,28,96,97,97,97,97,97,30,32,30,32,32,31,33,34,35,33,34,34,35,36
,41,38,38,41,40,39,44,44,43,46,48,51,128,129,129,131,131,131,60,60,61,63,61,63
,62,65,65,65,63,61,63,62,64,149,149,149,149,149,68,68,68,82,83,76,77,78,69,76,
78,81,74,73,74,73,75,78,76,77,79,81,76,78,79,81,82,83,90,91,92,93,94,187,96,97
,97,97,97,98,99,98,99,100,198,199,200,201,201,201,201,201,206,206,206,206,108,
109,110,111,112,114,128,129,129,131,133,134,144,145,147,142,141,143,143,229,
230,231,231,231,231,150,149,152,151,239,239,239,239,243,243,243,243,154,155,
159,161,156,159,161,160,168,166,167,169,187,189,190,191,192,188,198,199,200,
201,202,203,204,206,206,206,206,276,277,216,279,280,221,229,265],[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,1,1,2,3,4,1,2,4,1,4,3,30,31,32,33,34,35,36,37
,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63
,64,65,66,67,5,11,5,8,9,5,7,6,5,6,7,8,9,10,5,6,9,13,14,15,17,18,11,12,13,14,16
,18,96,97,99,98,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,24,24,26,24,26,25,134,135,
136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,30,33,
46,30,31,30,31,32,52,33,34,37,38,40,41,39,42,38,40,42,45,43,46,47,49,50,33,35,
52,53,54,55,59,187,188,189,190,192,191,194,193,196,195,197,60,61,60,61,62,63,
63,64,65,67,66,66,210,211,212,213,214,215,82,82,83,82,84,221,222,223,224,225,
226,227,228,96,96,97,101,99,98,235,236,237,238,239,240,241,242,243,244,245,246
,102,108,102,103,125,104,105,107,116,117,120,121,259,260,261,263,262,264,134,
136,135,138,140,139,139,141,143,142,142,149,277,157,187,187,281,188,221],,[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,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,1,1,2,3,4,1,2,4,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85
,86,87,88,89,90,91,92,93,94,95,96,97,99,98,100,101,102,103,104,105,106,107,108
,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,
128,129,130,131,132,133,5,11,11,12,5,8,9,5,7,6,13,14,16,15,18,149,150,151,152,
153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,
172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,
192,191,194,193,196,195,197,19,19,27,20,21,22,22,23,24,26,25,25,210,211,212,
213,214,215,216,217,218,219,220,30,54,55,56,38,39,42,42,229,230,231,232,234,
233,235,236,237,238,243,244,245,246,239,240,241,242,247,248,249,250,251,252,
253,254,255,256,257,258,259,260,261,263,262,264,68,69,90,70,72,71,71,73,75,74,
74,276,96,278,279,280,102,282,154],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43
,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69
,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95
,1,1,3,3,2,4,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,
118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,
137,138,139,140,141,142,143,144,145,146,147,148,149,150,152,151,153,154,155,
156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,
175,176,177,178,179,180,181,182,183,184,185,186,187,11,5,6,7,7,8,8,10,10,9,198
,199,200,201,202,204,203,205,206,207,209,208,210,211,212,213,214,215,216,217,
218,219,220,221,222,223,224,225,226,227,228,19,20,27,28,29,29,235,236,238,237,
243,244,245,246,239,240,241,242,247,248,249,250,251,252,253,254,255,256,257,
258,259,30,31,32,32,52,265,266,267,268,269,271,270,272,273,275,274,276,60,278,
280,279,281,69,283],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
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,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,1,3,4,4,2,154,155,156,157,158,159,
160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,
179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,
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ALF("2^24.Co1","Co1",[1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,4,4,5,6,6,6,6,7,7,7,
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MOT("2^1+24.Co1",
[
"maximal subgroup and 2B centralizer in the Monster,\n",
"constructed by Simon Norton, Dec. 2000"
],
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["ConstructProj",[["2^24.Co1",[]],["2^1+24.Co1",[]]]]);
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E(11)-E(11)^2+E(11)^3+E(11)^4+E(11)^5-E(11)^6-E(11)^7-E(11)^8+E(11)^9-E(11)^10
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E(11)-E(11)^2+E(11)^3+E(11)^4+E(11)^5-E(11)^6-E(11)^7-E(11)^8+E(11)^9-E(11)^10
,
E(11)-E(11)^2+E(11)^3+E(11)^4+E(11)^5-E(11)^6-E(11)^7-E(11)^8+E(11)^9-E(11)^10
,
E(11)-E(11)^2+E(11)^3+E(11)^4+E(11)^5-E(11)^6-E(11)^7-E(11)^8+E(11)^9-E(11)^10
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E(23)+E(23)^2+E(23)^3+E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13
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E(23)+E(23)^2+E(23)^3+E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13
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E(23)+E(23)^2+E(23)^3+E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13
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,
E(23)+E(23)^2+E(23)^3+E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13
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E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20
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E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20
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E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20
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E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20
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,
E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20
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59,60,60,61,61,62,63,64,65,65,66,67,68,68,69,70,70,71,72,73,73,74,75,76,
76,77,78,79,80,81,82,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,96,97,
97,98,99,100,101,102,103,104,105,106,107,108,108,109,110,111,112,113,114,
115,116,116,117,118,119,120,121,122,123,124,125,126,127,128,128,129,129,
130,131,131,132,133,134,134,135,136,137,138,138,139,140,141,141,142,143,
144,145,146,147,148,149,149,150,151,152,153,154,154,155,156,157,157,158,
159,159,160,161,162,163,164,165,166,166,167,168,169,170,171,171,172,173,
174,175,176,177,178,179,180,180,181,182,183,184,185,186,187,187,188,189,
189,190,191,192,193,194,195,196,197,198,198,199,199,200,200,201,201,202,
203,204,205,206,206,207,208,209,210,211,212,213,213,214,215,216,216,217,
217,218,219,219,220,221,221,222,223,224,225,225,226,227,228,229,229,230,
230,231,231,232,233,234,235,235,236,237,238,239,239,240,241,242,243,243,
244,245,246,247,248,248,249,250,251,252,253,254,255,255,256,257,258,259,
260,260,261,262,263,264,264,265,265,266,267,268,268,269,270,271,272,272,
273,274,275,276,276,277,277,278,278,279,279,280,280,281,281,282,283,283]);
ALF("2^1+24.Co1","M",[1,3,2,3,7,2,3,9,3,7,8,9,10,10,7,3,8,10,9,22,5,14,4,
15,13,15,35,17,5,16,36,6,18,38,18,7,9,21,9,9,9,25,10,24,7,9,10,8,9,24,21,
25,22,8,9,10,22,24,25,26,26,22,10,23,24,25,26,12,32,11,30,29,30,64,33,12,
31,66,16,17,40,15,13,35,37,14,16,17,42,13,15,39,15,35,37,39,16,17,43,41,
35,15,37,39,78,44,44,38,18,44,82,20,49,19,48,48,48,47,94,24,24,22,24,25,
54,21,25,25,56,25,25,24,55,26,21,25,24,22,25,23,26,56,55,54,23,26,55,28,
62,61,28,115,27,60,114,59,31,33,68,67,67,30,29,64,65,32,31,33,69,64,30,67,
65,124,34,75,75,132,133,74,36,42,43,41,43,36,80,35,39,79,39,83,39,39,81,
42,36,41,43,40,85,39,35,37,81,78,79,37,39,78,81,42,43,86,87,87,82,44,87,
46,90,96,47,48,95,48,48,94,94,95,95,93,52,98,51,101,53,102,50,100,99,100,
100,155,52,104,156,103,103,54,55,108,56,55,55,107,58,61,62,58,117,60,59,
116,66,69,124,67,123,66,69,68,125,126,73,129,71,131,72,130,176,130,130,
132,133,75,179,180,76,135,137,181,135,77,136,138,182,136,85,80,86,81,81,
84,78,81,141,80,86,85,84,83,145,94,95,148,95,95,149,150,103,104,158,159,
99,100,154,155,155,103,98,157,104,104,109,163,113,168,115,117,121,172,122,
173,125,126,175,156,157]);
ALN("2^1+24.Co1",["MC2B","MN2B"]);

MOT("2^1+24.2.Co1",
[
"double cover of the maximal subgroup 2^1+24.Co1,\n",
"constructed by Simon Norton, Dec. 2000"
],
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279023678252672656343040000,279023678252672656343040000,1419534382644854784000
,1419534382644854784000,16824111201716797440,16824111201716797440,
16635168546619392000,16635168546619392000,23378365985587200,23378365985587200,
23378365985587200,23378365985587200,97409858273280,97409858273280,
86586540687360,86586540687360,5411658792960,5411658792960,380507258880,
380507258880,360777252864,360777252864,16488647884800,16488647884800,
2013265920,3189013217280,3189013217280,1594506608640,12079595520,12079595520,
2013265920,1610612736,1557135360,1557135360,5380145971200,5380145971200,
5380145971200,5380145971200,963158999040,963158999040,963158999040,
963158999040,1274019840,1274019840,283115520,283115520,238878720,238878720,
3224862720,3224862720,3224862720,3224862720,59719680,59719680,44789760,
44789760,557383680,557383680,557383680,557383680,2322432,2322432,2064384,
2064384,380507258880,380507258880,380507258880,380507258880,1585446912,
1585446912,1409286144,1409286144,603979776,603979776,100663296,25165824,
25165824,8388608,1572864,3019898880,3019898880,3019898880,3019898880,251658240
,251658240,150994944,150994944,100663296,100663296,47185920,47185920,12582912,
12582912,4194304,4194304,3145728,3145728,150994944,150994944,12582912,8388608,
3145728,3145728,1572864,524288,6193152,6193152,49152,1966080,1966080,983040,
163840,163840,65536,65536,49152,12096000,12096000,12096000,12096000,36864000,
36864000,36864000,36864000,307200,307200,245760,245760,153600,153600,960000,
960000,960000,960000,96000,96000,48000,48000,39813120,39813120,39813120,
39813120,967680,967680,39813120,39813120,39813120,39813120,737280,737280,
552960,552960,39813120,39813120,39813120,39813120,737280,737280,552960,552960,
21233664,21233664,21233664,21233664,1769472,1769472,1179648,1179648,294912,
294912,110592,110592,98304,98304,995328,995328,995328,995328,165888,165888,
41472,41472,442368,442368,221184,36864,36864,12288,13824,13824,46080,46080,
1536,18432,18432,9216,1536,2304,2304,70560,70560,70560,70560,301056,301056,
301056,301056,21504,21504,21504,21504,7168,7168,5376,5376,2949120,2949120,
98304,196608,196608,98304,16384,24576,24576,393216,393216,393216,393216,65536,
65536,16384,16384,65536,65536,32768,16384,16384,16384,4096,196608,196608,
196608,196608,98304,98304,32768,32768,32768,32768,24576,24576,24576,24576,8192
,8192,8192,8192,4096,4096,24576,24576,4096,1024,7776,7776,7776,7776,7776,7776,
7776,7776,1296,1296,31104,31104,31104,31104,2592,2592,1728,1728,38400,38400,
38400,38400,2400,2400,38400,38400,1280,38400,38400,38400,38400,3840,3840,1920,
1920,38400,38400,38400,38400,3840,3840,1920,1920,5120,5120,2560,1280,1280,1280
,640,640,4224,4224,4224,4224,704,704,704,704,704,704,352,352,552960,552960,
552960,552960,18432,18432,9216,9216,41472,41472,41472,41472,6912,6912,110592,
110592,110592,110592,9216,9216,6144,6144,1728,1728,18432,18432,3072,768,18432,
18432,18432,18432,9216,9216,3072,3072,3072,3072,1152,1152,18432,18432,18432,
18432,9216,9216,4608,4608,1536,1536,1536,1536,9216,9216,1536,1536,1536,768,
4608,4608,4608,4608,768,768,576,576,96,384,384,192,96,624,624,624,624,336,336,
3584,3584,3584,3584,1792,1792,1792,1792,1792,1792,896,896,896,896,896,896,896,
896,448,448,21600,21600,21600,21600,3600,3600,3600,3600,720,720,720,720,5760,
5760,5760,5760,960,960,960,960,960,960,480,480,480,480,480,480,240,240,240,240
,240,240,512,512,256,256,256,1024,1024,1024,1024,512,512,256,256,864,864,864,
864,864,864,864,864,144,144,864,864,864,864,144,144,1920,1920,1920,1920,320,
320,160,160,160,320,320,320,320,160,160,160,160,160,160,1008,1008,1008,1008,
252,252,252,252,336,336,336,336,168,168,168,168,168,168,352,352,352,352,176,
176,176,176,176,176,368,368,368,368,184,184,184,184,184,184,368,368,368,368,
184,184,184,184,184,184,1152,1152,768,768,768,768,1152,1152,192,192,192,384,
384,192,192,192,384,384,384,384,192,192,192,192,192,192,104,104,448,448,448,
448,224,224,224,224,224,224,112,112,112,112,480,480,480,480,120,120,120,120,
480,480,480,480,240,240,240,240,240,240,480,480,480,480,240,240,240,240,240,
240,132,132,132,132,140,140,140,140,144,144,144,144,156,156,156,156,156,156,
156,156,160,160,160,160,168,168,240,240,240,240],
[,[1,1,1,1,1,1,1,1,3,3,1,1,1,1,3,3,1,1,7,7,5,5,7,7,4,4,8,7,7,1,5,5,7,7,9,9,37,
37,37,37,41,41,41,41,41,41,41,41,43,43,53,53,53,53,53,53,51,51,59,59,59,59,61,
61,59,59,14,14,14,14,16,16,18,18,14,14,18,16,16,18,24,17,17,17,17,13,13,11,11,
17,17,15,15,23,23,23,23,19,19,11,11,17,17,19,19,23,23,25,25,27,28,28,30,31,31,
34,34,33,119,119,119,119,123,123,123,123,123,123,123,123,125,125,135,135,135,
135,135,135,133,133,37,37,37,37,40,40,41,41,41,41,47,47,45,45,53,53,53,53,53,
53,51,51,41,41,41,41,43,43,41,41,47,47,45,45,47,47,53,53,53,53,51,51,55,55,47,
47,41,45,45,47,49,49,62,62,66,65,65,59,65,63,63,202,202,202,202,206,206,206,
206,206,206,206,206,206,206,208,208,70,70,74,67,67,73,73,71,71,75,75,75,75,77,
77,78,78,75,75,77,77,78,78,80,90,90,90,90,84,84,82,82,90,90,88,88,86,86,96,96,
96,96,94,94,100,100,103,107,266,266,266,266,272,272,272,272,270,270,276,276,
276,276,278,278,276,276,119,119,119,119,122,122,126,126,130,123,123,123,123,
129,129,127,127,135,135,135,135,135,135,133,133,129,129,123,129,127,127,131,
131,317,317,317,317,317,317,319,319,319,319,317,317,144,144,144,144,144,144,
141,141,180,180,180,180,182,182,166,166,166,166,168,168,170,170,145,145,166,
166,170,176,159,159,159,159,157,157,159,159,155,155,161,161,169,169,169,169,
163,163,167,167,171,171,175,175,163,163,169,171,171,175,180,180,180,180,182,
182,193,193,195,196,196,198,199,400,400,400,400,205,205,206,206,206,206,208,
208,206,206,206,206,210,210,212,212,210,210,212,212,214,214,426,426,426,426,
430,430,430,430,434,434,434,434,438,438,438,438,438,438,438,438,438,438,440,
440,450,450,450,450,452,452,450,450,450,450,227,227,231,233,233,235,235,235,
235,237,237,239,239,266,266,266,266,272,272,272,272,270,270,276,276,276,276,
282,282,287,287,287,287,309,309,311,313,313,305,305,305,305,301,301,307,307,
307,307,508,508,508,508,512,512,512,512,516,516,516,516,518,518,516,516,516,
516,321,321,321,321,317,317,325,325,323,323,536,536,536,536,536,536,538,538,
536,536,546,546,546,546,546,546,548,548,546,546,332,332,333,333,333,333,346,
346,350,335,335,343,343,349,347,347,363,363,363,363,357,357,361,361,365,365,
403,403,409,409,409,409,411,411,413,413,415,415,404,404,404,404,426,426,426,
426,433,433,437,437,438,438,438,438,442,442,444,444,446,446,450,450,450,450,
452,452,450,450,450,450,626,626,626,626,630,630,630,630,476,476,476,476,638,
638,638,638,642,642,642,642,492,492,492,492,511,511,601,601,601,601],[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
,33,34,35,36,1,2,3,4,1,2,3,4,5,6,7,8,9,10,3,4,1,2,5,6,9,10,1,2,3,4,9,10,7,8,67
,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
,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114
,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,
134,135,136,137,138,139,140,11,12,13,14,25,26,13,14,11,12,19,20,21,22,13,14,11
,12,17,18,15,16,11,12,13,14,15,16,17,18,19,20,21,22,23,24,11,12,13,14,15,16,21
,22,28,29,30,32,31,34,36,35,25,26,27,28,29,30,33,35,36,202,203,204,205,206,207
,208,209,212,213,210,211,214,215,216,217,218,219,220,221,222,223,224,225,226,
227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,
246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,
265,53,54,51,52,51,52,53,54,57,58,53,54,51,52,57,58,55,56,284,285,286,287,288,
289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,
308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,
327,328,67,68,69,70,75,76,100,101,69,70,67,68,71,72,67,68,69,70,71,72,73,74,
108,109,75,76,77,81,84,85,82,83,88,89,90,91,86,87,92,93,84,85,82,83,88,89,92,
93,98,99,94,95,100,101,102,104,105,106,76,75,75,76,79,78,108,109,110,111,112,
113,118,400,401,402,403,404,405,406,407,408,409,410,411,414,415,412,413,418,
419,416,417,422,423,420,421,424,425,119,120,121,122,123,124,125,126,119,120,
121,122,123,124,125,126,127,128,129,130,129,130,131,132,135,136,133,134,139,
140,137,138,137,138,460,461,462,463,464,465,466,467,468,469,470,471,472,177,
178,179,180,179,180,177,178,181,182,179,180,177,178,183,184,489,490,491,492,
493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,202,203,204,205,
202,203,204,205,206,207,208,209,216,217,212,213,210,211,526,527,528,529,530,
531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,
550,551,552,553,554,555,218,219,227,228,229,230,218,219,220,262,263,221,222,
223,226,225,242,243,244,245,246,247,252,253,254,255,582,583,584,585,586,587,
588,589,592,593,590,591,594,595,596,597,284,285,286,287,290,291,288,289,295,
296,293,294,299,300,297,298,297,298,303,304,301,302,307,308,305,306,305,306,
317,318,319,320,630,631,632,633,339,340,337,338,400,401,402,403,400,401,402,
403,646,647,648,649,404,405,489,490,491,492],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,114,115,116,117,118,1,2,3,4,1,2,3,4,5,6,7,8,9,10,3,4,1,2,5,6,9,10,141,142,
143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,
162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,
181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,
200,201,202,203,204,205,206,207,208,209,212,213,210,211,214,215,216,217,218,
219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,
238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,
257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,
276,277,278,279,280,281,282,283,11,12,13,14,25,26,25,26,27,13,14,11,12,19,20,
21,22,13,14,11,12,17,18,15,16,28,29,30,33,31,32,35,36,317,318,319,320,321,322,
323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,
342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,
361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,
380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,
399,400,401,402,403,404,405,406,407,408,409,410,411,414,415,412,413,418,419,
416,417,422,423,420,421,424,425,37,38,39,40,37,38,39,40,59,60,61,62,41,42,43,
44,45,46,47,48,47,48,49,50,53,54,51,52,57,58,55,56,55,56,460,461,462,463,464,
465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,
484,485,486,487,488,67,68,69,70,111,112,113,115,114,82,83,84,85,86,87,92,93,92
,93,508,509,510,511,512,513,514,515,516,517,518,519,520,521,524,525,522,523,
526,527,528,529,530,531,532,533,534,535,546,547,548,549,550,551,552,553,554,
555,536,537,538,539,540,541,542,543,544,545,556,557,558,559,560,561,562,563,
564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,
583,584,585,586,587,588,589,592,593,590,591,594,595,596,597,141,142,143,144,
145,146,193,194,149,150,147,148,153,154,151,152,151,152,157,158,155,156,161,
162,159,160,159,160,626,627,628,629,202,203,204,205,634,635,636,637,638,639,
640,641,642,643,644,645,218,219,219,218,650,651,329,330,331,332],,[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
,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59
,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85
,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,
128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,
147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,
185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,1,2,3,4,1,
2,3,4,7,8,7,8,5,6,9,10,218,219,220,221,222,223,224,225,226,227,228,229,230,231
,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,
251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,
270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,
289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,
308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,325,326,323,324,
327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,
346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,
365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,
384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,
403,25,26,11,12,13,14,15,16,17,18,17,18,19,20,19,20,23,24,23,24,21,22,426,427,
428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,446,447,444,
445,448,449,450,451,452,453,454,455,458,459,456,457,460,461,462,463,464,465,
466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,
485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,
504,505,506,507,37,38,39,40,41,42,43,44,59,60,61,62,63,64,65,66,65,66,529,528,
527,526,531,530,535,534,533,532,546,547,548,549,550,551,552,553,554,555,536,
537,538,539,540,541,542,543,544,545,556,557,558,559,560,561,562,563,564,565,
566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,67,68,
69,70,71,72,73,74,73,74,108,109,109,108,598,599,600,601,602,603,604,605,606,
607,608,609,610,611,614,615,612,613,616,617,618,619,620,621,624,625,622,623,
626,627,628,629,119,120,121,122,634,635,636,637,642,643,644,645,638,639,640,
641,646,647,648,649,145,146,652,653,654,655],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13
,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39
,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65
,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91
,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,
132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,
151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,
170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,
189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,
208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,
227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,
246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,
265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,
284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,
303,304,305,306,307,308,309,310,311,312,313,314,315,316,1,2,3,4,7,8,9,10,9,10,
5,6,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,
347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,
366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,
385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,
404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,
423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,
442,443,446,447,444,445,448,449,450,451,452,453,454,455,458,459,456,457,460,
461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,
480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,
499,500,501,502,503,506,507,504,505,508,509,510,511,512,513,514,515,516,517,
518,519,520,521,522,523,524,525,28,29,29,28,30,30,35,36,36,35,546,547,548,549,
550,551,552,553,554,555,536,537,538,539,540,541,542,543,544,545,556,557,558,
559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,
578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,597,596,595,
594,598,599,600,601,602,603,604,605,606,607,608,609,610,611,614,615,612,613,
616,617,618,619,620,621,624,625,622,623,37,38,39,40,630,631,632,633,634,635,
636,637,638,639,640,641,642,643,644,645,649,648,647,646,650,651,652,653,654,
655],,[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
,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53
,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
,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,
104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,
142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,
161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,
199,200,201,202,203,204,205,206,207,208,209,212,213,210,211,214,215,216,217,
218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,
237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,
256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,
275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,
294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,
313,314,315,316,317,318,319,320,321,322,325,326,323,324,327,328,329,330,331,
332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,
351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,
370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,
389,390,391,392,393,394,395,396,397,398,399,1,2,3,4,404,405,406,407,408,409,
410,411,414,415,412,413,418,419,416,417,422,423,420,421,424,425,426,427,428,
429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,446,447,444,445,
448,449,450,451,452,453,454,455,458,459,456,457,460,461,462,463,464,465,466,
467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,
486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,506,
507,504,505,508,509,510,511,512,513,514,515,516,517,518,519,520,521,524,525,
522,523,529,528,527,526,531,530,535,534,533,532,536,537,538,539,540,541,542,
543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,
562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,
581,25,26,584,585,586,587,588,589,592,593,590,591,594,595,596,597,598,599,600,
601,602,603,604,605,606,607,608,609,610,611,614,615,612,613,616,617,618,619,
620,621,624,625,622,623,626,627,628,629,630,631,632,633,634,635,636,637,37,38,
39,40,37,38,39,40,649,648,647,646,650,651,652,653,654,655],,,,,,,,,,[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,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,
127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,
146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,
165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,
203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,
222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,
241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,
260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,
279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,
298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,
317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,
336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,
355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,
374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,
393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,
412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,
431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,
450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,
469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,
488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,
507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,
526,527,528,529,530,531,532,533,534,535,1,2,3,4,5,6,9,10,7,8,1,2,3,4,5,6,9,10,
7,8,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,
574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,
593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,
612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,
631,632,633,634,635,636,637,642,643,644,645,638,639,640,641,646,647,648,649,
650,651,652,653,654,655]],
0,
[(210,212)(211,213)(412,414)(413,415)(416,418)(417,419)(420,422)(421,423)
(522,524)(523,525)(590,592)(591,593)
,(323,325)(324,326)(526,529)(527,528)(530,531)(532,535)(533,534),
(444,446)(445,447)(612,614)(613,615),(456,458)(457,459)(622,624)(623,625),
(504,506)(505,507),(594,597)(595,596),(638,642)(639,643)(640,644)(641,645),
(646,649)(647,648),
(536,546)(537,547)(538,548)(539,549)(540,550)(541,551)(542,552)(543,553)
(544,554)(545,555)],
["ConstructProj",[["2^1+24.Co1",[]],["2^1+24.2.Co1",[]]]]);
ALF("2^1+24.2.Co1","2.Co1",[1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,3,4,3,4,3,4,3,
4,5,5,5,6,6,6,6,6,6,6,6,6,7,8,7,8,9,10,9,10,9,10,9,10,9,10,11,12,11,12,11,
12,11,12,13,14,13,14,13,14,13,14,15,16,15,16,15,16,15,16,17,17,17,17,17,
17,17,18,19,18,19,18,19,18,19,18,19,18,19,18,19,18,19,18,19,20,20,20,20,
20,20,20,20,21,21,21,22,22,22,22,22,22,22,22,23,24,23,24,25,26,25,26,25,
26,25,26,25,26,27,28,27,28,27,28,27,28,29,30,29,30,31,31,32,33,32,33,32,
33,32,33,34,35,34,35,34,35,34,35,36,37,36,37,36,37,36,37,36,37,36,37,36,
37,38,39,38,39,38,39,38,39,40,40,40,40,40,40,40,40,41,41,41,42,42,42,42,
42,42,43,44,43,44,45,46,45,46,45,46,45,46,45,46,45,46,47,47,47,48,48,48,
48,48,48,49,50,49,50,49,50,49,50,51,51,51,51,51,51,51,52,53,52,53,52,53,
52,53,52,53,52,53,52,53,52,53,52,53,52,53,54,54,54,54,55,56,55,56,57,58,
57,58,57,58,59,60,59,60,59,60,59,60,61,62,61,62,63,63,64,64,64,65,66,65,
66,65,66,65,66,67,68,67,68,67,68,67,68,69,69,69,69,69,69,69,69,70,71,70,
71,70,71,70,71,70,71,70,71,72,73,72,73,74,74,75,75,76,77,76,77,76,77,78,
79,78,79,78,79,78,79,80,80,81,81,81,81,82,83,82,83,82,83,82,83,82,83,82,
83,84,85,84,85,84,85,84,85,84,85,84,85,86,86,86,86,86,86,87,88,87,88,87,
88,89,89,89,90,90,90,90,91,92,91,92,93,93,94,95,94,95,94,95,94,95,94,95,
94,95,94,95,94,95,94,95,94,95,96,97,96,97,98,99,98,99,100,101,100,101,102,
103,102,103,102,103,102,103,102,103,102,103,104,105,104,105,104,105,104,
105,104,105,106,106,106,106,106,107,108,107,108,107,108,107,108,109,110,
109,110,111,112,111,112,111,112,113,114,113,114,113,114,115,116,115,116,
117,117,117,117,117,118,119,118,119,118,119,118,119,118,119,120,121,120,
121,122,123,122,123,124,125,124,125,124,125,124,125,124,125,126,127,126,
127,126,127,126,127,126,127,128,129,128,129,128,129,128,129,128,129,130,
131,130,131,130,131,130,131,130,131,132,132,133,134,133,134,135,135,135,
136,136,137,137,137,137,137,138,139,138,139,138,139,138,139,138,139,140,
140,141,142,141,142,141,142,141,142,141,142,143,144,143,144,145,146,145,
146,147,147,148,148,149,150,149,150,149,150,149,150,149,150,151,152,151,
152,151,152,151,152,151,152,153,154,153,154,155,156,155,156,157,158,157,
158,159,160,159,160,161,162,161,162,163,164,163,164,165,165,166,167,166,
167]);
ALF("2^1+24.2.Co1","2^1+24.Co1",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
10,11,11,12,12,13,13,14,15,15,16,17,17,18,19,20,20,21,21,22,22,23,23,24,
24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,
36,37,37,38,38,39,39,40,40,41,42,42,43,44,45,45,46,46,47,47,48,48,49,49,
50,50,51,51,52,52,53,53,54,54,55,56,57,57,58,59,60,60,61,62,62,63,64,64,
65,66,67,68,68,69,69,70,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,
78,79,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,
90,91,91,92,92,93,93,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,
102,103,103,104,105,105,106,106,107,108,108,109,110,111,111,112,112,113,
113,114,114,115,115,116,116,117,117,118,118,119,119,120,120,121,122,122,
123,124,125,125,126,126,127,127,128,128,129,129,130,130,131,132,133,133,
134,135,135,136,136,137,137,138,138,139,139,140,140,141,141,142,142,143,
143,144,144,145,145,146,147,148,148,149,149,150,150,151,151,152,152,153,
153,154,154,155,155,156,156,157,157,158,158,159,159,160,160,161,162,162,
163,163,164,164,165,165,166,166,167,167,168,168,169,169,170,170,171,172,
173,173,174,174,175,175,176,176,177,177,178,178,179,179,180,180,181,181,
182,182,183,183,184,184,185,185,186,186,187,187,188,188,189,189,190,190,
191,191,192,192,193,193,194,195,196,196,197,197,198,198,199,199,200,200,
201,201,202,202,203,203,204,204,205,205,206,206,207,207,208,208,209,210,
210,211,212,212,213,213,214,214,215,215,216,217,217,218,219,220,220,221,
221,222,222,223,223,224,224,225,225,226,226,227,227,228,228,229,229,230,
230,231,231,232,232,233,233,234,234,235,235,236,236,237,237,238,238,239,
239,240,240,241,241,242,242,243,243,244,244,245,245,246,246,247,247,248,
248,249,249,250,250,251,252,252,253,253,254,254,255,255,256,256,257,257,
258,258,259,259,260,260,261,261,262,262,263,263,264,264,265,265,266,266,
267,267,268,269,269,270,270,271,271,272,272,273,273,274,274,275,275,276,
276,277,277,278,278,279,279,280,280,281,281,282,282,283,283,284,284,285,
285,286,286,287,287,288,288,289,289,290,290,291,291,292,292,293,293,294,
294,295,295,296,296,297,297,298,298,299,299,300,300,301,301,302,302,303,
304,304,305,305,306,307,307,308,308,309,309,310,310,311,311,312,312,313,
313,314,314,315,315,316,316,317,317,318,318,319,319,320,320,321,321,322,
322,323,323,324,324,325,325,326,326,327,327,328,328,329,329,330,330,331,
331,332,332,333,333,334,334,335,335,336,336,337,337,338,338,339,339,340,
340,341,341,342,342,343,343,344,344,345,345,346,346,347,347,348,348,349,
349]);
ALF("2^1+24.2.Co1","Co1",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,
8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,
11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,13,13,13,14,14,14,14,
14,14,14,14,15,15,15,15,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,
17,17,18,18,18,18,19,19,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,
22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,24,24,
24,24,24,24,24,24,25,25,25,26,26,26,26,26,26,27,27,27,27,28,28,28,28,28,
28,28,28,28,28,28,28,29,29,29,30,30,30,30,30,30,31,31,31,31,31,31,31,31,
32,32,32,32,32,32,32,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,
33,33,33,34,34,34,34,35,35,35,35,36,36,36,36,36,36,37,37,37,37,37,37,37,
37,38,38,38,38,39,39,40,40,40,41,41,41,41,41,41,41,41,42,42,42,42,42,42,
42,42,43,43,43,43,43,43,43,43,44,44,44,44,44,44,44,44,44,44,44,44,45,45,
45,45,46,46,47,47,48,48,48,48,48,48,49,49,49,49,49,49,49,49,50,50,51,51,
51,51,52,52,52,52,52,52,52,52,52,52,52,52,53,53,53,53,53,53,53,53,53,53,
53,53,54,54,54,54,54,54,55,55,55,55,55,55,56,56,56,57,57,57,57,58,58,58,
58,59,59,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,61,
61,61,61,62,62,62,62,63,63,63,63,64,64,64,64,64,64,64,64,64,64,64,64,65,
65,65,65,65,65,65,65,65,65,66,66,66,66,66,67,67,67,67,67,67,67,67,68,68,
68,68,69,69,69,69,69,69,70,70,70,70,70,70,71,71,71,71,72,72,72,72,72,73,
73,73,73,73,73,73,73,73,73,74,74,74,74,75,75,75,75,76,76,76,76,76,76,76,
76,76,76,77,77,77,77,77,77,77,77,77,77,78,78,78,78,78,78,78,78,78,78,79,
79,79,79,79,79,79,79,79,79,80,80,81,81,81,81,82,82,82,83,83,84,84,84,84,
84,85,85,85,85,85,85,85,85,85,85,86,86,87,87,87,87,87,87,87,87,87,87,88,
88,88,88,89,89,89,89,90,90,91,91,92,92,92,92,92,92,92,92,92,92,93,93,93,
93,93,93,93,93,93,93,94,94,94,94,95,95,95,95,96,96,96,96,97,97,97,97,98,
98,98,98,99,99,99,99,100,100,101,101,101,101]);

MOT("2xF4(2)",
0,
0,
0,
0,
[(80,81)(175,176),(78,79)(173,174),(69,70)(164,165),(2,3)(6,7)(9,10)(11,12)
(15,16)(18,19)(25,26)(27,28)(29,30)(31,32)(33,34)(36,37)(40,41)(42,43)(44,45)
(49,50)(51,52)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(72,73)(74,75)
(82,83)(86,87)(88,89)(90,91)(92,93)(94,95)(97,98)(101,102)(104,105)(106,107)
(110,111)(113,114)(120,121)(122,123)(124,125)(126,127)(128,129)(131,132)(135,
136)(137,138)(139,140)(144,145)(146,147)(149,150)(151,152)(153,154)(155,156)
(157,158)(159,160)(161,162)(167,168)(169,170)(177,178)(181,182)(183,184)(185,
186)(187,188)(189,190)],
["ConstructDirectProduct",[["Cyclic",2],["F4(2)"]]]);
ALF("2xF4(2)","2xF4(2).2",[1,2,2,3,4,5,5,6,7,7,8,8,9,10,11,11,12,13,13,14,
15,16,17,18,19,19,20,20,21,21,22,22,23,23,24,25,25,26,27,28,28,29,29,30,
30,31,32,33,34,34,35,35,36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,
45,46,47,48,48,49,49,50,51,52,53,54,54,55,55,56,57,58,58,59,59,60,60,61,
61,62,62,92,93,93,94,95,96,96,97,98,98,99,99,100,101,102,102,103,104,104,
105,106,107,108,109,110,110,111,111,112,112,113,113,114,114,115,116,116,
117,118,119,119,120,120,121,121,122,123,124,125,125,126,126,127,128,128,
129,129,130,130,131,131,132,132,133,133,134,134,135,136,137,138,139,139,
140,140,141,142,143,144,145,145,146,146,147,148,149,149,150,150,151,151,
152,152,153,153],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^2xF4(2)",
0,
0,
0,
0,
[(80,81)(175,176)(270,271)(365,366),
(78,79)(173,174)(268,269)(363,364),(69,70)(164,165)(259,260)(354,355),
(191,286)(192,287)(193,288)(194,289)(195,290)(196,291)(197,292)(198,293)
(199,294)(200,295)(201,296)(202,297)(203,298)(204,299)(205,300)(206,301)
(207,302)(208,303)(209,304)(210,305)(211,306)(212,307)(213,308)(214,309)
(215,310)(216,311)(217,312)(218,313)(219,314)(220,315)(221,316)(222,317)
(223,318)(224,319)(225,320)(226,321)(227,322)(228,323)(229,324)(230,325)
(231,326)(232,327)(233,328)(234,329)(235,330)(236,331)(237,332)(238,333)
(239,334)(240,335)(241,336)(242,337)(243,338)(244,339)(245,340)(246,341)
(247,342)(248,343)(249,344)(250,345)(251,346)(252,347)(253,348)(254,349)
(255,350)(256,351)(257,352)(258,353)(259,354)(260,355)(261,356)(262,357)
(263,358)(264,359)(265,360)(266,361)(267,362)(268,363)(269,364)(270,365)
(271,366)(272,367)(273,368)(274,369)(275,370)(276,371)(277,372)(278,373)
(279,374)(280,375)(281,376)(282,377)(283,378)(284,379)(285,380),
(96,191)(97,192)(98,193)(99,194)(100,195)(101,196)(102,197)(103,198)
(104,199)(105,200)(106,201)(107,202)(108,203)(109,204)(110,205)(111,206)
(112,207)(113,208)(114,209)(115,210)(116,211)(117,212)(118,213)(119,214)
(120,215)(121,216)(122,217)(123,218)(124,219)(125,220)(126,221)(127,222)
(128,223)(129,224)(130,225)(131,226)(132,227)(133,228)(134,229)(135,230)
(136,231)(137,232)(138,233)(139,234)(140,235)(141,236)(142,237)(143,238)
(144,239)(145,240)(146,241)(147,242)(148,243)(149,244)(150,245)(151,246)
(152,247)(153,248)(154,249)(155,250)(156,251)(157,252)(158,253)(159,254)
(160,255)(161,256)(162,257)(163,258)(164,259)(165,260)(166,261)(167,262)
(168,263)(169,264)(170,265)(171,266)(172,267)(173,268)(174,269)(175,270)
(176,271)(177,272)(178,273)(179,274)(180,275)(181,276)(182,277)(183,278)
(184,279)(185,280)(186,281)(187,282)(188,283)(189,284)(190,285),
(2,3)(6,7)(9,10)(11,12)(15,16)(18,19)(25,26)(27,28)
(29,30)(31,32)(33,34)(36,37)(40,41)(42,43)(44,45)(49,50)
(51,52)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)
(72,73)(74,75)(82,83)(86,87)(88,89)(90,91)(92,93)(94,95)
(97,98)(101,102)(104,105)(106,107)(110,111)(113,114)(120,121)(122,123)(124,
125)(126,127)(128,129)(131,132)(135,136)(137,138)(139,140)(144,145)
(146,147)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)
(167,168)(169,170)(177,178)(181,182)(183,184)(185,186)(187,188)(189,190)
(192,193)(196,197)(199,200)(201,202)(205,206)(208,209)(215,216)(217,218)
(219,220)(221,222)(223,224)(226,227)(230,231)(232,233)(234,235)(239,240)
(241,242)(244,245)(246,247)(248,249)(250,251)(252,253)(254,255)(256,257)
(262,263)(264,265)(272,273)(276,277)(278,279)(280,281)(282,283)(284,285)
(287,288)(291,292)(294,295)(296,297)(300,301)(303,304)(310,311)(312,313)
(314,315)(316,317)(318,319)(321,322)(325,326)(327,328)(329,330)(334,335)
(336,337)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(357,358)(359,360)(367,368)(371,372)(373,374)(375,376)(377,378)(379,380)],
["ConstructDirectProduct",[["2^2"],["F4(2)"]]]);
ALF("2^2xF4(2)","2xF4(2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
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,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,96,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,
162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,187,188,189,190]);
ALF("2^2xF4(2)","(2^2xF4(2)):2",[1,2,2,3,4,5,5,6,7,7,8,8,9,10,11,11,12,13,
13,14,15,16,17,18,19,19,20,20,21,21,22,22,23,23,24,25,25,26,27,28,28,29,
29,30,30,31,32,33,34,34,35,35,36,37,37,38,38,39,39,40,40,41,41,42,42,43,
43,44,45,46,47,48,48,49,49,50,51,52,53,54,54,55,55,56,57,58,58,59,59,60,
60,61,61,62,62,63,64,64,65,66,67,67,68,69,69,70,70,71,72,73,73,74,75,75,
76,77,78,79,80,81,81,82,82,83,83,84,84,85,85,86,87,87,88,89,90,90,91,91,
92,92,93,94,95,96,96,97,97,98,99,99,100,100,101,101,102,102,103,103,104,
104,105,105,106,107,108,109,110,110,111,111,112,113,114,115,116,116,117,
117,118,119,120,120,121,121,122,122,123,123,124,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,
125,127,126,128,129,131,130,132,134,133,136,135,137,138,140,139,141,143,
142,144,145,146,147,148,150,149,152,151,154,153,156,155,158,157,159,161,
160,162,163,165,164,167,166,169,168,170,171,172,174,173,176,175,177,179,
178,181,180,183,182,185,184,187,186,189,188,191,190,192,193,194,195,197,
196,199,198,200,201,202,203,205,204,207,206,208,209,211,210,213,212,215,
214,217,216,219,218]);

MOT("2xF4(2).2",
0,
0,
0,
0,
[(88,89)(179,180),(86,87)(177,178),(45,46)(83,84)(136,137)(174,175),(63,154)
(64,155)(65,156)(66,157)(67,158)(68,159)(69,160)(70,161)(71,162)(72,163)(73,
164)(74,165)(75,166)(76,167)(77,168)(78,169)(79,170)(80,171)(81,172)(82,173)
(83,174)(84,175)(85,176)(86,177)(87,178)(88,179)(89,180)(90,181)(91,182),(52,
53)(79,80)(143,144)(170,171)],
["ConstructDirectProduct",[["Cyclic",2],["F4(2).2"]]]);

MOT("(2^2xF4(2)):2",
[
"6th maximal subgroup of B,\n",
"constructed from the tables of 2^2xF4(2) and 2xF4(2).2"
],
[26489012826931200,190253629440,6039797760,75497472,17418240,373248,28311552,
22020096,11796480,11796480,786432,524288,196608,196608,131072,98304,65536,
28800,276480,55296,20736,18432,4608,4608,4704,16384,16384,6144,6144,4096,8192,
1024,1024,216,960,640,4608,3456,2304,2304,1536,384,384,384,384,384,104,224,360
,512,512,512,512,68,72,320,320,84,192,192,112,120,26489012826931200,
190253629440,6039797760,75497472,17418240,373248,28311552,22020096,11796480,
11796480,786432,524288,196608,196608,131072,98304,65536,28800,276480,55296,
20736,18432,4608,4608,4704,16384,16384,6144,6144,4096,8192,1024,1024,216,960,
640,4608,3456,2304,2304,1536,384,384,384,384,384,104,224,360,512,512,512,512,
68,72,320,320,84,192,192,112,120,13244506413465600,190253629440,190253629440,
3019898880,37748736,17418240,17418240,186624,28311552,28311552,22020096,
22020096,5898240,5898240,786432,786432,262144,196608,196608,98304,65536,49152,
32768,14400,276480,276480,55296,55296,20736,20736,18432,18432,4608,4608,2304,
4704,4704,8192,8192,6144,6144,6144,6144,4096,4096,4096,512,512,216,216,960,960
,320,4608,4608,3456,3456,2304,2304,2304,2304,1536,1536,384,384,384,384,192,192
,192,52,224,224,360,360,256,256,256,256,68,68,72,72,160,160,84,84,192,192,192,
192,112,112,120,120,143769600,81920,12288,864,5120,5120,1536,1024,768,512,512,
400,96,256,256,128,64,64,80,48,48,48,52,64,64,64,64,80,80,143769600,81920,
12288,864,5120,5120,1536,1024,768,512,512,400,96,256,256,128,64,64,80,48,48,48
,52,64,64,64,64,80,80],
[,[1,1,1,1,5,6,2,2,3,3,2,3,3,4,3,4,4,18,5,5,6,5,5,6,25,12,12,8,7,12,12,14,17,
34,18,18,20,21,22,22,20,22,21,24,24,24,47,25,49,26,27,31,31,54,34,36,36,58,41,
37,48,49,1,1,1,1,5,6,2,2,3,3,2,3,3,4,3,4,4,18,5,5,6,5,5,6,25,12,12,8,7,12,12,
14,17,34,18,18,20,21,22,22,20,22,21,24,24,24,47,25,49,26,27,31,31,54,34,36,36,
58,41,37,48,49,1,1,1,1,1,5,5,6,2,2,2,2,3,3,2,2,3,3,3,4,3,4,4,18,5,5,5,5,6,6,5,
5,5,5,6,25,25,12,12,8,8,7,7,12,12,12,14,17,34,34,18,18,18,20,20,21,21,22,22,22
,22,20,20,22,22,21,21,24,24,24,47,25,25,49,49,26,27,31,31,54,54,34,34,36,36,58
,58,41,41,37,37,48,48,49,49,1,3,4,6,9,9,14,12,16,14,15,18,24,31,31,26,33,33,36
,44,46,45,47,50,50,51,51,56,56,63,65,66,68,71,71,76,74,78,76,77,80,86,93,93,88
,95,95,98,106,108,107,109,112,112,113,113,118,118],[1,2,3,4,1,1,7,8,9,10,11,12
,13,14,15,16,17,18,2,2,2,3,4,4,25,26,27,28,29,30,31,32,33,6,35,36,7,7,9,10,8,
13,11,14,16,16,47,48,18,50,51,53,52,54,21,56,57,25,28,29,61,35,63,64,65,66,63,
63,69,70,71,72,73,74,75,76,77,78,79,80,64,64,64,65,66,66,87,88,89,90,91,92,93,
94,95,68,97,98,69,69,71,72,70,75,73,76,78,78,109,110,80,112,113,115,114,116,83
,118,119,87,90,91,123,97,125,126,127,128,129,125,125,125,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,126,127,127,126,126,127,128,128,
129,129,129,160,161,162,163,164,165,166,167,168,169,170,171,172,132,132,175,
176,177,134,133,133,134,137,137,138,138,136,135,142,143,139,140,144,146,146,
195,196,197,148,148,200,201,203,202,205,204,153,154,208,209,160,161,165,164,
167,166,216,217,175,176,220,221,222,220,224,225,226,227,228,229,230,231,222,
233,234,235,237,236,238,226,228,228,242,244,243,245,246,247,248,249,250,251,
249,253,254,255,256,257,258,259,260,251,262,263,264,266,265,267,255,257,257,
271,273,272,274,275,276,277],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,2,3,37,38,39,40,41,42,43,44,46,45
,47,48,5,50,51,52,53,54,55,9,10,58,59,60,61,19,63,64,65,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,63,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,64,65,
99,100,101,102,103,104,105,106,108,107,109,110,67,112,113,114,115,116,117,71,
72,120,121,122,123,81,125,126,127,128,129,130,131,132,133,134,135,136,137,138,
139,140,141,142,143,144,145,146,147,125,149,150,151,152,153,154,155,156,157,
158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,126,127,
128,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,194,193,195,
196,197,130,131,200,201,202,203,205,204,206,207,137,138,210,211,212,213,214,
215,216,217,149,150,220,221,222,223,224,225,226,227,228,229,230,220,232,233,
234,235,236,237,221,239,241,240,242,244,243,246,245,224,225,249,250,251,252,
253,254,255,256,257,258,259,249,261,262,263,264,265,266,250,268,270,269,271,
273,272,275,274,253,254],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,1,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,2,49,50,51,53,52,54,55,56,57,5,59,60,8,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,63,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,64,111,112,113,115,114,116,117,118,119
,67,121,122,70,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139
,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,
159,125,125,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,
178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,126,
127,198,199,200,201,203,202,205,204,206,207,208,209,130,131,212,213,214,215,
135,136,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,
235,237,236,238,239,240,241,242,243,244,246,245,247,248,249,250,251,252,253,
254,255,256,257,258,259,260,261,262,263,264,266,265,267,268,269,270,271,272,
273,275,274,276,277],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
1,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,
99,100,101,102,103,104,105,106,107,108,63,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,
157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,
176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,
125,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,
214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,
233,234,235,236,237,238,239,240,241,220,244,243,246,245,247,248,249,250,251,
252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,
249,273,272,275,274,276,277],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
46,45,47,48,49,50,51,52,53,1,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,108,107,109,110,111,112,113,114,115,63,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,
136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,
155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,
174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,
194,193,195,196,197,198,199,200,201,202,203,125,125,206,207,208,209,210,211,
212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,
231,232,233,234,235,236,237,238,239,241,240,242,243,244,245,246,247,248,249,
250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,
270,269,271,272,273,274,275,276,277]],
0,
[(204,205),(243,244)(272,273),
(126,127)(130,131)(133,134)(135,136)(139,140)(142,143)(149,150)(151,152)
(153,154)(155,156)(157,158)(160,161)(164,165)(166,167)(168,169)(173,174)
(175,176)(178,179)(180,181)(182,183)(184,185)(186,187)(188,189)(190,191)
(196,197)(198,199)(206,207)(210,211)(212,213)(214,215)(216,217)(218,219)
(243,244)(272,273),(243,244)(245,246)(272,273)(274,275),
( 52, 53)(114,115)(202,203)(236,237)(243,244)(245,246)(265,266)(272,273)
(274,275),
( 45, 46)(107,108)(193,194)(240,241)(243,244)(245,246)(269,270)(272,273)
(274,275)],
["ConstructMixed","2^2xF4(2)","2xF4(2).2",[[191,286],[192,287],[193,289],[194,
288],[195,290],[196,291],[197,292],[198,293],[199,295],[200,294],[201,297],
[202,296],[203,298],[204,300],[205,299],[206,301],[207,302],[208,304],[209,
303],[210,305],[211,306],[212,308],[213,307],[214,309],[215,310],[216,311],
[217,312],[218,314],[219,313],[220,316],[221,315],[222,317],[223,319],[224,
318],[225,321],[226,320],[227,322],[228,324],[229,323],[230,326],[231,325],
[232,327],[233,328],[234,329],[235,330],[236,332],[237,331],[238,334],[239,
333],[240,336],[241,335],[242,338],[243,337],[244,340],[245,339],[246,342],
[247,341],[248,343],[249,345],[250,344],[251,347],[252,346],[253,349],[254,
348],[255,351],[256,350],[257,353],[258,352],[259,355],[260,354],[261,356],
[262,357],[263,359],[264,358],[265,361],[266,360],[267,362],[268,364],[269,
363],[270,366],[271,365],[272,368],[273,367],[274,370],[275,369],[276,372],
[277,371],[278,374],[279,373],[280,375],[281,377],[282,376],[283,378],[284,
379],[285,380]],()]);
ALF("(2^2xF4(2)):2","2xF4(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,1,2,3,4,
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,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,60,61,62,92,93,93,94,95,96,96,97,98,98,99,99,100,101,102,
102,103,104,104,105,106,107,108,109,110,110,111,111,112,112,113,113,114,
114,115,116,116,117,118,119,119,120,120,121,121,122,123,124,125,125,126,
126,127,128,128,129,129,130,130,131,131,132,132,133,133,134,134,135,136,
137,138,139,139,140,140,141,142,143,144,145,145,146,146,147,148,149,149,
150,150,151,151,152,152,153,153,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,154,155,156,157,158,159,160,
161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,
179,180,181,182]);
ALF("(2^2xF4(2)):2","F4(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,1,2,3,4,5,
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,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,1,2,2,3,4,5,5,6,7,7,8,8,9,10,11,11,12,13,13,14,15,16,
17,18,19,19,20,20,21,21,22,22,23,23,24,25,25,26,27,28,28,29,29,30,30,31,
32,33,34,34,35,35,36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,45,46,
47,48,48,49,49,50,51,52,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
86,87,88,89,90,91,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89,90,91]);

MOT("S3xFi22.2",
[
"9th maximal subgroup of B"
],
0,
0,
0,
[(106,107)(218,219)(330,331)],
["ConstructDirectProduct",[["Dihedral",6],["Fi22.2"]]]);
ALF("S3xFi22.2","B",[1,2,3,5,6,7,6,7,9,11,10,12,14,18,20,23,26,22,21,27,
29,27,22,24,28,31,36,33,35,41,47,47,47,48,49,54,56,58,58,59,68,64,67,66,
62,60,75,77,81,83,92,93,94,103,109,110,114,116,138,2,5,4,9,8,11,13,15,21,
21,23,25,20,24,30,23,29,27,25,34,36,32,38,48,50,52,55,56,55,55,57,62,65,
59,63,71,76,78,84,93,92,97,95,99,115,117,119,119,122,137,139,156,166,6,20,
22,27,6,6,7,7,58,59,61,64,66,81,21,20,22,22,23,24,27,28,26,29,29,109,116,
114,120,123,47,47,46,138,140,151,58,58,55,62,64,60,61,66,65,68,160,167,81,
174,92,93,94,181,109,183,114,117,137,21,24,25,55,57,62,63,70,20,21,21,25,
23,27,25,23,28,29,30,115,117,118,122,137,139,141,55,55,58,56,57,59,62,65,
69,73,166,168,175,93,92,97,96,180,115,116,118,118,121,138,139,156,166,2,3,
5,5,20,23,21,23,10,14,13,15,14,48,22,26,29,27,22,27,28,24,24,27,29,77,33,
36,39,41,92,93,93,49,52,110,67,61,61,66,73,70,69,66,66,71,130,79,138,87,
94,94,95,104,167,111,116,114,140,4,4,5,11,11,13,14,17,25,25,30,24,25,25,
29,30,30,25,27,34,36,37,41,50,52,50,62,65,62,59,62,63,69,63,66,72,78,80,
87,97,97,95,97,103,115,117,124,124,123,139,141,157,168],[
"fusion map is unique"
]);
ALF("S3xFi22.2","2xFi22.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
111,112,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,
98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,
135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,
171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,
189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,
207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224]);
ALN("S3xFi22.2",["BM9","BN3A"]);

MOT("2xFi22",
[
"subquotient group of BM9, needed in the construction of 2^2.Fi22.2"
],
0,
0,
0,
[(55,56)(120,121),(53,54)(118,119),(49,50)(114,115),(42,43)(107,108),(36,37)
(61,62)(101,102)(126,127)],
["ConstructDirectProduct",[["Cyclic",2],["Fi22"]]]);
ALF("2xFi22","2xFi22.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,36,37,38,39,40,41,41,
42,43,44,45,46,47,47,48,49,50,50,51,51,52,53,54,55,56,56,57,58,59,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,148,149,
150,151,152,153,153,154,155,156,157,158,159,159,160,161,162,162,163,163,
164,165,166,167,168,168,169,170,171],[
"fusion map is unique"
]);

MOT("2xFi22.2",
[
"factor group of BM9, needed in the construction of 2^2.Fi22.2"
],
0,
0,
0,
[(106,107)(218,219),(60,172)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)
(67,179)(68,180)(69,181)(70,182)(71,183)(72,184)(73,185)(74,186)(75,187)(76,
188)(77,189)(78,190)(79,191)(80,192)(81,193)(82,194)(83,195)(84,196)(85,197)
(86,198)(87,199)(88,200)(89,201)(90,202)(91,203)(92,204)(93,205)(94,206)(95,
207)(96,208)(97,209)(98,210)(99,211)(100,212)(101,213)(102,214)(103,215)(104,
216)(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)],
["ConstructDirectProduct",[["Cyclic",2],["Fi22.2"]]]);

MOT("2x2.Fi22",
[
"subquotient of 2.BM9, needed in the construction of 2^2.Fi22.2"
],
0,
0,
0,
[(95,97)(96,98)(209,211)(210,212),(93,94)(207,208),(85,87)(86,88)(199,201)
(200,202),(115,116)(117,118)(119,120)(122,123)(124,125)(126,127)(128,129)(131,
132)(134,135)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(150,151)
(152,153)(154,155)(156,157)(158,159)(160,161)(165,166)(167,168)(169,170)(171,
172)(173,174)(175,176)(177,178)(179,180)(182,183)(185,186)(187,188)(189,190)
(191,192)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(209,210)(211,
212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(227,228),(63,65)
(64,66)(107,109)(108,110)(177,179)(178,180)(221,223)(222,224),(3,4)(17,18)(25,
26)(27,28)(33,34)(36,37)(42,43)(51,52)(59,60)(71,72)(73,75)(74,76)(81,82)(89,
90)(95,96)(97,98)(99,100)(103,104)(107,108)(109,110)(113,114)(117,118)(131,
132)(139,140)(141,142)(147,148)(150,151)(156,157)(165,166)(173,174)(185,186)
(187,189)(188,190)(195,196)(203,204)(209,210)(211,212)(213,214)(217,218)(221,
222)(223,224)(227,228)],
["ConstructDirectProduct",[["Cyclic",2],["2.Fi22"]]]);
ALF("2x2.Fi22","2xFi22",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,8,9,10,10,11,12,12,
13,14,14,15,15,16,16,17,17,18,18,19,19,20,21,21,22,22,23,23,24,24,25,25,
26,26,27,28,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,39,39,
40,41,41,42,42,43,43,44,44,45,46,47,47,48,48,49,49,50,50,51,51,52,52,53,
54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,64,65,65,66,66,67,
67,68,68,69,70,70,71,71,72,72,73,73,74,75,75,76,77,77,78,79,79,80,80,81,
81,82,82,83,83,84,84,85,86,86,87,87,88,88,89,89,90,90,91,91,92,93,94,95,
95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,103,104,104,105,106,
106,107,107,108,108,109,109,110,111,112,112,113,113,114,114,115,115,116,
116,117,117,118,119,120,120,121,121,122,122,123,123,124,124,125,125,126,
126,127,127,128,129,130,130]);
ALF("2x2.Fi22","2^2.Fi22.2",[1,2,3,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,
17,18,19,20,21,22,23,23,24,24,25,26,27,28,29,29,30,31,31,32,33,34,35,36,
36,37,38,39,40,41,42,43,44,44,45,46,47,48,49,50,51,51,52,53,54,55,54,55,
56,57,58,59,60,60,61,62,61,62,63,64,65,66,67,67,68,69,70,71,70,71,72,72,
73,74,75,75,76,77,77,76,78,78,79,80,81,81,82,83,84,85,85,84,86,87,88,88,
89,89,90,91,92,92,93,94,94,95,95,96,96,97,97,98,99,100,101,102,102,103,
104,104,105,106,107,108,109,109,110,110,111,112,113,114,115,116,116,117,
117,118,119,120,120,121,121,122,123,124,125,126,127,127,128,128,129,129,
130,131,132,132,133,134,134,133,135,136,136,137,138,139,140,141,141,140,
142,142,143,144,145,146,147,147,148,149,149,148,150,151,152,152,153,153,
154,155,154,155,156,157,158,158,159,160,161,161,162,163,162,163,164,165,
166,167]);
ALF("2x2.Fi22","Fi22",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,8,9,10,10,11,12,12,13,
14,14,15,15,16,16,17,17,18,18,19,19,20,21,21,22,22,23,23,24,24,25,25,26,
26,27,28,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,39,39,40,
41,41,42,42,43,43,44,44,45,46,47,47,48,48,49,49,50,50,51,51,52,52,53,54,
55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,64,65,65,1,1,2,2,3,3,4,
5,5,6,6,7,7,8,8,9,10,10,11,12,12,13,14,14,15,15,16,16,17,17,18,18,19,19,
20,21,21,22,22,23,23,24,24,25,25,26,26,27,28,29,30,30,31,31,32,32,33,33,
34,34,35,35,36,36,37,37,38,39,39,40,41,41,42,42,43,43,44,44,45,46,47,47,
48,48,49,49,50,50,51,51,52,52,53,54,55,55,56,56,57,57,58,58,59,59,60,60,
61,61,62,62,63,64,65,65]);

MOT("2^2.Fi22.2",
[
"table of a factor group of 2.BM9, of structure (2x2.Fi22).2"
],
[516494013235200,516494013235200,73574645760,424673280,424673280,7077888,
156764160,156764160,20155392,20155392,1119744,1119744,139968,139968,442368,
184320,49152,36864,36864,12288,4800,4800,622080,373248,82944,82944,55296,55296
,15552,13824,13824,13824,13824,6912,6912,1728,1728,1728,336,336,1536,1536,512,
128,2592,2592,1296,1296,216,216,240,320,320,88,88,3456,4608,4608,2304,1152,576
,576,1152,1152,384,384,288,288,288,52,52,56,240,240,64,432,432,216,288,288,80,
168,168,88,88,192,192,120,258247006617600,147149291520,147149291520,212336640,
7077888,78382080,10077696,559872,69984,442368,368640,368640,49152,18432,12288,
2400,1244160,1244160,746496,746496,41472,27648,31104,31104,13824,27648,27648,
6912,3456,3456,3456,864,168,1536,1536,512,256,256,1296,648,108,480,480,160,88,
88,3456,2304,2304,2304,2304,576,576,576,384,384,576,576,144,52,52,112,112,120,
64,432,432,432,432,144,160,160,84,88,88,192,192,240,240,4180377600,13271040,
11612160,2654208,491520,36864,24576,6144,622080,145152,46656,17280,15552,13824
,5184,2592,2592,1728,864,1536,1536,1536,384,2400,240,160,13824,5184,2304,1728,
1536,1152,576,288,192,48,168,56,64,216,216,72,36,80,192,192,96,96,48,120,120,
72,84,4180377600,13271040,11612160,2654208,491520,36864,24576,6144,622080,
145152,46656,17280,15552,13824,5184,2592,2592,1728,864,1536,1536,1536,384,2400
,240,160,13824,5184,2304,1728,1536,1152,576,288,192,48,168,56,64,216,216,72,36
,80,192,192,96,96,48,120,120,72,84],
[,[1,1,1,1,1,1,7,7,9,9,11,11,13,13,5,4,5,6,6,4,21,21,7,9,9,9,7,7,11,7,9,11,11,
11,11,11,13,13,39,39,15,15,17,18,45,45,47,47,49,49,21,21,21,54,54,26,28,28,28,
27,31,31,32,32,26,27,34,38,38,70,70,39,73,73,43,45,45,47,45,45,52,82,82,54,54,
58,57,73,1,1,1,1,1,7,9,11,13,5,4,4,5,6,4,21,7,7,9,9,9,7,11,11,7,9,9,11,11,11,
11,13,39,15,15,17,18,18,45,47,49,21,21,21,54,54,26,28,28,27,27,31,31,32,26,27,
34,34,38,70,70,39,39,73,43,45,45,47,47,45,52,52,82,54,54,58,57,73,73,1,1,2,5,5
,4,5,6,7,7,9,8,11,7,10,13,13,11,12,15,15,17,19,21,22,21,28,26,28,35,28,27,25,
34,35,38,39,40,43,45,47,48,49,53,58,57,65,65,64,73,74,80,82,2,2,1,4,4,5,4,6,8,
8,10,7,12,8,9,14,14,12,11,15,15,17,18,22,21,22,27,25,27,34,27,28,26,35,34,37,
40,39,43,46,48,47,50,52,57,58,65,65,63,74,73,79,83],[1,2,3,4,5,6,1,2,1,2,1,2,1
,2,15,16,17,18,19,20,21,22,3,3,4,5,4,5,3,6,6,6,6,4,5,6,6,6,39,40,41,42,43,44,9
,10,9,10,13,14,51,52,53,54,55,15,15,15,15,16,19,18,18,19,17,20,16,18,19,70,71,
72,21,22,75,24,24,24,25,26,81,39,40,84,85,42,41,51,89,90,91,92,93,89,89,89,89,
98,99,100,101,102,103,104,90,91,90,91,92,92,90,91,93,93,93,93,92,93,93,93,121,
122,123,124,125,126,95,95,97,130,131,132,133,134,98,98,98,99,100,102,102,102,
101,103,99,100,102,148,149,150,151,104,153,107,108,107,108,109,159,160,121,162
,163,123,122,130,131,168,169,170,171,172,173,174,175,168,168,168,170,168,169,
170,168,169,169,170,187,188,189,190,191,192,193,171,171,171,171,172,173,173,
173,174,175,204,205,206,178,178,182,184,211,187,188,189,189,190,191,192,195,
204,221,222,223,224,225,226,227,228,221,221,221,223,221,222,223,221,222,222,
223,240,241,242,243,244,245,246,224,224,224,224,225,226,226,226,227,228,257,
258,259,231,231,235,237,264,240,241,242,242,243,244,245,248,257],,[1,2,3,4,5,6
,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,3,4,5,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,7,8,75,77,76,78,79,80,16,82,83,84,85,86,87
,23,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,89,105,106,107,108,109,
110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,
129,90,91,92,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,149,
148,150,151,94,153,154,155,156,157,158,99,100,161,162,163,164,165,105,106,168,
169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,
188,189,190,168,170,169,194,195,196,197,198,199,200,201,202,203,204,205,206,
207,208,209,210,172,212,213,215,214,216,176,179,219,220,221,222,223,224,225,
226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,221,
223,222,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,
225,265,266,268,267,269,229,232,272,273],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,1,2,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,3,73,74,75,76,77,78,79,80,81,7,8,85,84,86,87,88,89,90,91,92,93,94,
95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115
,116,117,118,119,120,89,122,123,124,125,126,127,128,129,130,131,132,134,133,
135,136,137,138,139,140,141,142,143,144,145,146,147,149,148,90,91,152,153,154,
155,156,157,158,159,160,94,162,163,164,165,166,167,168,169,170,171,172,173,174
,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,
194,195,196,197,198,199,200,201,202,203,168,170,206,207,208,209,210,211,212,
213,215,214,216,217,218,219,177,221,222,223,224,225,226,227,228,229,230,231,
232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,
251,252,253,254,255,256,221,223,259,260,261,262,263,264,265,266,268,267,269,
270,271,272,230],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,1,2,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75
,77,76,78,79,80,81,82,83,3,3,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101
,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,
121,122,123,124,125,126,127,128,129,130,131,132,89,89,135,136,137,138,139,140,
141,142,143,144,145,146,147,149,148,150,151,152,153,154,155,156,157,158,159,
160,161,90,91,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,
199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,
218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,
237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,
256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273],,[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,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68,69,1,2,72,73,74,75,76,77,78,79,80,81,82,83
,85,84,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
126,127,128,129,130,131,132,134,133,135,136,137,138,139,140,141,142,143,144,
145,146,147,89,89,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,
165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,
203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,
222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,
241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,
260,261,262,263,264,265,266,267,268,269,270,271,272,273]],
0,
[(214,215)(267,268),(148,149),
( 90, 91)( 99,100)(105,106)(107,108)(111,112)(114,115)(118,119)(125,126)
(130,131)(133,134)(138,139)(140,141)(145,146)(150,151)(154,155)(156,157)
(159,160)(162,163)(166,167),( 84, 85)(133,134),(76,77)],
["ConstructMixed","2x2.Fi22","2xFi22.2",[[66,180],[67,182],[68,181],[69,
184],[70,183],[71,186],[72,185],[73,188],[74,187],[75,189],[76,191],[77,190],
[78,192],[79,193],[80,194],[81,195],[82,197],[83,196],[84,198],[85,200],[86,
199],[87,202],[88,201],[89,204],[90,203],[91,206],[92,205],[93,208],[94,207],
[95,210],[96,209],[97,212],[98,211],[99,213],[100,215],[101,214],[102,217],
[103,216],[104,218],[105,220],[106,219],[107,222],[108,221],[109,224],[110,
223],[111,226],[112,225],[113,228],[114,227]],()]);
ALF("2^2.Fi22.2","2xFi22.2",[1,1,2,3,3,4,5,5,6,6,7,7,8,8,9,10,11,12,12,13,
14,14,15,16,17,17,18,18,19,20,21,22,22,23,23,24,25,25,26,26,27,28,29,30,
31,31,32,32,33,33,34,35,35,36,36,37,38,38,39,40,41,41,42,42,43,44,45,46,
46,47,47,48,49,49,50,51,51,52,53,53,54,55,55,56,56,57,58,59,113,114,114,
115,116,117,118,119,120,121,122,122,123,124,125,126,127,127,128,128,129,
130,131,131,132,133,133,134,135,136,136,137,138,139,140,141,142,142,143,
144,145,146,146,147,148,148,149,150,151,152,152,153,153,154,155,156,157,
157,158,159,159,160,160,161,162,163,163,164,164,165,166,166,167,168,168,
169,170,171,171,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,112,172,173,174,175,176,177,178,
179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,
197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,
215,216,217,218,219,220,221,222,223,224]);
ALF("2^2.Fi22.2","Fi22.2",[1,1,2,3,3,4,5,5,6,6,7,7,8,8,9,10,11,12,12,13,
14,14,15,16,17,17,18,18,19,20,21,22,22,23,23,24,25,25,26,26,27,28,29,30,
31,31,32,32,33,33,34,35,35,36,36,37,38,38,39,40,41,41,42,42,43,44,45,46,
46,47,47,48,49,49,50,51,51,52,53,53,54,55,55,56,56,57,58,59,1,2,2,3,4,5,6,
7,8,9,10,10,11,12,13,14,15,15,16,16,17,18,19,19,20,21,21,22,23,24,24,25,
26,27,28,29,30,30,31,32,33,34,34,35,36,36,37,38,39,40,40,41,41,42,43,44,
45,45,46,47,47,48,48,49,50,51,51,52,52,53,54,54,55,56,56,57,58,59,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
107,108,109,110,111,112,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,
76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112]);

MOT("3x2.Fi22.2",
[
"subgroup of 2.BM9, needed in its construction"
],
0,
0,
0,
[(143,144)(293,294)(443,444),(141,142)(291,292)(441,442),
(84,85)(234,235)(384,385),(151,301)(152,302)(153,303)(154,304)(155,305)
(156,306)(157,307)(158,308)(159,309)(160,310)(161,311)(162,312)(163,313)
(164,314)(165,315)(166,316)(167,317)(168,318)(169,319)(170,320)(171,321)
(172,322)(173,323)(174,324)(175,325)(176,326)(177,327)(178,328)(179,329)
(180,330)(181,331)(182,332)(183,333)(184,334)(185,335)(186,336)(187,337)
(188,338)(189,339)(190,340)(191,341)(192,342)(193,343)(194,344)(195,345)
(196,346)(197,347)(198,348)(199,349)(200,350)(201,351)(202,352)(203,353)
(204,354)(205,355)(206,356)(207,357)(208,358)(209,359)(210,360)(211,361)
(212,362)(213,363)(214,364)(215,365)(216,366)(217,367)(218,368)(219,369)
(220,370)(221,371)(222,372)(223,373)(224,374)(225,375)(226,376)(227,377)
(228,378)(229,379)(230,380)(231,381)(232,382)(233,383)(234,384)(235,385)
(236,386)(237,387)(238,388)(239,389)(240,390)(241,391)(242,392)(243,393)
(244,394)(245,395)(246,396)(247,397)(248,398)(249,399)(250,400)(251,401)
(252,402)(253,403)(254,404)(255,405)(256,406)(257,407)(258,408)(259,409)
(260,410)(261,411)(262,412)(263,413)(264,414)(265,415)(266,416)(267,417)
(268,418)(269,419)(270,420)(271,421)(272,422)(273,423)(274,424)(275,425)
(276,426)(277,427)(278,428)(279,429)(280,430)(281,431)(282,432)(283,433)
(284,434)(285,435)(286,436)(287,437)(288,438)(289,439)(290,440)(291,441)
(292,442)(293,443)(294,444)(295,445)(296,446)(297,447)(298,448)(299,449)
(300,450),( 98, 99)(105,106)(107,108)(127,128)(132,133)(136,137)(147,148)
(149,150)(248,249)(255,256)(257,258)(277,278)(282,283)(286,287)(297,298)
(299,300)(398,399)(405,406)(407,408)(427,428)(432,433)(436,437)(447,448)
(449,450),( 76, 77)(147,148)(226,227)(297,298)(376,377)(447,448)],
["ConstructDirectProduct",[["Cyclic",3],["2.Fi22.2"]]]);
ALF("3x2.Fi22.2","2.Fi22.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,
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,
129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,
147,148,149,150,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,
132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,
150,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,
99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,
135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150]);
ALF("3x2.Fi22.2","(S3x2.Fi22).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
89,90,91,92,93,94,95,96,97,98,98,99,100,101,102,103,104,104,105,105,106,
107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,
124,125,126,127,128,128,129,130,131,131,132,133,134,135,136,137,137,138,
139,140,140,141,141,142,143,144,145,146,147,148,149,150,151,152,153,154,
155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,
173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,
191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,
209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,
227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,
245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,
263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,
281,282,283,284,285,286,287,288,289,290,291,142,143,144,145,146,147,148,
149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,
167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,
185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,
203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,
221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,
240,239,241,242,243,244,245,247,246,249,248,250,251,252,253,254,255,256,
257,258,259,260,261,262,263,264,265,266,267,269,268,270,271,272,274,273,
275,276,278,277,279,280,281,282,283,285,284,286,287,289,288,291,290]);

MOT("(S3x2.Fi22).2",
[
"9th maximal subgroup of 2.B",
],
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552960,147456,110592,110592,36864,14400,14400,1866240,1119744,248832,248832,
165888,165888,46656,41472,41472,41472,41472,20736,20736,5184,5184,5184,1008,
1008,4608,4608,1536,384,7776,7776,3888,3888,648,648,720,960,960,264,264,10368,
13824,13824,6912,3456,1728,1728,3456,3456,1152,1152,864,864,864,156,156,168,
720,720,192,1296,1296,648,864,864,240,504,504,264,264,576,576,360,12541132800,
39813120,34836480,7962624,1474560,110592,73728,18432,1866240,435456,139968,
51840,46656,41472,15552,7776,7776,5184,2592,4608,4608,4608,1152,7200,720,480,
41472,15552,6912,5184,4608,3456,1728,864,576,144,504,168,192,648,648,216,108,
240,576,576,288,288,144,360,360,216,252,774741019852800,774741019852800,
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30233088,1679616,1679616,209952,209952,663552,276480,73728,55296,55296,18432,
7200,7200,933120,559872,124416,124416,82944,82944,23328,20736,20736,20736,
20736,10368,10368,2592,2592,2592,504,504,2304,2304,768,192,3888,3888,1944,1944
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576,432,432,432,78,78,84,360,360,96,648,648,324,432,432,120,252,252,132,132,
288,288,180,6270566400,19906560,17418240,3981312,737280,55296,36864,9216,
933120,435456,435456,69984,25920,23328,20736,7776,7776,7776,7776,7776,2592,
1296,2304,2304,2304,576,3600,360,240,20736,7776,3456,2592,2304,1728,864,432,
288,144,144,252,84,96,648,648,324,108,108,108,120,288,288,144,144,144,144,180,
180,216,216,252,252,258247006617600,147149291520,147149291520,212336640,
7077888,78382080,10077696,559872,69984,442368,368640,368640,49152,18432,12288,
2400,1244160,1244160,746496,746496,41472,27648,31104,31104,13824,27648,27648,
6912,3456,3456,3456,864,168,1536,1536,512,256,256,1296,648,108,480,480,160,88,
88,3456,2304,2304,2304,2304,576,576,576,384,384,576,576,144,52,52,112,112,120,
64,432,432,432,432,144,160,160,84,88,88,192,192,240,240,4180377600,13271040,
11612160,2654208,491520,36864,24576,6144,622080,145152,46656,17280,15552,13824
,5184,2592,2592,1728,864,1536,1536,1536,384,2400,240,160,13824,5184,2304,1728,
1536,1152,576,288,192,48,168,56,64,216,216,72,36,80,192,192,96,96,48,120,120,
72,84],
[,[1,1,1,1,1,1,7,7,9,9,11,11,13,13,5,4,5,6,6,4,21,21,7,9,9,9,7,7,11,7,9,11,11,
11,11,11,13,13,39,39,15,15,17,18,45,45,47,47,49,49,21,21,21,54,54,26,28,28,28,
27,31,31,32,32,26,27,34,38,38,70,70,39,73,73,43,45,45,47,45,45,52,82,82,54,54,
58,57,73,1,1,2,5,5,4,5,6,7,7,9,8,11,7,10,13,13,11,12,15,15,17,19,21,22,21,28,
26,28,35,28,27,25,34,35,38,39,40,43,45,47,48,49,53,58,57,65,65,64,73,74,80,82,
142,142,142,142,142,142,148,148,150,150,152,152,154,154,146,145,146,147,147,
145,162,162,148,150,150,150,148,148,152,148,150,152,152,152,152,152,154,154,
180,180,156,156,158,159,186,186,188,188,190,190,162,162,162,195,195,167,169,
169,169,168,172,172,173,173,167,168,175,179,179,211,211,180,214,214,184,186,
186,188,186,186,193,223,223,195,195,199,198,214,142,142,143,146,146,145,146,
147,148,148,148,150,149,152,148,151,154,154,154,154,152,153,156,156,158,160,
162,163,162,169,167,169,176,169,168,166,175,176,179,179,180,181,184,186,186,
188,189,190,190,194,199,198,206,206,205,205,214,215,221,221,223,223,1,1,1,1,1,
7,9,11,13,5,4,4,5,6,4,21,7,7,9,9,9,7,11,11,7,9,9,11,11,11,11,13,39,15,15,17,18
,18,45,47,49,21,21,21,54,54,26,28,28,27,27,31,31,32,26,27,34,34,38,70,70,39,39
,73,43,45,45,47,47,45,52,52,82,54,54,58,57,73,73,2,2,1,4,4,5,4,6,8,8,10,7,12,8
,9,14,14,12,11,15,15,17,18,22,21,22,27,25,27,34,27,28,26,35,34,37,40,39,43,46,
48,47,50,52,57,58,65,65,63,74,73,79,83],[1,2,3,4,5,6,1,2,1,2,1,2,1,2,15,16,17,
18,19,20,21,22,3,3,4,5,4,5,3,6,6,6,6,4,5,6,6,6,39,40,41,42,43,44,9,10,9,10,13,
14,51,52,53,54,55,15,15,15,15,16,19,18,18,19,17,20,16,18,19,70,71,72,21,22,75,
24,24,24,25,26,81,39,40,84,85,42,41,51,89,90,91,92,93,94,95,96,89,89,89,91,89,
90,91,89,90,90,91,108,109,110,111,112,113,114,92,92,92,92,93,94,94,94,95,96,
125,126,127,99,99,103,105,132,108,109,110,110,111,112,113,116,125,1,2,3,4,5,6,
1,2,1,2,1,2,1,2,15,16,17,18,19,20,21,22,3,3,4,5,4,5,3,6,6,6,6,4,5,6,6,6,39,40,
41,42,43,44,9,10,9,10,13,14,51,52,53,54,55,15,15,15,15,16,19,18,18,19,17,20,16
,18,19,70,71,72,21,22,75,24,24,24,25,26,81,39,40,84,85,42,41,51,89,90,91,92,93
,94,95,96,89,89,89,89,91,89,90,91,89,89,90,90,90,91,108,109,110,111,112,113,
114,92,92,92,92,93,94,94,94,95,96,96,125,126,127,99,99,99,103,105,105,132,108,
109,110,110,111,111,112,113,116,116,125,125,292,293,294,295,296,292,292,292,
292,301,302,303,304,305,306,307,293,294,293,294,295,295,293,294,296,296,296,
296,295,296,296,296,324,325,326,327,328,329,298,298,300,333,334,335,336,337,
301,301,301,302,303,305,305,305,304,306,302,303,305,351,352,353,354,307,356,
310,311,310,311,312,362,363,324,365,366,326,325,333,334,371,372,373,374,375,
376,377,378,371,371,371,373,371,372,373,371,372,372,373,390,391,392,393,394,
395,396,374,374,374,374,375,376,376,376,377,378,407,408,409,381,381,385,387,
414,390,391,392,392,393,394,395,398,407],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,1,2,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47,48,49,50,3,4,5,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,
69,70,71,72,7,8,75,77,76,78,79,80,16,82,83,84,85,86,87,23,89,90,91,92,93,94,95
,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,89,91,90,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,93,133,134,136,135
,137,97,100,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,
156,157,158,159,160,161,142,143,164,165,166,167,168,169,170,171,172,173,174,
175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,144,145,
146,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,
213,148,149,216,218,217,219,220,221,157,223,224,225,226,227,228,164,230,231,
232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,
251,252,253,254,255,230,232,231,259,260,261,262,263,264,265,266,267,268,269,
270,271,272,273,274,275,276,277,278,234,280,281,283,282,284,285,238,242,289,
288,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,292,
308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,
327,328,329,330,331,332,293,294,295,336,337,338,339,340,341,342,343,344,345,
346,347,348,349,350,352,351,353,354,297,356,357,358,359,360,361,302,303,364,
365,366,367,368,308,309,371,372,373,374,375,376,377,378,379,380,381,382,383,
384,385,386,387,388,389,390,391,392,393,371,373,372,397,398,399,400,401,402,
403,404,405,406,407,408,409,410,411,412,413,375,415,416,418,417,419,379,382,
422,423],,[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,
26,27,28,29,30,31,32,33,34,35,36,37,38,1,2,41,42,43,44,45,46,47,48,49,50,51,52
,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,3,73,74,75,76,77,78,
79,80,81,7,8,85,84,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,
104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,89,91,127,128,129,130,131,132,133,134,136,135,137,138,139,140,98,142,
143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,
162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,142,
143,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,
200,201,202,203,204,205,206,207,208,209,210,211,212,144,214,215,216,217,218,
219,220,221,222,148,149,226,225,227,228,229,230,231,232,233,234,235,236,237,
238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,
257,258,259,260,261,262,263,264,265,266,267,268,269,230,232,272,273,274,275,
276,277,278,279,280,281,283,282,285,284,286,287,288,289,239,240,292,293,294,
295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,
314,315,316,317,318,319,320,321,322,323,292,325,326,327,328,329,330,331,332,
333,334,335,337,336,338,339,340,341,342,343,344,345,346,347,348,349,350,352,
351,293,294,355,356,357,358,359,360,361,362,363,297,365,366,367,368,369,370,
371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,
390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,371,373,
409,410,411,412,413,414,415,416,418,417,419,420,421,422,380],,,,[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,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,1,2,56,57,58,59,60
,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,77,76,78,79,80,81,82,83,3,3,86,
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,
129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,
167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,
186,187,188,189,190,191,192,193,194,142,143,197,198,199,200,201,202,203,204,
205,206,207,208,209,210,211,212,213,214,215,216,218,217,219,220,221,222,223,
224,144,144,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,
243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,
262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,
281,282,283,285,284,286,287,289,288,290,291,292,293,294,295,296,297,298,299,
300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,
319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,292,292,
338,339,340,341,342,343,344,345,346,347,348,349,350,352,351,353,354,355,356,
357,358,359,360,361,362,363,364,293,294,367,368,369,370,371,372,373,374,375,
376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,
395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,
414,415,416,417,418,419,420,421,422,423],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41
,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67
,68,69,1,2,72,73,74,75,76,77,78,79,80,81,82,83,85,84,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,
134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,
172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,
191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,
210,142,143,213,214,215,216,217,218,219,220,221,222,223,224,226,225,227,228,
229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,
248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,
267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,
286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,
305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,
324,325,326,327,328,329,330,331,332,333,334,335,337,336,338,339,340,341,342,
343,344,345,346,347,348,349,350,292,292,353,354,355,356,357,358,359,360,361,
362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,
381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,
400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,
419,420,421,422,423]],
0,
[(351,352),(284,285),
(239,240)(246,247)(248,249)(268,269)(273,274)(277,278)(288,289)(290,291),
(293,294)(302,303)(308,309)(310,311)(314,315)(317,318)(321,322)(328,329)
(333,334)(336,337)(341,342)(343,344)(348,349)(353,354)(357,358)(359,360)
(362,363)(365,366)(369,370),
( 84, 85)(225,226)(293,294)(302,303)(308,309)(310,311)(314,315)(317,318)
(321,322)(328,329)(333,334)(341,342)(343,344)(348,349)(353,354)(357,358)
(359,360)(362,363)(365,366)(369,370),
(135,136)(282,283)(293,294)(302,303)(308,309)(310,311)(314,315)(317,318)
(321,322)(328,329)(333,334)(336,337)(341,342)(343,344)(348,349)(353,354)
(357,358)(359,360)(362,363)(365,366)(369,370)(417,418),
( 76, 77)(135,136)(217,218)(282,283)(288,289)(293,294)(302,303)(308,309)
(310,311)(314,315)(317,318)(321,322)(328,329)(333,334)(336,337)(341,342)
(343,344)(348,349)(353,354)(357,358)(359,360)(362,363)(365,366)(369,370)
(417,418)],
["ConstructMixed","3x2.Fi22.2","2^2.Fi22.2",[[151,301],[152,302],[153,303],
[154,304],[155,305],[156,306],[157,307],[158,308],[159,309],[160,310],[161,
311],[162,312],[163,313],[164,314],[165,315],[166,316],[167,317],[168,318],
[169,319],[170,320],[171,321],[172,322],[173,323],[174,324],[175,325],[176,
326],[177,327],[178,328],[179,329],[180,330],[181,331],[182,332],[183,333],
[184,334],[185,335],[186,336],[187,337],[188,338],[189,339],[190,340],[191,
341],[192,342],[193,343],[194,344],[195,345],[196,346],[197,347],[198,348],
[199,349],[200,350],[201,351],[202,352],[203,353],[204,354],[205,355],[206,
356],[207,357],[208,358],[209,359],[210,360],[211,361],[212,362],[213,363],
[214,364],[215,365],[216,366],[217,367],[218,368],[219,369],[220,370],[221,
371],[222,372],[223,373],[224,374],[225,375],[226,376],[227,377],[228,378],
[229,379],[230,380],[231,381],[232,382],[233,383],[234,384],[235,385],[236,
386],[237,387],[238,388],[239,389],[240,390],[241,391],[242,392],[243,393],
[244,394],[245,395],[246,396],[247,397],[248,398],[249,399],[250,400],[251,
401],[252,402],[253,403],[254,404],[255,405],[256,406],[257,407],[258,408],
[259,409],[260,410],[261,411],[262,412],[263,414],[264,413],[265,415],[266,
416],[267,417],[268,418],[269,420],[270,419],[271,421],[272,423],[273,422],
[274,425],[275,424],[276,427],[277,426],[278,429],[279,428],[280,430],[281,
432],[282,431],[283,433],[284,434],[285,435],[286,436],[287,437],[288,438],
[289,439],[290,441],[291,440],[292,442],[293,443],[294,445],[295,444],[296,
446],[297,447],[298,448],[299,449],[300,450]],()]);
ALF("(S3x2.Fi22).2","2^2.Fi22.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,
186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,
204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,1,2,3,
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,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,168,169,170,171,172,173,174,175,176,177,
177,178,179,180,181,182,183,183,184,184,185,186,187,188,189,190,191,192,
193,194,195,196,197,198,199,200,201,202,203,203,204,205,206,207,207,208,
209,210,210,211,212,213,214,215,216,216,217,218,219,219,220,220,89,90,91,
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,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,
237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,
255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,
273]);
ALF("(S3x2.Fi22).2","2.B",[1,2,3,4,5,7,8,9,10,11,8,9,10,11,13,15,14,16,17,
19,23,24,27,31,34,35,29,30,28,36,39,36,36,29,30,32,37,38,41,42,47,44,46,
52,60,61,60,61,60,61,62,63,64,71,72,74,76,76,76,77,89,88,83,84,87,86,81,
78,79,97,98,100,105,106,109,120,120,121,122,123,134,141,142,143,144,151,
153,179,3,7,6,13,12,15,18,20,28,28,31,33,27,32,40,31,39,36,33,45,47,43,49,
62,65,68,73,74,73,73,75,81,85,77,82,92,99,101,110,121,120,127,124,130,152,
154,156,156,159,178,180,205,219,8,9,27,29,30,36,8,9,8,9,10,11,10,11,76,77,
80,83,84,86,105,106,28,27,29,30,29,30,31,32,36,38,37,34,35,39,39,39,141,
142,153,151,157,160,60,61,60,61,58,59,179,181,182,198,199,76,76,76,73,81,
84,83,78,79,80,86,85,88,89,211,212,220,105,106,232,120,120,121,122,123,
241,141,142,244,245,151,154,178,28,32,33,73,75,81,82,91,27,28,28,28,33,31,
36,33,31,31,37,38,39,40,152,154,155,159,178,180,183,73,73,76,74,75,77,81,
85,90,94,95,219,221,233,121,121,120,127,126,125,240,152,153,155,155,158,
158,179,180,205,205,219,219,3,4,5,7,7,27,31,28,31,14,19,19,18,20,19,62,29,
30,34,35,39,36,29,30,36,38,37,32,32,36,36,39,100,44,47,50,52,52,120,121,
121,63,64,68,144,143,87,80,80,86,86,94,95,91,90,86,86,86,92,169,169,102,
103,179,113,122,123,122,123,124,135,135,220,145,146,153,151,181,182,6,6,7,
15,15,18,19,22,33,33,40,32,33,33,39,40,40,33,36,45,47,48,52,65,68,65,81,
85,81,77,81,82,90,82,86,93,101,104,113,127,127,124,127,134,152,154,161,
161,160,180,183,206,221],[
"fusion map is unique up to table automorphisms"
]);
ALF("(S3x2.Fi22).2","2^2.Fi22.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,
186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,
204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,1,2,3,
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,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,168,169,170,171,172,173,174,175,176,177,
177,178,179,180,181,182,183,183,184,184,185,186,187,188,189,190,191,192,
193,194,195,196,197,198,199,200,201,202,203,203,204,205,206,207,207,208,
209,210,210,211,212,213,214,215,216,216,217,218,219,219,220,220,89,90,91,
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,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,
237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,
255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,
273]);
ALF("(S3x2.Fi22).2","S3xFi22.2",[1,1,2,3,3,4,5,5,6,6,7,7,8,8,9,10,11,12,
12,13,14,14,15,16,17,17,18,18,19,20,21,22,22,23,23,24,25,25,26,26,27,28,
29,30,31,31,32,32,33,33,34,35,35,36,36,37,38,38,39,40,41,41,42,42,43,44,
45,46,46,47,47,48,49,49,50,51,51,52,53,53,54,55,55,56,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112,113,113,114,115,115,116,117,117,118,118,119,119,120,
120,121,122,123,124,124,125,126,126,127,128,129,129,130,130,131,132,133,
134,134,135,135,136,137,137,138,138,139,140,141,142,143,143,144,144,145,
145,146,147,147,148,148,149,150,150,151,152,153,153,154,154,155,156,157,
158,158,159,159,160,161,161,162,163,163,164,165,165,166,167,167,168,168,
169,170,171,172,173,174,175,176,177,178,179,180,181,181,182,183,184,185,
186,187,187,188,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
202,203,204,205,206,207,207,208,209,210,211,211,212,213,214,214,215,216,
217,218,219,220,220,221,222,223,223,224,224,225,226,226,227,228,229,230,
231,232,233,234,234,235,236,237,238,239,239,240,240,241,242,243,243,244,
245,245,246,247,248,248,249,250,251,252,253,254,254,255,256,257,258,258,
259,260,260,261,262,263,264,264,265,265,266,267,268,269,269,270,271,271,
272,272,273,274,275,275,276,276,277,278,278,279,280,280,281,282,283,283,
284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,
302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,
320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336]);
ALN("(S3x2.Fi22).2",["2.BM9"]);

MOT("2xFi23",
[
"3rd maximal subgroup of 2.B"
],
0,
0,
0,
[( 78, 79)(176,177),( 63, 64)(161,162),( 57, 58)( 85, 86)( 95, 96)(155,156)
(183,184)(193,194),( 80, 81)(178,179)],
["ConstructDirectProduct",[["Cyclic",2],["Fi23"]]]);
ALF("2xFi23","2.B",[1,3,4,7,8,10,8,10,15,16,19,20,23,27,31,29,34,28,38,32,
39,36,31,29,36,32,37,39,41,52,52,53,58,60,60,58,60,62,63,68,71,77,78,83,
85,88,92,83,83,86,81,95,91,88,86,94,97,97,100,102,105,105,115,115,118,120,
121,124,126,122,122,125,121,134,135,141,145,143,144,147,149,160,162,160,
169,169,170,175,181,179,183,203,207,206,211,211,220,241,2,3,5,7,9,11,9,11,
15,17,19,20,24,27,31,30,35,28,37,32,39,36,31,30,36,32,38,39,42,52,52,54,
59,61,61,59,61,62,64,68,72,77,79,84,85,89,92,84,84,86,81,94,91,89,86,95,
98,98,100,103,106,106,115,115,119,120,121,124,125,123,123,126,121,134,135,
142,146,144,143,148,150,160,163,160,169,169,171,175,182,179,183,204,208,
206,212,212,220,241],[
"fusion map is unique up to table autom."
]);
ALN("2xFi23",["2.BM3"]);

MOT("2xTh",
[
"5th maximal subgroup of 2.B"
],
0,
0,
0,
[(47,48)(95,96),(42,43)(90,91),(37,38)(85,86),(34,35)(82,83),(25,26)(40,41)
(73,74)(88,89),(19,20)(32,33)(45,46)(67,68)(80,81)(93,94)],
["ConstructDirectProduct",[["Cyclic",2],["Th"]]]);
ALF("2xTh","2.B",[1,7,8,10,10,16,22,25,37,36,39,41,52,57,58,58,60,69,83,
83,88,93,97,104,107,107,126,124,128,140,141,160,160,165,165,170,170,170,
176,184,184,190,192,207,207,207,211,211,2,7,9,11,11,17,22,26,38,36,39,42,
52,57,59,59,61,70,84,84,89,93,98,104,108,108,125,124,129,140,142,160,160,
165,165,171,171,171,177,185,185,191,193,208,208,208,212,212],[
"fusion map is unique up to table autom."
]);
ALN("2xTh",["2.BM5"]);

MOT("2x47:23",
[
"30th maximal subgroup of 2.B"
],
0,
0,
0,
[( 2, 3)(27,28),( 4, 5, 7,11,19,12,21,16, 6, 9,15)( 8,13,23,20,14,25,24,22,18,
10,17)(29,30,32,36,44,37,46,41,31,34,40)(33,38,48,45,39,50,49,47,43,35,42),
( 4, 8, 5,13, 7,23,11,20,19,14,12,25,21,24,16,22, 6,18, 9,10,15,17)(29,33,30,
38,32,48,36,45,44,39,37,50,46,49,41,47,31,43,34,35,40,42)],
["ConstructDirectProduct",[["Cyclic",2],["47:23"]]]);
ALF("2x47:23","2.B",[1,228,230,147,147,147,147,149,147,149,147,147,149,
149,147,147,149,149,147,149,147,149,149,149,149,2,229,231,148,148,148,148,
150,148,150,148,148,150,150,148,148,150,150,148,150,148,150,150,150,150],[
"fusion map is unique up to table autom."
]);
ALF("2x47:23","M",[1,139,140,76,76,76,76,77,76,77,76,76,77,77,76,76,77,77,
76,77,76,77,77,77,77,2,185,186,137,137,137,137,138,137,138,137,137,138,
138,137,137,138,138,137,138,137,138,138,138,138],[
"fusion map is unique up to table autom."
]);
ALN("2x47:23",["2.BM30","MN47"]);

MOT("L3(3)xD8",
[
"factor group of a maximal subgroup 3^(3+6):(L3(3)xD8) of O8+(3).D8"
],
0,
0,
0,
[(31,36)(32,37)(33,38)(34,39)(35,40),(41,46)(42,47)(43,48)(44,49)(45,50)(51,
56)(52,57)(53,58)(54,59)(55,60),(41,51,46,56)(42,52,47,57)(43,53,48,58)(44,54,
49,59)(45,55,50,60),( 4, 5)( 9,10)(14,15)(19,20)(24,25)(29,30)(34,35)(39,40)
(44,45)(49,50)(54,55)(59,60)],
["ConstructDirectProduct",[["L3(3)"],["Dihedral",8]]]);

MOT("5:4xHS.2",
[
"15th maximal subgroup of B"
],
0,
0,
0,
[(37,38)(76,77)(115,116)(154,155)(193,194),(79,157)(80,158)(81,159)(82,160)
(83,161)(84,162)(85,163)(86,164)(87,165)(88,166)(89,167)(90,168)(91,169)(92,
170)(93,171)(94,172)(95,173)(96,174)(97,175)(98,176)(99,177)(100,178)(101,179)
(102,180)(103,181)(104,182)(105,183)(106,184)(107,185)(108,186)(109,187)(110,
188)(111,189)(112,190)(113,191)(114,192)(115,193)(116,194)(117,195)],
["ConstructDirectProduct",[["5:4"],["HS.2"]]]);
ALF("5:4xHS.2","B",[1,3,4,6,8,9,14,19,18,18,25,22,31,36,43,51,50,54,57,81,
100,2,5,8,11,16,21,20,24,34,33,48,52,59,76,106,100,100,137,18,49,50,81,99,
102,104,18,18,19,139,140,155,163,164,49,50,177,180,81,99,48,52,101,103,
106,137,138,141,162,161,48,53,181,184,106,101,101,137,8,13,14,57,12,15,17,
100,99,101,66,63,134,40,43,107,104,169,64,180,105,11,14,17,15,16,59,62,66,
40,40,103,104,70,135,106,108,108,181,3,5,4,22,13,13,14,51,49,49,25,27,79,
36,43,53,50,111,63,140,107,5,5,13,14,16,24,27,24,34,33,52,52,66,80,106,
107,107,141,8,13,14,57,12,15,17,100,99,101,66,63,134,40,43,107,104,169,64,
180,105,11,14,17,15,16,59,62,66,40,40,103,104,70,135,106,108,108,181],[
"fusion map is unique"
]);

MOT("S4x2F4(2)'.2",
[
"16th maximal subgroup of B"
],
0,
0,
0,
[(24,25)(53,54)(82,83)(111,112)(140,141),(10,11)(16,17)(18,19)(26,27)(28,29)
(39,40)(45,46)(47,48)(55,56)(57,58)(68,69)(74,75)(76,77)(84,85)(86,87)(97,98)
(103,104)(105,106)(113,114)(115,116)(126,127)(132,133)(134,135)(142,143)(144,
145)],
["ConstructDirectProduct",[["s4"],["2F4(2)'.2"]]]);
ALF("S4x2F4(2)'.2","B",[1,3,5,7,12,10,12,18,28,35,35,41,49,60,75,83,83,8,
8,15,13,32,38,71,71,84,84,99,99,4,4,4,30,17,14,17,50,30,39,39,38,50,72,
129,84,84,14,14,17,14,39,41,72,72,83,83,104,104,6,22,27,7,64,61,64,81,29,
120,120,123,140,68,160,174,174,57,57,70,63,118,122,73,73,175,175,180,180,
2,5,5,23,15,13,15,48,29,39,39,41,52,71,130,87,87,11,11,17,14,37,41,72,72,
87,87,103,103,16,16,16,74,16,16,16,106,74,43,43,45,106,74,176,88,88,16,16,
16,16,43,45,74,74,88,88,106,106],[
"fusion map is unique"
]);
ALN("S4x2F4(2)'.2",["S4x2F4(2)"]);

MOT("A5.2xM22.2",
[
"18th maximal subgroup of B"
],
0,
0,
0,
[(8,9)(20,21)(29,30)(41,42)(50,51)(62,63)(71,72)(83,84)(92,93)(104,105)(113,
114)(125,126)(134,135)(146,147)],
["ConstructDirectProduct",[["A5.2"],["M22.2"]]]);
ALF("A5.2xM22.2","B",[1,3,6,9,14,18,22,31,31,36,54,2,5,11,8,20,34,52,59,
76,76,3,5,22,13,14,49,27,79,79,36,111,5,5,14,13,27,34,52,66,80,80,6,22,7,
58,66,81,26,109,109,116,151,21,24,62,57,23,115,141,65,166,166,18,49,81,
102,104,19,140,155,155,163,177,48,52,103,101,138,162,53,181,184,184,2,5,
21,10,14,48,24,77,77,33,110,4,4,13,11,25,34,50,63,78,78,8,13,57,15,17,101,
63,134,134,40,169,11,14,15,17,62,40,104,70,135,135,20,27,23,61,66,138,29,
167,167,114,183,25,25,63,62,30,115,139,69,168,168],[
"fusion map is unique"
]);
ALN("A5.2xM22.2",["S5xM22.2"]);

MOT("5^2:4S4xS5",
[
"23rd maximal subgroup of B"
],
0,
0,
0,
[(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)
(47,54)(48,55)(49,56)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(92,99)
(93,100)(94,101)(95,102)(96,103)(97,104)(98,105)(113,120)(114,121)(115,122)
(116,123)(117,124)(118,125)(119,126)(127,134)(128,135)(129,136)(130,137)(131,
138)(132,139)(133,140)],
["ConstructDirectProduct",[["Fi22N5"],["A5.2"]]]);
ALF("5^2:4S4xS5","B",[1,4,6,19,2,16,21,5,4,27,53,5,16,24,3,4,22,51,5,16,
24,7,30,7,82,23,74,23,12,17,64,105,15,16,70,12,17,64,105,15,16,70,8,14,57,
100,11,16,59,8,14,57,100,11,16,59,13,14,63,107,14,16,66,13,14,63,107,14,
16,66,12,17,64,105,15,16,70,18,50,81,18,48,106,137,28,30,29,142,29,74,28,
38,41,122,165,41,45,123,38,41,122,165,41,45,123,49,50,140,49,52,106,141,
60,72,68,182,71,74,73,60,72,68,182,71,74,73,99,104,180,99,103,106,181,99,
104,180,99,103,106,181],[
"fusion map is unique"
]);

MOT("3^(3+6):(L3(3)xD8)",
[
"maximal subgroup (novelty) in O8+(3).D8,\n",
"normalizer of a 3^3 subgroup in B,\n",
"computed in March 2003 using the degree 3360 perm. repr. of O8+(3).S4"
],
[884317824,34012224,1889568,1889568,944784,944784,52488,22464,1213056,46656,
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[TENSOR,[148,2]],[2808,-108,54,-108,-27,54,0,0,0,0,0,0,0,0,0,0,24,-12,-12,6,6
,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,48,-6,0,-6,3,0,0,0,54,0,54,0,0,0,-27,0,0,0,0,0,0
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,0],
[TENSOR,[150,2]],[2808,-108,-108,54,54,-27,0,0,0,0,468,-18,-18,9,0,0,-8,4,-2,
4,1,-2,0,0,0,0,0,0,0,-12,6,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-27,-27,54,0,0,0,0,0
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,0,0,0,0,0,0,0],
[TENSOR,[152,2]],[3744,-144,288,288,-144,-144,0,0,-416,16,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,36,-72,72,18,-36,36,-36,0,0,0,0,0,0
,0,-20,16,-2,0,0,0,0,0,0,0,0,0,0,0,-12,6,0,0,0,0,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0],[3744,-144,288,288,-144,-144,0,0,416,-16,1248,-48,96,-48,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-72,-18,-36,18,18,-18,18,0,0,0,0,0,0,0
,-16,2,2,-30,6,-12,6,6,-12,6,0,0,0,0,6,-3,0,0,0,0,2,-1,0,-3,3,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[155,2]],[3744,-144,288,288,-144,-144,0,0,-416,16,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-72,-18,-36,18,18,-18,18,0,0,0,0,0,
0,0,16,-2,-2,-18,-18,36,0,18,0,-18,0,0,0,0,6,-3,0,0,0,0,-2,1,-6,3,3,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],
[TENSOR,[157,2]],[3744,-144,72,-144,-36,72,0,0,0,0,0,0,0,0,0,0,-32,16,16,-8,
-8,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,72,-36,90,0,63,-18,18,0,-36,0,0,0,0
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0,0,0,0,0,0,0,-8,4,-2,-2,4,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[5616,-216,-216,108,108,-54,0,0,0,0,936,-36,-36,18,0,0,16,-8,4,-8,-2,4,0,
0,0,0,0,0,0,24,-12,-12,6,0,0,0,0,0,0,0,0,-108,54,54,0,-27,-27,0,27,0,0,0,0,0,0
,0,0,0,-36,18,18,0,-9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,4,-2,-2,4,1,-5,1,0,0,0,0,0,0,-6,6,0,3,-3,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0],
[TENSOR,[160,2]],[5616,-216,-216,108,108,-54,0,0,0,0,936,-36,-36,18,0,0,16,-8
,4,-8,-2,4,0,0,0,0,0,0,0,24,-12,-12,6,0,0,0,0,0,0,0,0,108,-54,-54,0,27,0,-27,
27,0,0,0,0,0,0,0,0,0,18,-36,18,0,0,-9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2,-2,-5,1,4,1,0,0,0,0,0,0,6,0,-6,-3,0,3,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[162,2]],[5616,-216,-216,108,108,-54,0,0,0,0,936,-36,-36,18,0,0,16,-8
,4,-8,-2,4,0,0,0,0,0,0,0,24,-12,-12,6,0,0,0,0,0,0,0,0,0,0,0,0,0,27,27,-54,0,0,
0,0,0,0,0,0,0,18,18,-36,0,9,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,-8,4,4,1,-2,1,-2,0,0,0,0,0,0,0,-6,6,0,3,-3,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],
[TENSOR,[164,2]],[7488,-288,144,-288,-72,144,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-96,12,0,12,-6,0,144,-72,18,0,-36,-36,36,0,9,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,-3,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
],
[TENSOR,[166,2]],[8424,-324,-324,162,162,-81,0,0,0,0,1404,-54,-54,27,0,0,-24,
12,-6,12,3,-6,0,0,0,0,0,0,0,-36,18,18,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,4,-2,4,1,-2,
0,0,0,0,4,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[168,2]],[14976,-576,288,-576,-144,288,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-144,72,-72,0,-18,36,-36,0,18,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]
,
[(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(133,145)(134,146)
(135,147)(136,148)(137,149)(138,150),(151,156)(152,157)(153,158)(154,159)
(155,160)(161,166)(162,167)(163,168)(164,169)(165,170), 
(151,161,156,166)(152,162,157,167)(153,163,158,168)(154,164,159,169)
(155,165,160,170)]);
ALF("3^(3+6):(L3(3)xD8)","B",[1,7,7,6,6,7,7,16,4,30,2,23,21,23,4,30,5,28,
27,28,29,27,16,74,4,30,30,25,30,5,29,24,28,27,29,4,30,30,30,25,30,7,6,6,7,
7,7,6,7,7,7,47,47,46,74,30,25,30,21,20,23,23,23,23,21,93,30,25,30,7,47,47,
46,47,74,30,97,23,92,93,93,30,97,12,60,64,60,68,64,16,74,17,72,15,70,71,
73,17,72,28,27,27,24,29,28,29,74,74,30,25,30,97,29,27,24,28,29,27,95,96,
30,30,25,30,30,97,41,45,127,38,122,121,41,123,38,121,121,122,41,45,127,38,
122,121,41,123,38,121,121,122,75,176,129,130,129,75,176,129,130,129,75,
176,129,130,129,75,176,129,130,129],[
"fusion map is unique"
]);
ALF("3^(3+6):(L3(3)xD8)","O8+(3).S4",[1,4,4,5,5,6,8,148,39,45,101,107,109,
111,39,45,3,14,16,14,18,16,148,156,39,45,45,47,49,102,112,110,115,117,119,
39,45,45,45,47,49,4,5,5,8,6,8,7,6,8,8,24,24,25,156,45,47,49,109,108,107,
116,116,111,113,136,45,47,49,8,24,24,25,26,157,49,66,116,135,136,138,49,
66,9,28,29,28,31,29,149,158,44,64,106,130,129,133,44,64,14,16,16,19,18,20,
18,156,157,45,47,49,66,112,117,114,115,119,118,137,139,45,49,47,49,49,66,
22,154,165,51,70,68,120,141,51,68,68,70,22,154,165,51,70,68,120,141,51,68,
68,70,33,168,71,142,71,33,168,71,142,71,34,169,72,143,72,34,169,72,143,72],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^(3+6):(L3(3)xD8)","L3(3)xD8",[1,1,1,1,1,1,1,2,3,3,4,4,4,4,5,5,6,6,
6,6,6,6,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,
11,11,11,11,11,11,12,13,13,13,14,14,14,14,14,14,14,14,15,15,15,16,16,16,
16,16,17,18,18,19,19,19,19,20,20,21,21,21,21,21,21,22,22,23,23,24,24,24,
24,25,25,26,26,26,26,26,26,26,27,27,28,28,28,28,29,29,29,29,29,29,29,29,
30,30,30,30,30,30,31,32,32,33,33,33,34,34,35,35,35,35,36,37,37,38,38,38,
39,39,40,40,40,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
59,60]);

MOT("3^6.L4(3).D8",
[
"maximal subgroup in O8+(3).D8,\n",
"normalizer of a 3^6 subgroup in B,\n",
"computed in March 2003 using the degree 3360 perm. repr. of O8+(3).S4"
],
[35372712960,136048896,75582720,1866240,93312,31104,82944,20736,20736,3779136,
944784,944784,52488,629856,104976,78732,52488,11664,5832,1458,1458,11520,6912,
1728,1728,2304,288,1440,180,5184,1296,1296,2592,1296,432,1296,648,648,324,64,
972,486,162,160,864,216,216,144,52,52,80,2880,1728,216,384,384,96,48,96,48,64,
72,36,36,40,40,48,48,48522240,746496,23328,15552,207360,25920,933120,46656,
15552,2304,576,576,768,46656,7776,5184,648,2592,648,648,1296,648,216,648,576,
144,144,1440,180,160,1296,648,216,96,108,80,52,52,50388480,699840,629856,
559872,622080,311040,62208,10368,7776,5184,10368,1728,1296,864,1152,576,1152,
576,69984,34992,2916,23328,5832,5832,1296,11664,5832,5832,2916,648,7776,3888,
7776,1296,972,648,2592,1296,1296,648,864,432,108,54,96,48,120,60,120,60,144,72
,144,72,144,72,108,54,108,54,606528,23328,192,96,1944,972,324,108,54,1152,576,
1152,576,192,96,160,160,144,72,144,72,52,52,52,52,80,80,80,80],
[,[1,2,3,1,2,3,1,2,3,10,11,12,13,14,15,16,17,18,19,20,21,4,7,9,8,4,6,28,29,10,
11,12,14,15,18,14,15,17,16,23,41,42,43,28,30,32,31,33,50,49,44,69,70,71,81,81,
78,80,78,80,81,84,85,92,98,98,102,102,1,1,2,3,1,3,4,5,6,4,6,5,7,10,14,10,13,14
,17,15,14,17,18,19,23,24,25,28,29,28,33,34,35,30,41,44,50,49,1,3,2,3,1,3,1,3,2
,3,4,6,5,6,7,9,4,6,10,11,13,14,17,15,18,14,15,17,16,18,10,11,14,15,16,17,14,15
,14,17,14,18,19,20,23,24,28,29,28,29,30,31,33,35,33,34,41,42,41,43,1,2,7,8,10,
12,13,19,21,23,25,23,25,23,25,22,22,45,46,45,46,49,49,50,50,51,51,51,51],[1,1,
1,4,4,4,7,7,7,1,1,1,1,1,1,1,1,2,1,2,2,22,23,23,23,26,26,28,28,7,7,7,4,4,5,7,7,
7,7,40,10,10,11,44,23,23,23,22,49,50,51,52,53,53,55,56,57,57,59,59,61,53,53,52
,65,66,56,55,69,70,70,70,73,73,75,75,75,78,78,78,81,69,69,70,70,73,73,73,70,70
,71,69,93,93,93,96,96,98,75,75,76,81,82,104,105,106,107,107,107,107,111,111,
113,113,113,113,117,117,117,117,121,121,123,123,107,107,107,107,107,107,109,
107,107,107,107,109,111,111,113,113,113,113,111,111,111,111,113,115,113,115,
151,151,153,153,155,155,121,121,117,119,123,123,137,137,125,126,167,167,169,
169,167,167,167,167,168,176,176,178,178,180,180,182,183,178,178,176,176,188,
189,190,191,192,193,194,195],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
,20,21,22,23,24,25,26,27,1,3,30,31,32,33,34,35,36,37,38,39,40,41,42,43,4,45,46
,47,48,50,49,22,52,53,54,56,55,59,60,57,58,61,62,63,64,52,52,68,67,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,73,74,69
,99,100,101,102,103,75,106,105,107,108,109,110,111,112,113,114,115,116,117,118
,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,107,108,111,112,
157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,
178,179,176,177,180,181,183,182,186,187,184,185,191,190,188,189,183,182,183,
182],,,,,,,,[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
,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,1,1,51,
52,53,54,56,55,59,60,57,58,61,62,63,64,66,65,68,67,69,70,71,72,73,74,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,69,69,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,
142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,
161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,178,179,176,177,
180,181,183,182,186,187,184,185,167,167,167,167,193,192,195,194]],
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[TENSOR,[194,2]]],
[( 65, 66)(192,194)(193,195),
( 55, 56)( 57, 59)( 58, 60)( 65, 66)( 67, 68)(176,178)(177,179)(182,183)
(184,186)(185,187)(192,193)(194,195)
,(188,189)(190,191),( 49, 50)(105,106)(188,190,189,191)]);
ALF("3^6.L4(3).D8","O8+(3).D8",[1,5,6,2,17,20,4,19,22,5,8,7,10,6,9,8,10,
32,10,34,33,12,11,40,39,12,44,15,50,19,26,23,20,24,52,22,27,28,26,30,32,
34,35,36,38,41,43,44,46,47,54,194,193,201,199,199,198,209,198,209,200,201,
202,203,204,204,210,210,56,56,62,64,57,63,58,75,76,60,80,79,61,62,64,62,
66,63,67,65,64,66,83,66,68,87,85,72,93,74,76,78,94,81,83,84,88,89,146,153,
152,154,147,155,147,159,157,162,148,170,169,172,151,175,150,173,152,156,
161,153,161,158,180,154,158,161,156,181,157,160,155,163,160,164,159,163,
162,164,162,182,164,184,165,186,167,190,168,191,174,178,172,192,173,177,
182,184,181,183,97,103,102,125,103,105,107,107,127,109,130,109,130,111,
132,113,113,129,133,129,133,135,135,134,134,142,142,143,143],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^2.(U3(3).2xS4)",
[
"origin: Dixon's Algorithm,\n",
"maximal subgroup of O8+(3).S4"
],
[1161216,387072,193536,193536,36288,96768,96768,48384,288,3072,1536,3072,9216,
3072,768,768,768,768,1536,1536,768,18432,6144,3072,3072,576,96,192,192,384,384
,2304,768,72,864,1728,1728,648,6912,20736,3456,3456,192,384,384,144,384,1152,
96,96,48,36,96,288,96,96,48,36,96,288,24,192,64,32,64,64,256,256,128,96,512,
512,1024,3072,96,96,96,96,36,192,384,384,384,1152,48,48,24,18,48,144,144,144,
72,54,288,288,576,1728,192,384,384,384,1152,144,64,64,64,64,24,128,256,256,256
,768,21,112,224,224,224,672,56,56,56,56],
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39,40,40,38,41,39,40,38,40,40,39,39,25,23,22,26,22,22,32,33,31,34,32,32,32,33,
31,34,32,32,70,74,74,72,73,74,22,23,24,26,23,23,22,22,33,32,30,30,34,33,33,33,
32,32,97,98,96,94,98,98,98,97,95,94,97,97,98,98,4,1,2,1,1,5,14,13,10,12,9,14,
14,14,13,13,115,119,119,119,120,120,119,120,117,118],[1,2,3,4,1,6,7,8,13,10,11
,12,13,14,15,16,17,18,19,20,21,22,23,24,25,22,21,19,20,24,25,22,23,22,8,7,6,1,
2,1,3,4,43,44,45,48,47,48,45,44,43,48,47,48,45,44,43,48,47,48,62,62,63,64,65,
66,67,68,69,74,71,72,73,74,16,15,18,17,13,11,12,10,14,13,101,100,99,103,102,
103,6,7,8,1,3,4,2,1,99,100,101,102,103,103,105,106,107,108,114,110,111,112,113
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[(117,118)(123,124),(49,55)(50,56)(51,57)(52,58)(53,59)(54,60),
( 10, 12)( 17, 18)( 77, 78)( 81, 82)(107,108)(111,112)]);
ALF("2^2.(U3(3).2xS4)","O8+(3).S4",[1,2,42,41,80,101,104,150,89,41,42,43,
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161,160,90,60,62,58,28,30,132,118,163,83,48,19,113,131,162,81,65,61,17,7,
151,102,105,40,3,82,120,121,151,153,96,52,53,51,23,23,94,73,74,75,35,21,
144,134,170,171]);

MOT("3^(1+8).2^(1+6).U4(2).2",
[
"13th maximal subgroup in B,\n",
"3B normalizer in B,\n",
"computed in April 2003 using a degree 19683 perm. repr."
],
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[( 95, 96),
(157,158)(166,167)(172,173)(176,177)(181,182)(188,189)(194,195)(200,201)
(202,203)(205,206)(208,209)(212,213)]);
ALN("3^(1+8).2^(1+6).U4(2).2",["BM13","BN3B"]);
ALF("3^(1+8).2^(1+6).U4(2).2","B",[1,7,6,7,5,28,3,12,26,22,60,2,5,11,15,
23,20,29,21,23,27,65,71,62,4,9,10,13,17,30,25,30,38,56,55,67,58,69,72,61,
121,6,7,7,24,28,29,46,47,7,6,7,28,26,27,22,47,60,64,94,6,7,7,27,29,47,46,
64,68,12,15,42,68,73,64,125,16,32,37,40,45,74,74,119,124,118,126,127,19,
53,51,82,105,142,143,144,182,23,23,21,29,28,27,96,93,23,21,20,27,29,24,23,
65,62,59,92,93,95,157,21,24,23,28,29,70,73,93,30,25,30,56,55,69,63,97,121,
122,156,47,46,46,96,96,95,131,68,64,60,71,73,70,158,4,17,30,25,38,38,38,5,
14,24,28,27,29,41,41,41,66,16,33,40,40,74,114,34,34,36,40,45,115,115,117,
116,30,30,72,121,121,121,25,30,97,122,122,27,29,95,96,123,123,41,41,89,
123,123,108,165,165,74,74,126,126]);

LIBTABLE.LOADSTATUS.ctomaxi7:="userloaded";
ALN:= NotifyCharTableName;

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