/* www-ATLAS of Group Representations. Sz(32) represented as 124 x 124 matrices over GF(41). */ F:=GF(41); x:=CambridgeMatrix(3,F,124,\[ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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26,23,0,40,38,37,7,40,8,10,5,32,35,18,27,7,5,22,3,25,19,13,4,30,16,6,4,20,16,20,24,18,18,36,30,27,33,15,20,40,24,37,0,0,12,9,13,20,22,0,19,9,11,12,28,36,7,27,37,9,18,22,30,17,32,32,7,18,33,31,12,29,26,30,37,29,12,22,23,26,34,9,32,25,29,10,2,23,4,4,7,3,34,9,22,0,29,18,38,19,30,13,8,5,21,32,7,5,3,22,29,24,25,18,4,7,16,13,5,7,35,35,33,26, 16,32,11,3,34,7,3,40,38,20,5,32,6,10,30,36,38,16,3,15,16,19,0,7,37,9,40,10,27,6,27,26,30,40,6,13,28,40,6,15,16,34,7,22,29,19,32,10,15,16,37,20,32,17,17,14,35,18,35,31,27,32,2,32,14,13,5,4,24,13,24,33,9,19,33,14,30,26,0,25,31,9,5,15,8,19,13,12,26,26,0,33,38,32,12,27,31,30,39,35,0,6,11,21,34,32,27,21,40,19,13,14,3,11,1,11,34,10,31,31,2,32,18,37, 23,40,24,21,0,28,32,7,30,38,28,32,21,40,21,27,16,3,5,31,37,13,25,16,25,8,19,8,27,9,17,39,36,10,21,7,9,26,11,0,9,34,35,24,6,38,24,34,28,29,0,37,20,15,14,15,13,6,26,31,30,10,7,40,29,10,2,7,3,32,25,27,27,12,15,34,27,3,34,9,5,28,9,12,30,35,26,13,29,30,40,5,5,10,21,37,35,11,2,28,9,33,25,26,17,38,39,27,40,6,23,28,8,5,24,3,37,15,38,24,6,7,10,33, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 22,7,0,9,6,24,17,0,23,2,32,27,38,34,31,9,22,36,21,20,39,19,29,18,38,11,25,21,28,13,20,36,13,3,24,3,39,12,27,29,10,37,11,20,21,18,38,9,3,34,26,11,13,34,26,15,18,29,3,14,21,26,1,18,33,39,4,22,34,34,2,30,30,6,26,1,33,11,17,3,14,16,15,14,35,8,0,5,3,10,16,37,31,4,19,16,39,30,37,39,27,12,29,27,25,0,22,32,40,16,34,14,22,24,24,13,24,39,2,19,19,1,8,31, 9,28,5,12,40,13,19,2,0,38,1,6,12,3,6,5,32,21,21,10,15,28,7,19,37,29,16,31,18,37,15,34,24,27,13,3,39,30,29,38,8,3,17,23,4,26,36,13,21,33,6,27,7,24,19,26,5,10,18,10,34,29,14,36,38,29,31,12,0,37,28,25,13,12,14,17,40,37,32,39,5,38,16,28,22,3,30,18,5,0,20,29,11,2,3,29,20,7,7,28,1,10,23,20,34,6,38,6,21,27,26,6,1,24,33,23,4,6,4,36,5,3,18,21, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 17,0,38,28,1,39,38,12,18,37,16,38,22,5,21,3,32,19,16,40,18,8,20,19,25,38,25,37,25,0,1,16,20,31,26,24,12,23,0,31,37,20,21,25,20,9,1,12,4,31,33,5,9,31,30,7,12,3,7,10,36,18,6,24,39,0,12,7,22,38,22,22,23,32,34,39,19,18,2,25,0,30,38,4,14,0,15,25,22,38,16,12,22,8,0,16,17,20,1,12,9,8,8,3,8,10,29,14,28,9,28,18,36,7,14,16,4,30,36,7,23,12,36,15, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 10,4,2,19,10,20,31,27,15,34,12,0,33,32,37,31,40,25,30,2,16,20,27,24,5,24,2,7,29,26,37,0,17,20,8,40,27,20,2,5,21,19,38,18,38,1,38,22,5,21,10,33,18,31,3,19,16,24,22,7,15,15,10,30,20,21,26,12,7,8,32,30,31,18,1,17,28,35,11,4,40,25,23,18,2,12,6,38,23,36,18,35,40,20,15,13,23,17,1,10,1,28,4,39,36,2,19,29,38,12,10,29,38,35,23,4,23,2,12,13,8,38,35,24, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 16,12,33,17,3,15,24,23,26,3,40,17,6,23,32,8,2,19,7,12,36,15,24,24,21,9,6,33,18,18,2,9,5,37,37,25,40,17,23,2,34,17,19,35,26,20,6,26,23,36,11,12,30,3,26,16,11,24,6,7,10,12,30,11,40,4,4,35,21,11,28,38,20,28,25,8,34,38,5,11,7,40,21,7,30,19,3,29,9,25,20,37,25,31,24,29,40,25,15,24,7,40,13,1,17,21,39,5,36,12,28,27,16,10,30,25,27,33,16,21,22,20,26,2, 13,12,12,4,0,0,37,10,26,12,17,35,37,39,33,40,1,30,27,28,4,35,26,16,13,27,34,2,38,40,3,32,5,34,39,31,23,29,16,4,22,22,30,40,10,22,5,15,33,2,11,37,9,29,9,30,10,12,11,6,29,11,37,29,37,7,20,18,29,8,8,27,18,4,21,16,7,21,34,15,28,17,0,1,22,3,38,11,5,27,38,4,1,7,27,37,37,4,0,20,22,14,15,0,22,1,28,1,35,3,1,2,34,4,35,2,13,23,34,15,20,22,35,32, 9,24,4,35,16,12,0,38,21,23,30,36,32,19,7,39,20,27,0,17,26,34,10,21,14,29,19,8,28,40,10,16,13,25,22,8,3,30,28,36,3,28,10,40,7,40,19,31,39,27,37,20,7,9,19,14,29,12,15,36,19,9,23,36,2,28,20,35,29,4,33,24,27,25,3,2,34,27,7,33,34,30,8,37,9,0,28,35,0,20,2,24,13,29,31,17,31,34,18,6,7,40,23,20,20,15,25,22,30,28,14,27,1,5,24,20,40,24,12,36,6,17,11,4, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 3,19,1,13,16,5,22,5,5,13,39,34,13,10,11,9,23,8,33,0,27,11,26,24,1,10,33,34,28,18,30,11,38,18,20,12,20,5,11,19,40,17,6,31,11,22,15,28,22,40,33,35,29,17,16,26,40,36,33,27,20,22,35,19,20,2,30,26,12,35,27,8,15,37,13,40,37,37,16,4,39,18,18,39,3,22,0,2,27,9,15,32,11,4,17,19,21,2,22,36,16,10,33,12,7,38,20,39,24,12,7,36,19,18,34,27,7,10,21,36,14,24,12,25, 35,18,24,31,19,11,20,3,12,0,9,34,26,6,38,4,29,22,3,22,8,23,10,19,34,15,13,38,30,28,28,20,21,26,19,37,36,0,1,29,5,11,35,27,22,2,14,6,18,18,34,30,36,6,4,35,6,16,0,22,29,14,4,11,4,12,12,24,7,40,32,19,28,34,39,36,27,23,20,11,6,20,22,36,35,13,29,23,6,21,13,27,28,20,32,2,12,18,39,36,21,18,3,9,2,1,10,9,5,20,11,34,30,12,32,2,19,35,32,7,11,36,34,40, 18,28,27,11,8,20,4,38,7,20,31,12,12,21,34,28,27,39,3,2,13,30,6,27,13,30,6,23,21,34,1,28,10,20,34,0,3,19,21,18,11,36,0,22,24,14,32,20,3,17,24,1,22,36,0,10,13,13,18,9,19,33,40,35,11,28,7,19,40,11,37,18,14,35,20,26,38,27,32,25,12,14,40,22,5,7,33,33,34,9,7,32,4,35,36,1,25,15,18,13,32,16,17,23,34,37,6,10,36,21,31,7,17,16,7,39,4,12,13,39,35,2,20,33, 5,33,20,19,34,18,33,23,8,39,5,36,32,24,6,31,25,28,13,35,33,22,4,23,17,39,4,22,24,11,29,32,14,22,35,20,10,18,13,25,5,37,11,40,22,14,22,17,14,25,38,34,9,28,27,17,12,17,36,8,10,5,33,12,10,36,33,19,39,31,11,18,24,9,3,20,25,22,36,5,5,10,22,27,0,31,19,30,36,15,4,23,28,6,32,14,0,9,36,4,36,35,3,33,20,9,1,36,9,37,5,16,39,14,18,23,37,1,40,5,0,21,37,14, 20,23,4,26,2,26,22,7,37,2,4,6,19,0,27,16,2,16,9,28,38,5,18,12,8,32,17,39,13,22,10,29,8,1,9,23,9,1,7,33,18,1,16,26,31,25,26,5,26,35,27,18,32,19,5,35,4,13,21,5,8,29,3,19,24,26,8,20,4,13,35,6,18,11,37,21,34,2,0,14,36,25,13,10,31,14,40,32,0,30,35,4,35,10,11,0,29,3,30,17,7,34,23,26,28,39,6,27,12,25,25,19,34,1,4,33,35,2,12,1,12,0,22,3, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 19,3,2,30,25,0,25,9,0,8,10,0,4,3,10,38,21,4,12,36,2,38,13,32,27,6,24,6,19,11,36,17,35,24,38,9,16,25,5,33,11,40,25,24,22,8,5,12,5,34,4,30,20,39,17,24,12,7,12,8,40,32,24,38,15,20,31,12,13,30,14,40,13,24,12,3,40,14,17,36,33,10,39,31,36,1,19,20,26,19,16,27,30,16,37,17,8,12,20,39,22,18,14,25,15,15,32,14,16,20,35,22,23,23,0,23,28,8,36,39,34,40,29,2, 33,38,8,18,21,8,21,39,36,10,10,8,16,24,11,36,24,30,33,7,13,30,5,0,11,18,3,26,39,15,3,27,39,11,12,8,12,19,32,10,13,33,3,10,14,4,37,28,3,0,38,2,11,17,31,22,29,30,3,14,20,28,10,30,25,32,15,19,11,26,24,13,37,8,31,21,19,38,28,15,7,18,18,34,10,37,33,20,2,35,35,39,30,21,33,14,23,26,11,38,12,10,35,23,6,10,13,15,3,13,17,39,16,27,40,38,12,38,17,5,33,16,40,5, 0,28,35,8,13,30,13,14,35,18,33,12,22,12,1,39,16,10,31,16,12,7,12,32,21,7,17,26,19,16,40,39,26,16,0,2,8,36,23,39,2,0,12,34,26,35,29,35,2,32,19,18,19,32,6,6,32,12,8,7,1,32,34,36,19,40,0,16,9,7,25,33,17,24,31,34,36,27,4,33,2,15,28,3,4,27,13,5,17,2,2,22,19,0,30,28,3,22,15,29,29,17,1,33,18,33,2,12,19,7,22,31,14,17,19,9,1,26,29,2,12,23,21,2, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 40,5,38,35,37,11,6,18,3,26,16,23,39,38,27,32,23,23,11,19,11,5,15,28,34,24,35,6,36,28,38,35,12,27,7,10,37,4,9,26,18,32,26,1,36,33,5,32,20,36,13,31,36,5,1,35,20,8,24,7,17,32,12,6,22,26,10,0,32,30,0,4,17,27,29,4,34,33,18,6,24,23,7,30,34,31,12,28,22,22,12,10,17,32,26,26,5,29,13,34,1,6,36,17,23,27,34,16,5,0,13,16,0,36,40,40,11,34,7,6,17,31,6,25, 20,38,0,40,19,11,12,3,13,4,11,16,36,24,32,8,11,36,10,21,31,17,13,36,1,9,38,27,11,30,19,1,31,14,33,22,24,16,2,38,1,8,6,15,26,21,22,12,37,23,13,2,30,39,33,19,21,18,11,18,6,18,22,10,23,34,6,19,7,23,18,29,11,20,11,13,34,34,23,2,35,38,25,15,25,14,14,31,1,28,18,24,21,7,8,9,29,7,6,4,12,15,21,9,6,6,35,39,7,10,33,16,8,32,34,10,32,0,26,18,6,15,21,36]); G:=MatrixGroup<124,F|x,y>; print "Group G is Sz(32) < GL(124,GF(41))";