/* www-ATLAS of Group Representations. Sz(8) represented as 91 x 91 matrices over GF(13). */ F:=GF(13); x:=CambridgeMatrix(3,F,91,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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9,4,0,6,0,0,4,10,0,0,0,0,5,0,0,7,3,0,6,0,0,0,0,0,10,0,0,0,0,0,0,3,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 10,7,4,11,7,6,0,5,0,0,7,0,10,7,5,5,4,6,8,0,10,6,7,10,11,8,6,3,6,6,3,3,12,7,6,3,2,2,6,10,12,5,9,0,11,2,7,3,9,0,3,0,2,11,10,4,2,11,0,1,11,3,3,3,0,7,5,7,11,5,8,0,2,2,3,10,11,7,10,0,4,6,9,12,0,9,4,5,3,0,3, 7,1,4,8,4,12,7,5,2,10,10,5,10,8,0,3,5,6,12,6,7,1,3,7,0,1,1,11,10,10,5,6,11,3,6,10,9,1,5,12,9,8,1,7,10,12,2,1,11,0,11,10,10,7,8,4,8,7,4,12,6,11,7,1,5,11,0,7,10,5,1,6,10,0,7,0,2,3,6,0,3,8,4,10,10,11,1,10,9,0,11, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 7,1,7,11,0,6,6,11,0,8,4,5,7,0,2,4,7,5,5,9,9,5,3,12,11,7,6,7,12,7,2,11,8,6,5,10,8,9,10,2,7,11,11,9,8,1,7,12,5,12,7,3,3,10,1,1,1,9,11,3,5,2,6,8,6,5,4,8,4,12,10,6,8,3,2,1,3,1,12,1,11,11,11,3,6,12,7,2,12,6,0, 4,8,0,0,4,4,2,12,9,7,1,4,11,1,7,11,4,8,3,4,6,12,10,4,11,4,12,2,10,12,0,2,12,9,11,3,0,2,6,2,9,8,1,1,4,11,10,9,5,12,6,3,12,7,1,7,3,0,12,6,3,8,11,8,5,9,7,10,8,5,7,10,0,6,12,4,4,3,2,12,4,9,11,3,4,8,6,9,5,5,3, 1,0,9,2,0,3,12,10,3,5,3,5,8,4,10,1,9,0,8,1,4,5,8,6,9,2,6,4,10,3,0,0,6,12,1,10,9,7,7,6,12,9,5,7,1,9,3,11,6,11,10,11,4,4,6,6,8,7,9,8,10,12,9,6,8,8,0,12,1,2,5,12,6,0,3,0,2,7,12,9,3,8,5,7,3,11,12,11,6,7,10, 12,6,5,4,8,4,7,10,10,2,10,7,9,3,2,11,11,6,10,3,12,2,6,10,6,12,3,7,0,0,8,9,7,1,10,1,5,10,7,9,7,4,9,11,0,0,8,8,12,11,11,9,10,12,4,9,4,0,6,9,8,4,9,8,7,12,7,3,12,4,12,3,1,9,5,3,3,4,1,7,5,10,10,5,8,11,12,6,11,10,4, 8,5,11,0,12,5,12,5,9,2,12,12,5,6,4,1,7,8,7,3,9,7,11,3,10,1,1,6,3,4,0,11,12,8,1,12,8,1,8,11,6,8,5,3,7,7,1,3,7,1,5,4,0,7,6,8,8,5,3,12,11,10,11,0,6,12,3,12,7,3,1,2,3,8,7,7,9,11,10,12,6,1,2,0,11,9,9,4,0,4,4, 8,5,3,2,5,11,9,6,7,5,8,2,5,11,5,4,8,6,1,11,11,12,10,6,7,0,9,10,1,10,10,4,2,8,7,3,11,5,7,6,8,7,10,5,5,11,6,10,2,1,3,1,2,0,10,11,4,10,0,2,10,10,5,12,5,10,11,0,8,10,6,11,5,1,12,6,0,4,5,9,4,12,9,12,11,7,6,12,7,1,2, 2,5,12,0,4,11,6,4,11,4,9,2,5,4,8,5,8,7,5,11,10,9,6,11,6,5,11,5,2,9,9,5,2,11,9,0,0,3,9,4,9,1,2,0,3,12,3,10,0,6,11,10,9,6,8,1,8,10,1,6,4,4,1,5,3,8,3,12,2,1,11,11,0,8,2,4,1,2,2,11,10,0,5,11,8,4,3,4,9,10,2, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 7,6,3,0,12,8,2,6,11,2,11,9,8,9,0,5,11,12,4,9,10,7,1,12,1,11,7,0,0,5,9,7,3,1,8,5,11,7,3,2,7,2,4,10,5,5,2,10,10,1,12,8,3,1,6,5,5,3,10,11,6,12,10,2,5,6,12,2,5,6,12,5,5,0,7,11,0,0,9,8,11,9,11,10,4,2,6,10,11,6,1, 7,3,7,1,11,9,7,0,9,5,11,0,0,5,0,0,0,11,0,4,0,0,3,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0, 1,5,7,4,8,4,8,5,10,3,7,0,4,10,1,0,11,6,2,4,12,12,0,1,3,4,10,5,1,6,8,9,3,3,12,5,1,5,1,4,8,5,6,7,2,3,6,8,0,8,0,0,6,2,0,2,8,4,2,5,6,2,8,11,11,10,3,8,5,8,1,12,3,4,12,4,7,5,1,10,5,12,8,12,10,5,0,5,1,5,7, 10,3,1,11,10,6,12,11,6,4,8,11,6,12,5,2,8,11,1,10,7,1,0,4,4,12,9,6,10,12,2,12,5,7,10,4,1,4,6,9,7,9,5,8,6,7,9,4,5,2,0,0,7,7,9,2,6,2,1,1,12,7,5,2,9,5,1,4,0,2,8,12,5,9,7,8,2,5,0,3,7,11,9,8,0,8,1,2,1,9,1, 1,3,6,4,12,10,6,12,2,1,4,6,0,3,10,0,3,9,7,0,11,11,12,2,1,1,3,5,5,3,7,6,8,11,4,1,0,9,4,3,9,6,12,5,7,7,0,12,7,3,9,8,5,8,4,9,11,3,8,4,8,4,0,12,1,4,10,6,10,7,10,7,1,12,6,1,11,1,4,8,9,9,10,2,6,2,12,5,10,6,9, 8,6,8,5,12,5,1,7,11,12,5,0,9,7,0,1,9,1,6,0,8,12,12,4,4,1,2,2,8,11,4,3,1,0,2,7,8,12,9,9,12,8,6,9,11,12,3,9,3,6,1,9,11,12,11,8,12,4,11,10,0,6,3,7,5,12,2,1,5,12,10,1,4,10,4,0,5,2,2,3,5,3,8,12,10,3,12,11,7,4,5]); G:=MatrixGroup<91,F|x,y>; print "Group G is Sz(8) < GL(91,GF(13))";