/* www-ATLAS of Group Representations. Sz(8) represented as 65 x 65 matrices over GF(13). */ F:=GF(13); x:=CambridgeMatrix(3,F,65,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 1,1,7,10,7,5,2,6,4,6,4,8,12,7,1,7,3,3,3,9,7,5,6,5,4,10,5,12,11,7,4,0,10,5,10,12,5,10,10,1,12,1,9,11,12,7,2,6,0,9,6,1,10,5,10,7,6,11,8,6,1,11,7,3,6, 6,9,10,3,10,8,8,10,6,4,0,8,7,1,5,2,4,10,4,4,0,11,7,9,11,7,4,12,1,1,10,8,11,5,0,11,8,7,10,11,4,11,6,10,10,2,9,8,11,8,9,0,0,9,8,7,2,9,5,9,0,10,12,9,9, 0,0,1,6,3,8,11,0,5,8,7,4,2,10,10,1,0,1,3,8,10,10,7,9,1,12,12,2,5,10,7,3,9,10,10,9,12,10,10,1,8,9,7,12,9,3,10,0,10,6,11,1,7,2,10,11,10,10,11,8,6,12,7,1,5, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,10,6,4,5,3,12,4,12,4,11,0,4,4,4,9,4,4,10,3,10,10,7,5,10,1,4,8,7,3,3,6,8,2,4,10,9,7,7,8,12,5,8,9,11,1,0,1,0,3,9,10,5,7,8,1,7,10,6,9,7,4,3,11,10, 12,3,0,4,0,0,12,0,0,0,3,0,0,0,0,0,0,9,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 11,7,12,12,10,1,10,9,5,4,11,5,2,3,1,5,6,9,3,0,8,3,10,1,7,0,3,1,9,4,10,9,1,7,1,0,8,6,0,10,9,1,10,8,4,0,4,4,0,11,5,3,6,5,9,0,5,1,0,6,6,11,9,2,12, 10,0,5,9,0,11,0,5,6,2,3,3,3,5,8,11,10,9,9,10,0,7,5,12,2,12,8,12,6,10,6,12,5,0,11,11,1,12,0,9,12,4,7,7,3,10,12,8,8,1,10,5,10,7,7,3,0,6,0,11,0,6,6,7,2, 2,11,12,4,12,3,8,4,7,4,9,5,12,3,5,1,0,0,5,7,12,4,3,10,12,12,6,11,0,3,10,0,11,6,7,5,6,11,11,1,9,8,12,5,6,0,6,3,8,2,9,0,10,2,12,1,3,11,5,8,1,2,12,7,6, 12,0,6,7,9,10,0,7,11,9,8,10,2,0,1,11,10,11,8,6,2,3,4,9,6,8,1,12,3,12,6,8,6,1,5,2,1,5,6,3,0,9,6,11,11,4,6,2,4,3,10,0,3,7,6,12,2,12,12,8,6,8,1,9,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,7,1,2,12,10,11,9,0,0,11,6,7,3,9,7,2,2,9,8,4,7,4,7,12,5,9,9,11,1,9,5,7,12,9,9,1,3,10,0,1,5,8,5,12,12,5,4,11,0,12,5,7,4,11,7,7,2,5,0,9,1,12,12,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 8,7,9,1,1,11,7,5,5,7,7,5,8,5,5,12,2,12,11,4,11,3,8,12,7,12,6,12,9,5,0,0,4,12,11,0,7,7,2,2,4,8,11,11,8,3,3,5,9,7,0,0,6,10,1,5,7,12,4,10,5,4,6,11,7, 7,1,11,1,5,8,0,0,6,6,11,8,6,2,6,12,9,10,12,12,10,3,1,5,5,2,9,11,4,6,9,9,1,8,12,6,7,4,12,1,10,0,4,4,8,8,1,0,2,3,0,8,2,0,6,5,9,8,4,9,5,9,9,9,9]); G:=MatrixGroup<65,F|x,y>; print "Group G is Sz(8) < GL(65,GF(13))";