/* www-ATLAS of Group Representations. S8(2) represented as 51 x 51 matrices over GF(17). */ F:=GF(17); x:=CambridgeMatrix(3,F,51,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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9,8,16,1,9,14,8,9,3,11,9,8,3,6,0,8,9,0,14,13,13,0,0,8,8,5,0,15,4,0,4,0,0,9,0,1,12,0,0,0,2,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 16,1,4,13,14,10,3,7,7,14,1,10,8,3,10,16,1,0,9,1,13,7,0,6,16,14,0,6,16,0,4,0,0,11,0,0,3,1,0,0,11,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,14,3,7,6,10,15,11,2,16,2,13,15,5,1,9,0,4,3,6,12,0,7,8,9,6,4,14,0,11,0,0,10,0,0,8,0,11,1,13,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 12,5,16,1,13,1,4,11,16,8,9,6,16,9,2,8,0,0,1,16,14,15,0,11,0,7,11,4,1,0,3,0,0,6,0,0,10,0,6,0,13,1,0,0,0,0,0,0,0,0,0, 12,5,5,12,15,6,2,9,11,6,5,8,11,11,6,12,6,0,6,1,0,11,0,16,11,6,11,16,16,0,0,0,0,1,0,0,11,0,6,0,1,0,1,0,0,0,0,0,0,0,0, 6,11,12,5,3,8,14,12,9,12,4,5,8,5,13,13,1,0,9,13,5,4,0,13,16,8,7,2,4,0,12,0,0,4,0,0,9,0,10,0,15,0,0,1,0,0,0,0,0,0,0, 7,10,12,5,3,13,14,14,4,2,15,3,3,15,11,2,3,0,14,13,1,6,0,10,14,12,13,5,4,0,16,0,0,7,0,0,5,0,4,0,12,0,0,0,1,0,0,0,0,0,0, 2,15,2,15,15,0,2,13,0,0,15,4,4,0,10,2,3,0,13,14,4,7,0,9,14,0,2,8,3,0,13,0,0,8,0,0,0,0,15,0,9,0,0,0,0,1,0,0,0,0,0, 10,7,7,10,6,4,11,4,13,6,2,13,4,11,7,15,4,0,13,15,14,10,0,1,13,16,9,15,2,0,3,0,0,16,0,0,1,0,8,0,2,0,0,0,0,0,1,0,0,0,0, 13,4,11,6,5,0,12,5,0,16,10,12,10,1,12,7,5,0,7,3,16,5,0,4,12,7,12,4,14,0,1,0,0,13,0,0,10,0,5,0,13,0,0,0,0,0,0,1,0,0,0, 10,7,14,3,7,10,10,16,7,2,9,1,14,15,1,8,12,0,3,14,8,16,0,1,5,4,4,7,3,0,9,0,0,16,0,0,13,0,13,0,10,0,0,0,0,0,0,0,1,0,0, 10,7,10,7,5,6,12,10,11,15,14,7,6,2,8,3,1,0,11,14,6,9,0,11,16,4,0,0,3,0,11,0,0,6,0,0,13,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 8,9,5,12,0,12,0,3,5,16,13,14,12,1,0,4,14,0,5,10,4,0,0,5,3,3,2,10,7,0,13,0,0,12,0,0,14,0,15,0,7,0,0,0,0,0,0,0,0,0,1]); y:=CambridgeMatrix(3,F,51,\[ 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 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, 10,8,1,10,2,9,15,14,15,3,15,15,15,6,13,11,15,0,4,3,7,0,16,13,7,0,16,14,13,2,5,13,9,8,10,7,16,7,13,4,11,5,9,2,14,12,2,11,6,5,7, 3,9,14,11,11,13,4,2,6,2,1,5,5,13,15,13,14,3,4,12,14,4,5,5,5,15,15,6,9,0,6,16,9,10,12,7,13,14,15,8,7,0,4,16,13,4,7,14,14,0,16, 15,13,9,5,14,3,2,3,11,13,3,2,11,16,0,10,11,14,9,6,3,2,6,4,14,1,7,1,5,9,9,12,8,8,3,8,10,1,14,1,13,14,6,12,14,4,12,4,2,13,15, 6,0,11,10,11,15,4,4,9,5,6,2,2,11,11,2,15,6,16,0,15,5,12,6,9,4,11,11,10,7,9,2,4,11,5,4,9,11,7,4,2,3,13,10,2,2,3,3,10,8,1, 12,1,16,16,1,14,9,9,2,5,6,15,10,2,3,8,1,16,0,5,2,12,16,7,5,12,9,10,1,9,11,16,5,10,5,8,1,5,8,8,4,3,5,13,4,2,15,2,5,15,16, 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, 15,12,1,0,10,12,16,16,14,5,15,14,1,7,16,3,2,8,10,14,15,5,14,4,11,15,3,1,15,10,7,16,12,9,13,13,7,15,13,3,12,2,15,3,8,2,12,3,14,1,16, 11,1,15,9,2,15,10,4,6,8,2,6,4,14,15,2,3,11,2,14,11,13,15,14,8,4,16,14,4,0,0,6,4,13,15,0,3,3,11,6,11,4,14,3,4,8,2,11,4,11,9, 0,16,15,13,16,10,7,5,4,8,9,10,11,10,8,13,13,12,16,0,6,13,11,7,3,0,14,12,15,0,0,16,6,13,9,6,8,16,15,6,7,9,9,16,15,16,16,4,13,16,11, 8,10,13,10,2,9,13,5,0,11,0,9,6,10,11,14,6,14,10,5,14,16,1,16,1,0,13,2,0,13,0,6,13,12,8,15,7,10,9,10,4,4,9,0,0,5,16,11,16,4,16, 6,10,9,15,9,0,11,7,4,10,16,15,12,12,5,14,10,8,15,10,1,10,13,10,7,1,14,13,1,4,6,10,10,16,11,16,14,8,15,5,6,12,4,3,15,0,5,10,4,16,8, 8,8,0,1,2,3,15,4,14,9,14,9,2,11,13,5,13,7,7,9,9,11,9,11,11,5,6,6,6,9,8,15,11,11,2,1,15,16,9,4,9,4,3,16,13,4,15,0,0,13,10, 14,5,2,3,1,8,2,3,1,3,7,15,15,6,10,0,7,0,7,10,2,3,15,9,10,6,7,9,7,16,14,16,7,13,0,15,4,14,11,0,3,10,3,6,2,11,10,14,1,2,1]); G:=MatrixGroup<51,F|x,y>; print "Group G is S8(2) < GL(51,GF(17))";