/* www-ATLAS of Group Representations. L2(16):4 represented as 68 x 68 matrices over GF(17). */ F:=GF(17); x:=CambridgeMatrix(3,F,68,\[ 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, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 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, 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0,1,0,16,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 0,7,5,4,2,8,11,0,12,2,6,6,13,3,14,3,9,7,2,11,4,12,4,7,2,11,11,3,1,13,2,4,11,9,4,7,14,16,1,16,16,5,13,3,16,9,10,1,12,11,8,7,6,14,1,3,2,11,16,8,8,14,14,2,10,14,6,6, 10,4,6,7,13,11,16,5,10,14,2,4,14,14,13,13,3,13,10,0,15,7,8,14,1,9,6,12,15,2,16,12,4,2,11,11,0,7,6,2,14,15,1,5,6,7,7,16,6,8,5,10,15,5,8,13,3,11,10,11,4,7,10,6,4,5,9,12, 2,1,7,9,1,7,8,15,3,8,6,10,15,14,8,13,3,5,0,5,15,3,15,4,1,15,4,12,16,9,10,15,10,12,2,0,13,8,15,13,6,16,9,13,16,11,12,5,4,3,15,9,1,11,16,11,4,16,1,2,14,14,14,7,4,16,10,6, 3,12,13,9,15,9,8,10,2,10,7,9,13,7,0,6,8,3,11,14,10,3,8,7,2,0,10,11,12,2,16,14,10,5,13,16,16,1,15,5,7,7,11,16,13,0,1,10,3,1,10,1,7,0,4,1,8,4,15,3,7,7,3,9,11,15,14,0, 12,13,9,13,0,3,1,9,14,0,6,16,3,13,2,10,3,9,2,0,2,10,8,6,10,11,8,5,13,0,3,12,1,11,5,0,1,7,5,5,9,7,14,9,15,1,2,8,10,8,7,13,7,5,1,2,15,14,14,2,13,9,4,12,4,6,6,15, 1,13,8,7,5,13,12,15,16,14,13,1,5,7,9,2,4,15,10,16,3,4,0,7,11,8,10,11,5,13,9,3,4,13,8,14,9,0,7,2,0,3,10,8,13,14,0,2,3,2,4,14,1,5,3,15,11,8,13,4,13,4,12,8,16,11,16,3, 12,7,15,6,16,6,14,16,5,3,10,7,0,2,2,14,8,0,11,15,16,16,9,3,14,8,9,16,9,14,3,15,16,15,16,5,13,4,0,6,3,15,7,1,15,16,10,11,10,11,12,15,11,14,9,1,10,8,14,3,10,4,13,2,16,3,8,11, 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, 2,3,8,1,7,8,10,2,13,1,3,6,7,4,13,8,11,16,10,6,6,1,14,16,7,0,8,15,0,2,7,0,0,6,5,1,8,4,4,6,3,12,2,15,3,14,15,16,7,15,8,10,2,9,8,13,7,8,13,13,1,12,3,15,0,3,13,13, 1,7,7,16,15,2,12,2,3,16,1,11,15,16,9,11,5,11,3,11,6,6,13,10,14,11,13,15,15,12,9,4,10,16,0,3,10,12,7,1,5,0,13,11,15,11,8,14,7,13,5,13,3,12,1,10,4,0,10,15,11,4,4,16,13,12,11,14, 11,7,1,15,5,1,5,15,2,6,7,0,5,15,1,7,13,2,15,7,2,12,2,13,4,1,9,1,4,16,6,9,2,12,12,14,15,14,0,14,6,9,13,2,4,6,1,14,16,15,0,15,0,1,7,0,13,13,1,13,3,7,11,16,1,5,7,13, 6,14,16,9,5,4,2,8,7,12,11,6,9,12,12,8,12,11,3,1,6,13,0,5,12,15,2,4,8,5,4,14,9,11,14,2,7,11,9,11,0,11,5,14,15,16,5,9,7,1,13,3,10,9,1,15,1,6,16,6,4,4,12,3,13,11,12,4, 0,8,16,0,9,0,13,4,14,6,14,5,1,7,11,15,3,1,16,7,4,14,16,15,14,3,11,7,9,11,1,7,2,11,12,15,8,12,3,7,5,3,4,16,5,1,0,9,4,7,4,2,3,3,3,8,6,16,13,14,16,16,12,9,0,5,0,8, 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, 8,15,14,9,15,6,10,15,11,9,13,6,9,14,11,9,12,3,0,1,5,8,11,4,16,10,8,8,11,2,8,5,2,14,8,14,2,3,12,16,14,13,13,7,16,11,9,16,6,11,1,6,11,8,1,11,6,4,16,12,12,10,4,8,0,6,16,4, 16,16,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0, 12,16,16,1,5,5,15,14,11,10,16,0,1,2,6,9,15,2,16,16,4,13,6,3,11,13,0,5,3,15,3,13,11,7,8,0,5,10,14,15,9,8,15,0,10,8,13,7,7,7,16,0,8,14,5,15,3,7,8,1,3,3,11,2,5,16,6,10, 0,4,5,12,15,6,10,15,8,13,12,3,8,7,3,11,15,10,1,6,7,7,16,14,6,1,12,10,5,10,1,16,8,1,4,16,6,15,6,13,5,15,2,6,16,13,14,11,3,10,11,12,13,16,6,5,4,9,5,5,5,3,0,1,16,10,11,5, 5,12,14,8,4,2,3,8,13,15,14,13,13,6,10,15,6,4,2,14,12,12,0,7,4,14,11,1,9,2,1,15,2,12,2,15,16,9,13,14,2,0,10,14,11,13,5,5,5,8,5,5,8,5,12,7,6,13,5,3,1,15,12,3,14,2,6,9]); G:=MatrixGroup<68,F|x,y>; print "Group G is L2(16):4 < GL(68,GF(17))";