/* www-ATLAS of Group Representations. G2(4).2 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, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 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, 7,8,11,0,2,0,2,9,12,5,0,1,10,5,8,0,5,8,8,12,11,4,10,12,12,5,8,8,3,12,7,11,10,2,8,5,11,0,4,10,10,2,5,7,12,7,3,9,12,8,12,0,4,4,9,8,11,9,0,9,11,12,2,2,1, 6,0,12,9,6,3,11,5,9,11,0,11,2,6,6,6,2,9,0,6,12,2,0,2,9,6,6,4,0,7,10,7,8,5,7,1,3,12,11,5,8,6,11,4,12,1,10,11,12,9,0,1,1,4,5,4,12,7,12,0,5,5,12,9,11, 12,7,0,2,1,10,6,8,3,8,1,1,3,7,5,6,9,4,4,9,4,9,12,4,4,0,11,4,6,5,1,11,7,0,4,0,8,1,9,11,11,1,5,5,7,2,5,6,12,2,0,12,5,8,6,3,3,0,9,11,5,11,4,3,7, 5,3,2,3,12,7,8,9,8,9,8,8,11,6,6,0,10,8,2,12,8,6,2,1,10,4,6,10,12,3,5,5,0,11,0,6,5,9,11,2,8,0,11,0,11,12,5,12,10,0,8,4,11,11,12,10,3,12,5,3,7,9,5,10,11, 7,10,1,12,5,4,2,6,12,12,12,2,5,7,11,6,5,9,2,1,5,8,1,3,9,7,12,3,1,8,11,9,5,8,9,12,4,12,8,12,9,5,5,11,0,8,6,2,3,0,0,1,2,7,9,3,9,5,9,4,10,12,6,12,1, 0,12,12,1,0,12,0,1,1,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,12,0,0,12,1,0,0,0,0,0,1,0,1,0,1,1,12,0,0,0,0,0,0,0,0,12,0,12,12,0,0,0,12,0,0,0,0,12,0,0, 11,11,8,11,1,8,8,11,12,9,11,9,6,11,9,6,9,12,11,12,7,11,6,3,7,7,6,4,0,3,12,1,3,6,1,4,0,11,5,7,4,1,1,1,9,8,3,2,2,9,8,2,0,1,8,4,9,12,12,1,5,5,9,8,2, 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, 1,6,3,5,8,8,6,2,11,5,8,7,2,4,5,7,9,5,12,2,9,3,0,8,10,9,11,10,2,0,9,11,11,9,11,7,2,8,4,11,3,8,6,10,5,12,8,5,7,4,1,5,1,9,10,10,1,3,7,6,4,9,12,4,1, 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, 3,7,1,11,8,0,4,11,12,6,1,0,5,2,9,11,12,0,4,1,3,12,0,5,0,7,6,8,7,0,11,6,2,5,12,1,11,0,7,2,6,7,3,10,6,2,2,5,12,11,1,0,6,0,11,8,2,8,8,11,11,3,3,12,5, 8,4,12,9,2,4,7,5,9,4,2,1,8,3,2,0,12,2,2,2,9,4,4,3,10,2,2,1,1,12,12,10,12,1,2,9,7,1,5,9,9,2,8,2,0,5,0,4,4,0,6,12,0,3,11,1,2,12,2,3,11,4,11,4,1, 6,7,6,9,7,2,0,11,6,0,4,3,1,10,11,5,6,1,0,12,3,11,2,9,8,0,4,8,0,3,1,2,11,5,11,1,7,4,2,0,12,7,5,11,3,11,1,5,4,4,10,9,12,7,10,8,3,2,0,9,12,4,3,0,0, 5,5,0,3,11,10,1,4,6,0,10,9,8,12,2,4,1,5,8,1,1,12,1,11,6,2,7,7,4,11,2,5,7,9,7,8,8,9,1,6,11,10,7,8,4,11,1,5,10,12,7,4,5,2,6,7,0,10,10,5,2,11,11,8,6, 5,8,3,4,12,2,8,6,5,3,0,12,1,9,12,7,0,11,7,2,8,11,12,3,0,10,12,6,11,0,6,1,9,5,0,0,0,0,12,7,1,12,5,1,1,9,3,1,11,4,5,0,10,11,2,6,9,10,8,4,1,9,5,6,12, 12,0,9,5,5,11,2,10,6,5,11,0,11,9,6,4,1,10,6,11,3,9,8,3,3,4,6,2,5,12,4,9,12,9,11,4,4,11,1,12,11,5,2,11,8,6,7,3,8,4,4,2,5,10,3,2,10,7,1,1,2,7,11,0,4, 7,9,9,3,2,2,9,7,5,5,11,10,11,8,6,12,12,10,9,5,0,7,12,2,0,11,11,2,9,9,9,0,8,7,12,12,12,11,0,4,2,2,4,11,2,11,11,0,9,6,2,2,9,10,0,3,8,11,6,6,11,10,5,8,8, 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, 3,10,11,9,0,1,4,4,3,9,6,6,6,4,9,11,0,0,10,8,11,5,12,1,6,11,6,2,11,5,4,6,10,9,6,6,6,6,0,3,1,0,3,6,8,5,1,6,4,10,1,7,10,11,8,1,4,5,10,4,0,5,8,10,12]); G:=MatrixGroup<65,F|x,y>; print "Group G is G2(4).2 < GL(65,GF(13))";