/* www-ATLAS of Group Representations. L3(3):2 represented as 13 x 13 matrices over GF(13). */ F:=GF(13); x:=CambridgeMatrix(3,F,13,\[ 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, 0,0,0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,12,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,1, 0,0,0,0,0,0,0,0,0,0,0,1,0]); y:=CambridgeMatrix(3,F,13,\[ 12,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0, 0,1,12,0,1,0,0,0,0,0,0,0,0, 1,0,0,12,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,12,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,1,0, 0,1,12,0,0,12,0,0,0,0,1,0,0, 12,0,0,0,0,0,0,1,0,12,0,1,0, 0,0,0,0,0,0,1,0,0,0,0,0,1]); G:=MatrixGroup<13,F|x,y>; print "Group G is L3(3):2 < GL(13,GF(13))";