/* www-ATLAS of Group Representations. U3(4) represented as 63 x 63 matrices over GF(13). */ F:=GF(13); x:=CambridgeMatrix(3,F,63,\[ 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, 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, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 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2,0,9,2,6,2,8,9,10,6,5,10,4,7,5,0,12,4,0,2,11,6,9,11,5,0,6,10,9,0,5,7,4,2,7,9,6,1,11,9,4,11,12,6,9,5,2,12,10,6,0,11,3,6,12,9,11,3,5,1,9,2,11, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 7,10,4,0,4,6,11,1,2,8,2,0,12,1,1,7,5,3,2,11,2,2,6,9,12,3,8,7,1,9,11,4,10,11,12,5,2,8,8,11,9,8,9,7,5,0,7,12,1,12,11,9,2,8,6,0,5,4,1,10,11,12,9, 5,9,11,8,9,11,9,11,2,8,4,7,4,2,10,11,4,11,11,1,9,8,12,7,9,1,5,10,12,1,9,3,5,4,5,0,6,10,9,6,11,1,1,1,4,6,11,8,4,2,4,9,0,7,3,5,2,6,1,0,1,1,2, 5,2,0,5,8,5,2,7,8,12,12,3,1,4,5,12,4,3,1,3,3,10,5,9,6,4,2,2,0,6,8,10,7,9,3,3,12,1,6,12,0,2,12,11,10,5,3,8,8,10,8,4,9,10,12,5,10,6,8,9,3,8,9, 12,1,9,2,10,4,11,12,9,3,1,12,6,9,4,10,9,1,0,2,7,11,5,1,3,0,1,3,7,1,7,2,0,7,10,7,10,0,12,5,8,3,7,2,9,2,8,0,12,5,6,4,0,11,2,7,5,12,6,7,4,12,7, 0,0,0,0,12,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0, 2,6,12,12,4,1,5,8,1,5,6,6,1,11,2,6,7,5,7,10,0,10,10,12,11,10,10,11,10,10,11,8,3,1,4,5,3,9,1,0,2,11,3,4,2,5,2,7,11,8,2,7,5,1,6,0,11,6,3,1,7,9,3, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,6,2,0,8,2,1,1,2,0,8,10,11,0,11,8,0,6,1,6,3,2,8,10,0,5,11,11,10,0,11,3,4,4,3,1,6,9,3,9,7,7,7,10,6,2,11,10,9,3,3,7,3,4,10,8,10,9,0,3,9,4,6, 2,1,6,6,12,11,0,4,5,2,0,0,8,1,3,3,2,5,2,12,12,12,3,0,5,7,8,4,4,8,8,6,8,3,8,10,8,8,11,8,3,8,0,2,1,1,11,1,11,11,3,5,6,11,10,10,3,11,11,11,7,6,1, 6,12,6,6,11,5,8,0,6,7,6,6,0,4,4,6,7,0,0,1,3,9,8,1,4,1,8,7,7,5,8,5,3,12,11,10,10,2,1,8,4,2,5,6,7,1,10,8,0,11,8,5,1,11,5,3,10,5,1,4,12,1,8, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 6,5,4,6,4,8,2,6,3,2,4,3,10,8,9,2,5,10,10,7,10,6,1,11,3,5,4,11,6,6,9,0,11,11,11,5,11,12,11,3,1,1,3,9,10,12,2,4,2,9,1,9,1,0,0,9,9,11,0,8,9,6,5]); G:=MatrixGroup<63,F|x,y>; print "Group G is U3(4) < GL(63,GF(13))";