/* www-ATLAS of Group Representations. U3(4):4 represented as 78 x 78 matrices over GF(13). */ F:=GF(13); x:=CambridgeMatrix(3,F,78,\[ 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, 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, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 11,6,2,3,9,10,11,6,9,9,11,9,4,0,7,2,9,1,12,12,5,4,2,1,1,9,6,3,4,6,6,6,7,9,2,11,11,2,10,8,12,2,4,11,2,9,4,1,5,8,4,11,8,6,7,4,12,10,4,3,8,6,8,10,1,5,5,2,2,7,7,7,6,0,8,8,11,3, 2,2,8,1,10,10,1,3,2,11,4,12,5,4,2,8,1,10,5,6,6,1,9,1,1,2,3,2,6,4,4,1,3,3,3,10,3,5,8,3,6,6,8,3,6,11,7,5,6,10,4,0,12,6,12,3,1,6,5,7,0,9,2,4,7,8,12,11,10,2,7,12,7,11,9,12,6,8, 2,3,7,10,0,2,0,3,12,0,10,9,0,12,10,11,8,11,9,11,4,0,2,10,3,1,3,11,9,7,0,0,9,5,2,5,6,12,0,11,3,9,0,4,9,2,9,8,1,10,11,11,6,8,6,8,10,11,10,1,1,0,9,7,10,12,2,4,9,6,10,10,1,8,12,4,3,7, 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, 11,4,1,5,5,8,5,12,4,6,5,11,11,8,5,3,6,0,10,0,2,11,12,6,7,11,6,1,1,11,3,12,12,2,11,7,7,0,6,0,0,6,10,8,11,0,5,9,9,4,7,12,2,6,11,10,4,4,9,8,1,10,0,7,11,2,9,8,5,9,12,1,12,0,6,1,6,1, 11,9,7,6,7,8,6,4,12,11,7,1,8,2,0,12,1,5,3,11,0,0,9,1,4,6,2,6,0,6,12,4,7,12,5,10,3,6,11,0,12,3,4,5,6,9,7,10,0,6,2,10,3,11,2,3,0,1,4,1,10,6,3,8,2,10,4,2,2,10,6,7,10,11,10,1,2,1, 12,12,0,12,0,11,1,6,8,2,5,2,12,11,6,4,3,6,12,3,6,3,12,7,3,8,12,5,2,0,10,1,12,11,0,6,10,7,4,5,1,2,11,8,6,12,4,0,9,8,12,1,8,2,7,2,3,1,3,8,7,8,6,10,4,3,2,9,7,12,8,5,1,10,4,10,10,1, 9,2,8,4,2,11,2,3,3,4,12,3,9,0,10,5,1,11,10,8,10,9,0,5,8,2,11,12,10,2,10,5,2,7,6,2,7,3,10,3,4,9,10,2,8,7,10,11,1,11,10,4,4,1,1,10,9,5,3,1,1,5,3,6,10,6,5,8,4,8,7,11,7,5,6,9,3,4, 12,9,12,8,0,6,11,1,2,2,1,2,9,10,8,1,9,6,5,1,4,0,0,9,8,1,1,8,1,2,2,4,2,5,10,1,6,8,11,10,1,3,2,2,6,2,5,6,4,10,7,5,2,0,7,9,7,8,9,9,4,0,11,11,5,0,7,1,9,8,4,8,5,8,9,4,11,9, 9,3,6,4,4,4,1,4,11,4,1,12,12,1,0,3,9,4,1,10,2,12,11,8,6,7,2,5,2,10,3,3,9,12,8,9,12,5,9,7,4,8,12,12,0,6,5,12,6,7,9,9,11,10,0,6,5,8,12,11,7,2,2,6,1,6,5,3,12,11,1,9,2,5,4,6,11,2, 11,9,3,4,5,12,2,5,9,12,1,5,3,7,9,5,1,10,4,11,8,12,2,10,11,8,4,6,1,7,12,5,5,10,5,4,3,12,7,8,2,3,3,9,11,12,4,12,3,0,6,4,5,2,10,11,11,2,1,3,2,3,2,10,5,8,10,9,3,2,12,6,2,6,5,12,4,2, 5,0,8,12,0,12,6,7,8,11,4,3,0,9,3,11,8,8,8,11,5,9,8,5,1,0,2,4,6,1,10,10,12,1,8,10,3,8,9,12,4,8,5,2,11,1,0,8,3,9,11,12,1,0,0,12,7,12,10,12,3,11,1,7,4,6,10,10,10,11,9,8,2,8,6,10,5,9, 9,9,3,2,6,9,2,9,10,10,5,9,9,3,3,12,9,0,1,6,10,7,11,6,1,5,0,4,9,2,4,2,11,4,9,0,2,6,12,4,1,12,11,7,6,6,5,10,2,10,9,0,3,11,9,4,9,9,10,4,12,1,3,0,4,0,8,3,12,5,6,9,5,6,1,5,10,3, 3,1,1,1,11,4,9,7,2,1,4,3,9,0,7,4,1,10,9,7,9,12,1,8,3,2,11,4,11,4,5,9,10,8,4,3,5,8,4,3,6,5,6,3,6,3,11,3,5,4,3,12,4,3,10,11,6,8,4,5,1,1,8,12,4,5,9,6,9,3,1,11,3,6,4,4,0,6, 5,2,5,2,9,0,3,6,7,4,8,11,7,7,0,5,11,3,3,4,4,10,5,6,11,3,7,5,7,4,3,11,2,1,1,9,3,9,12,10,9,4,0,11,2,0,5,6,12,7,8,9,6,0,12,6,7,1,9,6,0,7,3,8,4,12,2,9,3,10,8,8,8,6,6,4,6,3, 11,8,8,4,10,3,8,0,4,7,0,6,12,0,1,6,1,7,10,11,11,2,1,8,9,5,3,6,8,10,8,0,4,4,8,12,1,7,2,3,9,0,11,7,1,7,10,1,11,9,11,1,0,1,6,3,12,11,1,4,6,10,11,3,4,7,10,9,3,2,7,7,9,5,6,9,5,5, 3,3,8,2,3,5,4,3,12,7,4,3,3,1,5,5,2,6,9,6,1,5,3,6,1,10,11,0,12,6,2,7,11,4,0,8,4,0,7,8,10,1,2,8,5,3,10,3,7,7,7,11,5,11,6,5,4,7,11,12,3,7,4,6,10,12,8,2,8,3,8,11,9,2,2,9,6,5, 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, 10,11,12,2,12,10,10,1,5,6,4,1,4,5,11,9,11,9,11,8,1,0,10,10,10,7,4,8,9,3,10,0,1,3,10,11,3,0,2,6,1,11,3,5,8,5,12,12,4,6,2,4,8,1,1,7,11,4,6,11,12,10,10,12,0,5,6,0,2,12,5,10,11,9,8,11,1,2, 4,7,2,5,10,9,6,0,4,4,5,10,8,10,9,0,0,0,0,11,10,9,8,11,1,4,7,12,8,2,8,11,11,4,0,4,7,10,5,9,0,7,2,9,2,9,5,0,7,4,2,0,8,3,11,0,1,9,1,1,10,9,6,8,1,12,12,10,0,4,7,8,9,0,11,1,9,8, 7,11,5,3,10,3,1,9,9,8,10,2,8,5,0,9,0,10,10,3,1,10,0,5,10,12,3,5,10,0,10,1,6,7,3,6,8,4,3,9,6,5,12,2,6,4,3,11,5,3,3,3,1,12,6,3,11,11,8,9,3,11,2,2,2,11,4,12,5,12,11,5,0,11,9,8,6,7, 11,9,3,2,3,1,8,5,9,9,4,11,2,9,10,8,1,6,6,11,0,11,1,8,6,5,3,5,6,0,8,5,1,0,0,9,1,1,0,8,11,9,11,4,9,3,8,12,3,10,0,12,2,3,0,4,12,8,7,6,8,8,8,4,10,6,12,1,10,11,9,4,3,1,7,10,4,10, 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, 0,3,2,12,4,12,7,6,7,7,1,8,12,12,10,8,5,11,3,5,11,7,6,9,3,2,0,8,10,4,11,4,1,12,8,8,9,8,1,10,10,1,8,9,1,5,11,11,1,3,0,6,11,2,3,4,6,7,0,5,6,3,11,7,12,11,3,7,7,0,9,7,4,4,8,5,4,7, 6,3,3,12,5,0,5,5,1,8,2,0,8,1,2,2,5,9,12,0,4,10,9,1,11,1,12,11,10,8,9,5,2,6,11,4,5,0,7,10,6,10,0,0,1,4,10,6,2,11,9,5,12,3,4,12,12,9,12,6,11,12,5,10,11,10,4,3,11,4,0,2,4,4,2,7,11,6]); G:=MatrixGroup<78,F|x,y>; print "Group G is U3(4):4 < GL(78,GF(13))";