/*
www-ATLAS of Group Representations.
U3(4):4 represented as 12 x 12 matrices over GF(13).
*/

F:=GF(13);

x:=CambridgeMatrix(3,F,12,\[
0,1,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,
9,9,2,2,4,1,4,1,12,0,0,0,
0,0,4,4,4,5,4,5,0,12,0,0,
1,1,11,11,3,9,3,9,0,0,12,0,
1,1,7,7,5,12,5,12,0,0,0,12]);

y:=CambridgeMatrix(3,F,12,\[
0,12,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,
12,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,1,
1,7,9,5,4,1,12,11,7,4,3,11,
12,0,6,3,12,4,9,6,9,6,9,8,
0,0,0,1,0,0,0,0,0,0,0,0]);

G<x,y>:=MatrixGroup<12,F|x,y>;
print "Group G is U3(4):4 < GL(12,GF(13))";