/*
www-ATLAS of Group Representations.
U3(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,
0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,
4,4,12,12,12,12,12,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,
6,6,0,0,3,3,0,7,7,12,0,0,
0,0,1,1,7,7,0,7,7,0,12,0,
7,7,5,5,3,3,0,9,9,0,0,12]);

y:=CambridgeMatrix(3,F,12,\[
10,12,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,
11,4,3,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,1,0,0,0]);

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