/*
www-ATLAS of Group Representations.
U3(4) represented as 9 x 9 matrices over GF(16).
*/

F<w>:=GF(16);

x:=CambridgeMatrix(3,F,9,\[
0,1,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,
0,0,0,0,1,0,0,0,0,
12,12,0,0,8,8,1,0,0,
0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,1,0]);

y:=CambridgeMatrix(3,F,9,\[
0,0,1,0,0,0,0,0,0,
0,1,1,0,0,0,0,0,0,
1,0,1,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,1,0,
0,0,0,1,0,0,0,0,0,
9,12,1,1,14,7,15,1,1,
8,0,5,14,15,6,1,6,1]);

G<x,y>:=MatrixGroup<9,F|x,y>;
print "Group G is U3(4) < GL(9,GF(16))";