/*
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,
15,15,0,0,12,12,1,0,0,
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,
13,15,1,1,11,6,10,1,1,
12,0,2,11,10,7,1,7,1]);

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