/*
www-ATLAS of Group Representations.
L2(16):4 represented as 15 x 15 matrices over GF(17).
*/

F:=GF(17);

x:=CambridgeMatrix(3,F,15,\[
16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
1,0,0,1,16,0,1,0,16,16,1,1,1,0,16,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
16,1,1,8,10,15,4,15,8,6,10,15,6,16,12,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0]);

y:=CambridgeMatrix(3,F,15,\[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,1,1,16,16,1,0,16,16,1,0,1,1,16,
0,16,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,16,1,0,0,0,1,1,16,0,0,0,0,
0,0,0,1,16,0,0,0,16,0,1,0,1,0,0]);

G<x,y>:=MatrixGroup<15,F|x,y>;
print "Group G is L2(16):4 < GL(15,GF(17))";