/*
www-ATLAS of Group Representations.
L3(3) represented as 16 x 16 matrices over GF(16).
*/

F<w>:=GF(16);

x:=CambridgeMatrix(3,F,16,\[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
9,15,10,12,6,6,10,8,12,8,6,11,1,11,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
2,0,11,13,6,3,12,1,8,5,0,11,10,14,13,5,
13,8,14,10,5,9,14,4,3,5,12,2,11,14,3,13]);

y:=CambridgeMatrix(3,F,16,\[
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
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,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
11,0,11,1,10,15,11,0,11,10,15,4,10,1,15,0,
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]);

G<x,y>:=MatrixGroup<16,F|x,y>;
print "Group G is L3(3) < GL(16,GF(16))";