/*
www-ATLAS of Group Representations.
L3(3):2 represented as 16 x 16 matrices over GF(13).
*/

F:=GF(13);

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,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
4,9,6,7,6,6,7,7,1,9,9,12,1,4,0,4,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,7,6,11,6,2,7,4,0,10,9,0,0,1,3,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0]);

y:=CambridgeMatrix(3,F,16,\[
4,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
8,1,10,0,9,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
3,5,12,5,10,4,3,3,10,11,11,5,10,0,7,8,
3,6,11,11,3,8,7,6,11,2,12,9,5,7,3,5,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
4,4,7,10,8,5,6,9,10,12,3,6,10,10,11,7,
9,5,5,10,2,12,11,11,3,4,3,0,6,4,3,0,
10,12,0,12,6,11,1,2,6,10,4,6,2,11,7,8]);

G<x,y>:=MatrixGroup<16,F|x,y>;
print "Group G is L3(3):2 < GL(16,GF(13))";