/*
www-ATLAS of Group Representations.
L2(13) represented as 13 x 13 matrices over GF(13).
*/

F:=GF(13);

x:=CambridgeMatrix(3,F,13,\[
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,
0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,
2,5,8,11,10,4,5,3,5,11,8,5,11,
3,5,9,9,2,1,7,10,10,6,8,3,7,
5,1,8,12,8,4,1,10,2,2,6,8,3]);

y:=CambridgeMatrix(3,F,13,\[
4,12,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,
11,10,9,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,1,0,0,0,0,0,0,0,
6,4,7,6,10,0,10,6,11,12,7,3,1,
11,2,3,11,3,6,12,8,7,3,12,6,11]);

G<x,y>:=MatrixGroup<13,F|x,y>;
print "Group G is L2(13) < GL(13,GF(13))";