/*
www-ATLAS of Group Representations.
2.L2(13) represented as 6 x 6 matrices over GF(13).
*/

F:=GF(13);

x:=CambridgeMatrix(3,F,6,\[
0,1,0,0,0,0,
12,0,0,0,0,0,
0,0,0,1,0,0,
0,0,12,0,0,0,
0,0,0,0,0,1,
0,0,0,0,12,0]);

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

G<x,y>:=MatrixGroup<6,F|x,y>;
print "Group G is 2.L2(13) < GL(6,GF(13))";