/*
www-ATLAS of Group Representations.
2.L2(13) represented as 12 x 12 matrices over GF(13).
*/

F:=GF(13);

x:=CambridgeMatrix(3,F,12,\[
0,1,0,0,0,0,0,0,0,0,0,0,
12,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,
0,0,12,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,12,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,12,0,0,0,0,0,
0,0,0,0,0,0,0,12,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,8,0,
0,0,0,0,0,0,0,0,0,0,0,5]);

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

G<x,y>:=MatrixGroup<12,F|x,y>;
print "Group G is 2.L2(13) < GL(12,GF(13))";