/*
www-ATLAS of Group Representations.
2.L2(13) represented as 12 x 12 matrices over GF(27).
*/

F<w>:=GF(27);

x:=CambridgeMatrix(3,F,12,\[
0,1,0,0,0,0,0,0,0,0,0,0,
2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,
0,0,2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,2,0,0,0,0,0,
0,0,0,0,0,0,0,2,0,0,0,0,
2,25,14,16,15,20,23,18,21,24,2,24,
1,8,16,13,19,6,12,17,5,21,5,1]);

y:=CambridgeMatrix(3,F,12,\[
15,2,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,
10,10,21,0,0,0,0,0,0,0,0,0,
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,
1,10,8,19,11,6,20,8,21,8,14,0,
0,0,0,0,0,1,0,0,0,0,0,0,
23,15,19,20,1,18,21,3,23,16,1,4]);

G<x,y>:=MatrixGroup<12,F|x,y>;
print "Group G is 2.L2(13) < GL(12,GF(27))";