/*
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,
2,20,10,13,12,22,26,23,24,19,2,19,
1,7,13,9,21,8,11,14,3,24,3,1]);

y:=CambridgeMatrix(3,F,12,\[
12,2,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,
17,17,24,0,0,0,0,0,0,0,0,0,
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,
1,17,7,21,15,8,22,7,24,7,10,0,
0,0,0,0,0,1,0,0,0,0,0,0,
26,12,21,22,1,23,24,4,26,13,1,5]);

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