/*
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,
2,22,17,9,11,25,18,26,19,21,2,21,
1,6,9,16,24,7,15,10,4,19,4,1]);

y:=CambridgeMatrix(3,F,12,\[
11,2,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,
14,14,19,0,0,0,0,0,0,0,0,0,
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,
1,14,6,24,12,7,25,6,19,6,17,0,
0,0,0,0,0,1,0,0,0,0,0,0,
18,11,24,25,1,26,19,5,18,9,1,3]);

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