/*
www-ATLAS of Group Representations.
2.G2(4) represented as 12 x 12 matrices over GF(13).
*/

F:=GF(13);

x:=CambridgeMatrix(3,F,12,\[
0,12,0,0,0,0,0,0,0,0,0,0,
12,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,12,0,0,0,0,0,0,0,0,
0,0,12,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,12,0,0,0,0,0,
0,0,0,0,0,0,0,12,0,0,0,0,
0,0,0,0,12,0,0,0,0,0,0,0,
0,0,0,0,0,12,0,0,0,0,0,0,
11,11,1,1,8,7,8,7,1,0,0,0,
7,7,10,10,7,11,7,11,0,1,0,0,
11,11,2,2,1,12,1,12,0,0,1,0,
11,11,12,12,6,4,6,4,0,0,0,1]);

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,
0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,
1,12,12,0,12,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,1,
6,0,7,4,4,7,1,8,8,8,10,0,
0,0,11,9,2,1,3,12,7,7,4,12,
0,0,0,12,0,12,0,0,12,0,0,12]);

G<x,y>:=MatrixGroup<12,F|x,y>;
print "Group G is 2.G2(4) < GL(12,GF(13))";