/*
www-ATLAS of Group Representations.
G2(3):2 represented as 14 x 14 matrices over GF(13).
*/

F:=GF(13);

x:=CambridgeMatrix(3,F,14,\[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,2,0,0,1,2,0,12,6,6,
12,0,0,6,12,0,12,0,0,0,0,7,0,0,
0,12,6,0,0,0,7,1,0,1,0,2,7,0,
12,0,12,0,0,0,0,0,7,0,12,0,2,0,
0,0,0,12,0,0,0,12,0,12,0,1,0,0,
12,0,12,0,0,6,0,0,0,6,12,0,0,12,
2,0,2,1,2,0,0,7,0,7,0,0,11,1,
1,0,0,0,0,7,0,0,0,7,1,6,1,1,
0,12,0,0,0,1,0,12,1,1,0,12,6,0,
12,0,12,6,12,0,0,0,0,0,0,0,1,0,
6,0,6,3,6,2,0,1,1,3,0,12,0,6,
0,0,7,0,0,0,0,0,1,0,0,12,6,0]);

y:=CambridgeMatrix(3,F,14,\[
0,1,7,0,0,10,0,0,12,10,0,1,7,7,
12,0,0,6,11,0,0,0,0,0,0,7,0,0,
0,1,7,12,0,0,0,0,0,11,0,1,0,0,
0,7,12,0,0,6,12,7,0,6,0,7,11,12,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,
1,7,11,0,0,0,0,0,0,6,1,0,0,0,
7,1,7,11,7,11,0,0,0,11,0,1,0,7,
1,6,1,7,2,0,12,0,0,7,0,6,0,0,
0,0,1,7,1,0,2,6,0,0,0,6,1,0,
0,0,0,6,12,7,0,0,0,0,0,7,0,1,
0,1,7,11,7,2,0,0,1,0,0,1,6,6,
0,0,1,0,0,0,12,7,0,0,0,7,11,0,
0,1,7,0,0,0,6,11,0,11,0,12,6,0,
6,1,0,0,0,3,0,0,0,1,6,0,0,6]);

G<x,y>:=MatrixGroup<14,F|x,y>;
print "Group G is G2(3):2 < GL(14,GF(13))";