/*
www-ATLAS of Group Representations.
2.Sz(8) represented as 16 x 16 matrices over GF(13).
*/

F:=GF(13);

x:=CambridgeMatrix(3,F,16,\[
12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
1,11,7,2,8,12,5,5,2,4,3,7,3,8,12,9,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
8,2,0,8,4,8,4,9,6,2,7,5,9,12,7,1,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
11,12,2,3,7,5,11,6,0,1,1,9,1,12,10,8]);

y:=CambridgeMatrix(3,F,16,\[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
7,8,11,3,4,12,0,11,12,0,7,8,4,4,5,3,
6,7,9,10,10,7,2,9,9,0,11,0,8,0,0,5,
8,11,11,4,11,11,5,4,4,10,2,0,8,7,10,5,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
3,3,10,0,11,0,1,6,7,11,9,11,9,2,1,10,
6,0,9,6,5,10,1,6,2,11,11,11,11,5,11,10]);

G<x,y>:=MatrixGroup<16,F|x,y>;
print "Group G is 2.Sz(8) < GL(16,GF(13))";