/*
www-ATLAS of Group Representations.
S6(3) represented as 13 x 13 matrices over GF(25).
*/

F<w>:=GF(25);

x:=CambridgeMatrix(3,F,13,\[
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,
0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,
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,
0,0,0,0,0,1,0,0,0,0,0,0,0,
1,1,7,7,10,9,10,23,9,4,0,23,0,
16,16,17,17,9,11,9,19,11,0,4,19,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,
7,7,0,0,15,6,15,22,6,0,0,22,4]);

y:=CambridgeMatrix(3,F,13,\[
0,0,1,0,0,0,0,0,0,0,0,0,0,
21,4,4,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,
17,18,1,0,4,0,0,1,0,0,0,0,0,
15,0,5,11,17,6,2,6,18,4,4,2,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,
0,21,13,21,4,4,7,12,17,9,13,8,0,
6,23,2,3,0,7,0,3,8,0,1,3,0,
23,23,9,4,0,4,0,9,0,4,0,0,4]);

G<x,y>:=MatrixGroup<13,F|x,y>;
print "Group G is S6(3) < GL(13,GF(25))";