/*
www-ATLAS of Group Representations.
2.M22 represented as 10 x 10 matrices over GF(25).
*/

F<w>:=GF(25);

x:=CambridgeMatrix(3,F,10,\[
0,0,0,0,0,4,0,0,0,0,
0,0,0,0,0,0,0,4,0,0,
2,0,2,4,1,2,0,0,0,0,
0,1,0,1,0,0,0,1,0,0,
3,1,2,3,3,3,0,1,0,0,
4,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,4,
0,4,0,0,0,0,0,0,0,0,
9,0,9,21,9,9,1,0,1,1,
0,0,0,0,0,0,4,0,0,0]);

y:=CambridgeMatrix(3,F,10,\[
8,8,21,12,6,15,1,12,16,11,
14,1,4,17,23,12,18,23,13,7,
22,20,20,6,4,3,5,14,3,23,
3,6,4,3,11,13,8,0,2,11,
5,24,6,12,12,7,4,11,13,19,
13,10,24,5,7,24,2,0,2,4,
6,7,5,22,9,12,0,22,13,4,
21,17,22,16,12,2,24,18,13,23,
5,4,16,10,9,3,23,5,17,6,
13,3,14,3,9,2,10,4,14,15]);

G<x,y>:=MatrixGroup<10,F|x,y>;
print "Group G is 2.M22 < GL(10,GF(25))";