/*
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,\[
0,1,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,1,0,0,
0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,
23,7,14,16,4,18,1,12,1,0,
19,11,20,5,13,15,17,10,0,1]);

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

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