/*
www-ATLAS of Group Representations.
3.M22 represented as 21 x 21 matrices over GF(25).
*/

F<w>:=GF(25);

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

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

G<x,y>:=MatrixGroup<21,F|x,y>;
print "Group G is 3.M22 < GL(21,GF(25))";