/*
www-ATLAS of Group Representations.
12.M22 represented as 48 x 48 matrices over GF(25).
*/

F<w>:=GF(25);

x:=CambridgeMatrix(3,F,48,\[
2,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
23,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
18,13,11,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
20,13,9,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
10,10,6,20,0,12,20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
9,11,22,15,0,5,17,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
9,10,21,10,17,12,22,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
23,9,0,13,6,14,9,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,2,7,4,14,12,6,8,4,6,21,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
3,11,20,14,1,23,10,24,11,7,11,3,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
12,1,20,20,12,9,14,5,1,1,21,2,13,20,18,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
20,22,22,10,0,21,15,17,13,23,0,10,7,3,9,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
20,14,24,11,3,10,4,0,16,0,6,17,14,4,14,2,9,13,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
13,19,22,21,15,8,2,2,4,17,2,20,20,9,17,14,21,17,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
6,20,11,20,16,13,13,14,23,7,23,7,17,0,20,5,12,17,13,17,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
20,18,24,23,10,21,11,2,22,24,11,15,7,0,22,0,20,0,24,7,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
19,18,17,17,14,3,16,1,15,3,23,13,15,15,2,2,13,24,24,16,1,18,4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
5,13,11,6,3,6,4,23,7,22,22,22,7,4,17,8,7,9,12,3,8,0,3,4,13,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
14,23,18,7,24,22,7,18,15,21,13,15,13,1,9,7,22,8,5,10,14,5,0,14,22,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
18,3,6,16,7,12,5,22,3,19,1,24,10,0,6,24,23,17,18,12,12,24,11,18,3,2,19,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
23,2,24,14,17,24,13,18,6,17,16,21,21,3,0,5,24,9,19,10,21,6,6,5,9,16,9,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,18,22,5,17,1,23,24,4,23,9,24,11,1,19,23,7,7,5,14,8,10,7,0,4,24,3,9,15,1,14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
15,20,3,6,1,19,9,4,0,10,20,8,9,6,7,11,22,9,0,16,14,17,16,0,12,24,0,23,7,21,24,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
19,7,18,24,15,4,22,14,1,5,20,10,7,5,23,4,24,14,18,1,18,19,22,16,11,12,6,7,15,8,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
24,21,13,18,17,8,21,4,16,15,13,15,21,13,7,22,13,11,24,20,18,19,18,3,22,3,19,15,19,8,5,20,17,15,15,0,0,0,0,0,0,0,0,0,0,0,0,0,
23,19,8,13,4,3,24,19,18,20,1,7,11,18,14,14,1,13,19,3,17,1,2,7,21,8,14,7,5,13,20,6,8,24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,
20,8,14,0,19,19,8,6,12,3,7,6,8,20,16,7,15,20,11,16,8,15,0,16,3,8,11,6,3,14,5,17,12,11,2,15,18,0,0,0,0,0,0,0,0,0,0,0,
15,10,0,19,23,19,7,12,2,2,1,11,20,16,16,13,17,17,21,5,7,24,7,10,6,22,23,14,10,18,7,19,19,10,23,16,2,0,0,0,0,0,0,0,0,0,0,0,
10,6,16,19,2,19,13,0,8,12,1,17,20,18,9,9,6,23,8,9,12,1,22,19,10,2,16,12,1,20,17,22,10,21,14,14,3,17,1,13,0,0,0,0,0,0,0,0,
2,3,18,21,8,14,13,22,16,4,9,6,2,2,6,0,19,12,0,20,21,8,3,19,8,5,14,20,18,4,10,1,11,14,3,23,19,24,14,9,7,6,0,0,0,0,0,0,
0,14,1,2,16,6,19,16,8,12,18,8,24,18,7,3,23,23,17,21,17,17,22,1,16,12,22,10,13,24,9,8,14,10,18,4,1,19,23,2,2,20,0,0,0,0,0,0,
17,21,13,6,1,20,0,10,20,24,6,14,6,8,17,19,1,20,8,21,2,10,9,20,2,15,2,19,17,22,8,3,0,22,19,15,6,12,5,16,7,6,0,0,0,0,0,0,
9,10,6,4,1,18,1,24,1,8,10,0,24,16,8,6,9,18,13,0,5,21,0,3,14,13,3,17,8,5,9,2,21,5,1,9,21,3,3,4,6,8,9,2,3,0,0,0,
14,24,15,23,9,14,9,17,11,9,8,7,10,4,6,17,5,16,13,24,9,20,9,1,20,5,24,24,0,8,7,14,20,4,12,16,6,6,21,2,6,12,21,24,10,9,16,0,
15,24,15,1,19,13,4,21,10,6,15,24,5,12,2,14,10,22,17,6,20,2,12,23,6,1,23,6,3,5,8,22,23,23,0,20,6,13,17,22,6,16,18,0,21,21,14,0,
14,23,7,10,17,1,23,16,19,15,2,8,2,8,7,22,0,12,4,15,24,7,21,14,7,14,18,6,0,2,21,5,21,8,17,24,18,22,13,19,21,20,23,17,17,22,5,8,
15,2,3,7,9,13,14,15,23,1,7,10,11,7,12,24,14,10,3,11,7,6,9,13,3,2,17,14,5,10,23,7,11,7,17,17,11,1,7,3,14,10,21,2,8,15,21,9,
11,7,12,1,21,4,23,1,23,12,10,15,5,6,8,23,8,10,1,13,2,0,14,3,3,5,7,9,12,7,1,1,18,6,14,17,13,2,2,24,24,5,19,5,1,22,10,12,
18,1,24,22,12,13,0,7,14,22,0,21,4,23,12,19,24,17,6,7,22,13,12,5,11,18,6,15,16,20,22,2,17,1,7,4,14,3,0,23,21,18,11,19,18,16,16,3,
1,9,4,2,5,2,19,6,10,4,9,5,11,22,4,14,5,10,8,7,16,14,18,10,7,5,15,19,12,16,14,5,2,13,11,17,23,23,21,17,17,9,8,15,1,1,10,22,
11,20,8,24,15,17,12,9,14,7,19,8,20,21,11,11,11,6,16,2,12,23,16,19,10,12,19,24,10,4,23,2,16,8,5,9,21,2,2,4,6,13,10,15,6,5,10,1,
10,4,7,8,8,24,0,15,12,7,21,0,12,4,21,8,3,24,23,1,22,14,20,19,15,17,23,24,5,1,1,1,5,13,4,13,11,12,20,21,24,23,11,15,24,6,10,21,
16,14,15,3,19,22,10,1,6,21,9,12,24,7,19,24,14,7,11,21,14,24,3,17,13,10,5,10,24,8,3,2,16,10,19,22,12,16,4,7,14,11,16,4,9,14,10,22,
5,22,12,4,17,18,3,23,14,16,13,20,12,11,15,22,12,2,20,11,5,13,20,4,15,12,2,20,15,16,2,10,7,17,6,0,17,0,13,0,4,18,17,8,5,17,11,4,
13,6,14,8,2,1,7,8,10,4,2,15,23,18,22,2,22,12,2,2,24,22,17,14,20,8,8,6,13,2,16,22,4,2,15,7,17,15,4,18,11,8,4,10,0,14,14,19,
21,12,15,24,20,22,14,8,1,0,18,24,24,18,19,18,5,23,22,9,4,23,21,1,17,0,18,16,7,5,19,6,17,10,11,6,14,23,3,17,2,12,10,24,6,10,4,17,
2,15,8,13,19,23,18,18,23,2,17,2,11,20,8,21,13,22,16,15,14,9,0,14,3,9,20,8,4,23,11,15,10,19,21,17,11,12,5,17,10,22,8,0,19,8,3,9,
1,11,16,4,6,4,3,24,9,22,12,18,3,19,16,4,17,13,17,22,3,5,8,22,8,6,9,15,19,16,8,8,12,16,15,16,13,10,6,11,6,23,11,8,19,14,20,21]);

y:=CambridgeMatrix(3,F,48,\[
16,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,17,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
2,5,18,2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
24,6,10,19,6,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
4,15,16,10,10,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
19,22,10,6,15,15,1,11,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
14,0,9,22,5,15,24,14,22,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
6,1,7,1,9,4,7,18,10,22,20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
16,20,6,1,24,16,9,18,21,18,15,14,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
3,24,21,19,24,9,13,2,7,17,0,24,2,22,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
3,16,6,3,4,11,11,17,3,20,20,0,18,15,7,14,14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
10,2,17,4,4,5,7,18,12,14,7,7,8,17,20,9,24,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
4,11,23,1,22,15,4,2,10,18,9,24,19,5,20,1,20,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
21,0,7,9,0,10,23,11,19,19,6,10,9,14,12,11,5,3,19,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
21,22,19,1,22,12,9,2,10,0,15,19,3,15,12,24,17,10,12,18,10,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
19,7,13,10,10,1,22,6,13,2,16,24,4,4,13,14,20,18,6,3,20,4,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
14,17,17,21,15,12,7,0,20,20,18,20,5,15,20,12,14,22,8,10,14,24,16,10,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
3,6,6,21,8,19,6,24,8,18,7,9,13,18,5,21,5,14,10,12,11,4,20,12,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
23,4,7,7,4,14,4,24,24,21,16,20,16,1,0,18,21,17,22,10,6,23,16,23,11,6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,13,12,24,24,4,14,3,24,14,16,1,24,7,12,15,18,4,0,17,23,8,24,17,4,8,4,23,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,22,11,23,1,3,17,17,5,3,16,0,7,4,10,21,4,22,5,10,10,21,23,2,7,2,11,3,17,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
13,3,8,20,13,8,24,7,20,14,5,16,24,6,12,5,18,20,15,14,12,8,15,0,9,21,12,4,6,22,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
7,14,18,24,6,15,18,15,5,5,19,20,15,23,24,12,11,2,16,12,13,15,1,22,5,21,6,24,9,17,13,23,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
13,4,8,12,0,0,23,12,21,20,13,12,20,24,7,12,21,10,2,21,24,24,21,8,5,13,1,22,11,9,8,17,12,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
8,19,19,5,17,6,8,22,8,1,7,1,23,10,9,17,12,22,22,24,14,1,2,20,5,9,1,4,11,1,1,7,24,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
12,14,10,14,21,23,2,24,14,22,20,12,13,17,10,21,1,1,11,9,23,8,1,7,14,15,1,19,3,2,23,23,17,24,20,9,0,0,0,0,0,0,0,0,0,0,0,0,
3,11,20,24,14,23,14,0,8,24,19,24,24,5,0,1,23,0,17,14,4,3,3,14,10,4,13,6,7,5,5,16,11,1,15,22,6,21,0,0,0,0,0,0,0,0,0,0,
12,1,6,19,10,16,14,23,12,2,17,0,18,19,0,22,18,7,14,9,24,11,20,11,2,11,13,21,13,18,19,11,8,0,12,8,15,5,21,0,0,0,0,0,0,0,0,0,
9,17,24,15,4,16,10,13,21,13,11,14,22,14,2,11,0,16,0,5,4,16,17,15,9,9,10,7,6,2,8,3,23,13,20,23,19,18,12,23,21,0,0,0,0,0,0,0,
17,12,13,0,24,6,21,17,5,14,3,8,15,5,21,5,15,23,17,5,6,18,0,6,0,15,11,7,19,20,22,17,23,3,18,1,17,18,15,7,9,0,0,0,0,0,0,0,
19,21,23,5,5,21,10,2,6,6,16,20,18,12,4,7,14,10,15,14,21,3,3,20,1,0,13,5,3,15,8,16,8,1,3,8,10,11,3,9,12,12,16,0,0,0,0,0,
12,19,10,16,0,22,24,21,16,3,0,10,6,17,3,15,1,23,20,0,14,9,21,21,13,15,11,1,24,9,23,24,1,14,19,21,7,8,14,6,1,2,23,3,0,0,0,0,
4,5,0,10,19,12,15,9,9,1,0,19,2,3,1,17,18,16,14,3,22,3,8,6,10,0,23,7,13,8,8,7,4,14,23,2,10,9,14,23,5,22,22,1,18,3,0,0,
15,17,17,13,24,17,15,23,10,6,19,22,15,21,4,16,6,0,5,15,5,21,13,11,22,1,8,9,13,10,19,19,11,13,19,14,20,18,9,9,19,5,4,10,3,11,12,24,
13,13,19,21,15,5,19,8,11,24,0,17,8,21,6,24,13,6,4,19,5,1,13,3,18,8,22,16,22,12,18,6,20,22,23,15,8,7,22,18,8,19,15,19,0,5,1,18,
18,8,16,13,4,18,11,21,4,20,24,22,22,10,5,3,6,13,9,14,21,6,20,13,13,21,12,4,16,22,18,8,13,23,21,5,11,5,3,18,5,9,21,7,0,20,4,11,
9,9,1,5,20,19,6,0,5,5,8,18,12,0,21,20,8,2,8,20,13,23,1,16,24,7,15,1,21,23,19,9,18,0,24,19,13,17,6,23,3,12,5,21,18,17,10,9,
1,8,8,12,0,20,4,14,18,4,10,24,4,17,10,9,3,5,13,11,13,18,11,16,7,3,13,12,18,17,17,5,18,23,5,1,15,19,21,1,13,3,17,15,2,2,3,0,
18,14,20,12,13,16,15,12,13,11,20,15,7,24,6,15,24,13,21,24,20,0,10,15,6,9,6,17,1,3,8,2,8,6,7,20,18,20,1,22,6,7,14,16,20,12,16,0,
3,5,9,21,8,0,16,20,3,20,20,6,15,20,8,21,19,2,24,1,7,11,13,13,13,9,1,21,11,13,11,19,23,15,20,12,17,21,8,4,16,23,21,0,5,18,1,1,
17,5,12,19,15,20,20,16,12,22,22,6,4,16,21,2,24,2,11,13,20,6,1,7,23,0,18,5,18,11,2,6,1,13,22,12,15,18,4,5,11,17,5,14,16,23,20,2,
12,22,9,7,20,19,18,4,3,12,24,4,8,5,14,11,22,22,8,2,1,3,4,8,4,4,11,1,16,3,15,20,13,4,6,18,20,5,10,4,14,10,24,10,6,3,9,13,
18,24,5,11,9,24,7,22,23,1,7,5,24,6,9,13,23,20,8,23,7,16,5,18,13,7,18,21,21,17,13,12,1,15,22,19,13,2,8,7,23,17,23,16,13,21,4,15,
9,24,14,22,1,8,7,5,20,18,14,1,24,8,5,23,24,19,16,15,4,22,12,21,15,19,0,23,15,5,6,8,11,15,9,23,9,4,16,11,11,24,0,15,5,4,0,4,
24,17,2,20,20,5,15,17,20,6,2,5,5,20,13,1,24,12,18,15,3,0,3,11,20,2,0,1,11,16,5,1,12,6,20,10,5,3,11,4,20,16,22,20,20,14,3,5,
20,1,2,8,20,4,19,17,5,21,13,8,21,0,10,18,1,2,22,2,22,4,5,0,22,15,5,17,4,9,7,20,13,19,23,1,16,15,15,14,9,22,24,2,12,22,17,21,
13,10,23,23,7,11,8,3,20,10,17,15,9,6,12,20,5,5,9,16,1,9,20,23,1,14,24,23,11,20,7,16,22,1,8,21,11,1,21,8,9,6,15,12,13,2,9,3,
19,9,8,9,16,7,11,4,1,4,4,5,23,1,9,15,0,2,21,22,20,10,0,6,12,22,4,9,13,1,20,8,19,11,22,15,10,24,23,4,20,24,9,18,6,9,1,16]);

G<x,y>:=MatrixGroup<48,F|x,y>;
print "Group G is 12.M22 < GL(48,GF(25))";