/*
www-ATLAS of Group Representations.
3.A7 represented as 18 x 18 matrices over GF(25).
*/

F<w>:=GF(25);

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

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

G<x,y>:=MatrixGroup<18,F|x,y>;
print "Group G is 3.A7 < GL(18,GF(25))";