/*
www-ATLAS of Group Representations.
3.L3(4):2a represented as 15 x 15 matrices over GF(25).
*/

F<w>:=GF(25);

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

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

G<x,y>:=MatrixGroup<15,F|x,y>;
print "Group G is 3.L3(4):2a < GL(15,GF(25))";