/*
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,\[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
17,13,7,23,23,7,7,23,22,11,1,8,0,19,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
19,11,7,23,10,7,15,23,2,0,0,3,1,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
2,3,21,9,10,7,15,23,16,0,0,14,0,0,1]);

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

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