/*
www-ATLAS of Group Representations.
L2(23) represented as 15 x 15 matrices over GF(23).
*/

F:=GF(23);

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,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
13,13,5,5,20,20,12,21,12,21,6,1,22,6,1,
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]);

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

G<x,y>:=MatrixGroup<15,F|x,y>;
print "Group G is L2(23) < GL(15,GF(23))";