/*
www-ATLAS of Group Representations.
L2(19) represented as 9 x 9 matrices over GF(19).
*/

F:=GF(19);

x:=CambridgeMatrix(3,F,9,\[
0,1,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,
0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,1,
1,18,18,1,17,2,1,1,18,
0,0,0,0,0,0,1,0,0]);

y:=CambridgeMatrix(3,F,9,\[
9,18,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,
6,14,10,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,1,0,
0,0,0,1,0,0,0,0,0,
0,17,7,11,11,6,8,11,16,
14,0,4,5,6,9,14,17,8]);

G<x,y>:=MatrixGroup<9,F|x,y>;
print "Group G is L2(19) < GL(9,GF(19))";