/*
www-ATLAS of Group Representations.
3.L3(4) represented as 21 x 21 matrices over GF(25).
*/

F<w>:=GF(25);

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

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

G<x,y>:=MatrixGroup<21,F|x,y>;
print "Group G is 3.L3(4) < GL(21,GF(25))";