/*
www-ATLAS of Group Representations.
4b.L3(4) represented as 20 x 20 matrices over GF(49).
*/

F<w>:=GF(49);

x:=CambridgeMatrix(3,F,20,\[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
31,11,30,2,32,3,23,21,23,46,40,22,18,8,11,6,16,22,17,6,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
37,38,6,33,33,32,27,24,1,10,47,17,22,36,47,3,35,27,4,17,
34,0,0,29,12,41,9,15,9,32,22,16,30,8,19,32,17,7,4,46,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
39,34,45,17,16,41,46,14,30,23,15,38,26,46,22,24,6,15,1,3]);

y:=CambridgeMatrix(3,F,20,\[
1,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,6,6,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,1,0,0,0,0,0,0,0,0,6,0,0,1,0,0,0,0,
0,0,0,1,0,6,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
4,31,44,17,40,33,47,18,10,8,4,43,13,10,26,40,40,38,19,5,
26,44,25,5,23,4,33,28,34,10,16,34,38,48,46,1,40,34,39,1,
8,3,44,12,24,9,4,39,19,42,18,33,9,18,29,38,11,28,40,46,
28,12,45,7,19,7,31,40,37,8,4,14,21,24,5,45,31,4,37,18]);

G<x,y>:=MatrixGroup<20,F|x,y>;
print "Group G is 4b.L3(4) < GL(20,GF(49))";