/*
www-ATLAS of Group Representations.
TD4(3) represented as 8 x 8 matrices over GF(27).
*/

F<w>:=GF(27);

x:=CambridgeMatrix(3,F,8,\[
5,0,9,15,5,14,23,15,
0,6,23,24,6,22,9,19,
17,25,16,1,1,0,11,12,
10,22,2,15,2,4,22,22,
8,5,2,0,15,19,11,7,
10,25,14,26,25,21,0,1,
15,19,17,20,10,1,22,1,
24,15,6,0,20,1,2,22]);

y:=CambridgeMatrix(3,F,8,\[
1,13,20,21,23,6,18,16,
19,26,9,20,1,4,13,10,
23,13,17,0,23,25,0,5,
9,8,6,10,1,12,1,10,
4,18,16,12,21,1,20,12,
7,23,13,10,3,12,21,24,
22,4,9,9,3,12,1,0,
12,14,2,0,21,5,0,18]);

G<x,y>:=MatrixGroup<8,F|x,y>;
print "Group G is TD4(3) < GL(8,GF(27))";