/*
Realisation of the presentation in L227P4 as 3 x 3 matrices over GF(27).
Generators are x and y and the orthogonal form is B with det(B) = w^-5.
*/

F<w>:=FiniteField(27);

G<x,y>:=MatrixGroup<3,F|[
1,0,0,
w^17,-1,0,
w^17,0,-1]
,[
0,1,0,
0,0,1,
1,0,0]
>;

B:=GL(3,F)![
2,w^17,w^17,
w^17,2,w^17,
w^17,w^17,2];