/*
L2(27) presented on its (2,3,13D/E/F;13)-generators.
*/

G<x,y>:=Group<x,y|
x^2,
y^3,
(x*y)^13,
// (x*y*x*y*x*y^-1)^2*(x*y*x*y^-1*x*y^-1)^2*x*y*x*y^-1, // Is redundant.
(x*y*x*y*x*y*x*y^-1*x*y^-1)^3
>;

M1:=sub<G|y,x*y*x*y*x*y*x*y*x*y^-1*x*y^-1*x>;
M2:=sub<G|x,x^(y*x*y)>;
M3:=sub<G|x,x^y>;
M4:=sub<G|x,y^(x*y*x*y)>;

H1:=sub<G|y,x^(y*x*y*x)>;