/*
L2(27) presented on its (2,3,13A/B/C;14)-generators.
*/

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

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

H1:=sub<G|x,x^(y*x*y^-1)>;
H2:=sub<G|y,y^(x*y*x*y*x)>;