/*
A presentation for U5(2) in terms of standard generators.
*/

G<x,y>:=Group<x,y|
x^2,
y^5,
(x*y)^11,
(x,y)^3,
(x,y^2)^3,
(x,y*x*y)^3,
(x,y*x*y^2)^3
>;

M1:=sub<G|x,y*x*y^-1*x*y,y^2*x*y^-2*x*y^2>;
M2:=sub<G|x,y*x*y*x*y^-2*x*y>;
M3:=sub<G|y,x*y^-1*x*y^-1*x*y*x*y*x*y*x,x*y*x*y^-2*x*y*x*y^-2*x*y^2*x*y*x>;
M4:=sub<G|x,y*x*y*x*y^-1>;

H1:=sub<G|x,x^y,y*x*y^-1,y^2*x*y^-2>;
H2:=sub<G|x,y*x*y^-2*x*y,y^2*x*y*x*y^2>;
H3:=sub<G|x,y^2*x*y^-2,y^-2*x*y^2,y*x*y^-2*x*y>;
H4:=sub<G|x,y^2*x*y*x*y^-2>;