/*
L2(32) presented on generators x and y satisfying:
o(x) = 2, o(y) = 5, o(xy) = 5, o([x,y^2]) = 11 and o([x,y^2xy]) = 31.
These imply that o([x,yxy^2]) = 33.
The reciprocal map swaps the orders of the last two elements.
*/

G<x,y>:=Group<x,y|
x^2,
y^5,
(x*y)^5,
(x*y^2)^10, // Is redundant.
// (x,y^2*x*y^2)^2, // Is redundant.
// (x*y*x*y^-2*x*y^2*x*y^-1*x*y^2*x*y^-2)^2, // Is redundant.
x*y*x*y^-2*x*y^2*x*y^-1*x*y*x*y^-2*x*y^-2*x*y*x*y^-1*x*y^2*x*y^2*x*y^-1
>;

M0:=sub<G|x,x^y,y*x*y^-1>;
M1:=sub<G|y,x*y*x*y^2*x>;
M2:=sub<G|x,y^2*x*y^2*x*y^2*x*y>;
M3:=sub<G|x,y*x*y^-2*x*y^-2>;

M0a:=sub<G|x,x^y,y*x*y^-1,y^2*x*y^-2>;
H0:=sub<G|x,y*x*y*x*y^-2>;