/*
Presentation of S8(2) with respect to a certain triple of (2A,9B,17)-gens.
This triple of (2A,9B,17)-gens satisfies o(xyy) = 15 (rather than o(xyy) = 17).
*/

G<x,y>:=Group<x,y|
x^2,
y^9,
(x*y)^17,
(x,y)^2,
(x,y^2)^2,
(x,y^3)^3,
(x,y^4)^3,
(x,y*x*y)^2,
(x,y^3*x*y^3)^2
>;

M1:=sub<G|x,y*x*y^3>;
M2:=sub<G|x,y^3*x*y^4>;

H1:=sub<G|y*x*y^3,x*y*x*y^3*x>;
H2:=sub<G|y^3*x*y^4,x*y^3*x*y^4*x>;