/*
A presentation for S13 in terms of some `near-standard' generators.
*/

G<x,y>:=Group<x,y|
x^13,
y^2,
(x*y)^12,
(x,y)^3,
(x^2,y)^2,
(x^3,y)^2,
(x^4,y)^2,
// (x^6,y)^2, // This is redundant.
(x^5,y)^2
>;

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