/*
S14 as permutations on 39916800 points [primitive action].
Made by coset enumeration.
*/

G<x,y>:=Group<x,y|
x^2,
y^13,
(x*y)^14,
(x,y)^3,
(x,y*x*y)^2,
(x,y*x*y*x*y)^2,
(x,(x*y)^4)^2,
// (x,(x*y)^6)^2, // redundant.
// (x,(x*y)^7)^2, // redundant.
(x,(x*y)^5)^2
>;

H:=sub<G|y,x*x^(y*x*y)*x^(y^2*x*y^3)*x^(y^3*x*y^4)*x^(y^3*x*y^6)*x^(y^2*x*y^-5)*x^(y*x*y^-2)>;
CS:=CosetSpace(G,H:Print:=2,Hard:=true,CosetLimit:=41000000);

_,G<x,y>:=CosetAction(CS);
delete(CS);
// c:=x;d:=y;