/*
A presentation for the JTits group 2F4(2)' in terms of standard generators.
SGens are (2A,3[A],13)-generators.
*/

G<x,y>:=Group<x,y|
x^2,
y^3,
(x*y)^13,
(x,y)^5,
(x,y*x*y)^4,
// (x,y*x*y*x*y)^5, // Is redundant.
(x*y*x*y*x*y*x*y*x*y^-1)^6
>;

M1:=sub<G|y,(x*y)^3*(x*y^-1)^4*x*y*(x*y^-1)^2*x*y*x*y*x>;
M2:=sub<G|y,x*y*x*y*x*y^-1*x*y^-1*x*y*x*y*x>;
M3:=sub<G|x,y^-1*x*y*x*y*x*y^-1*x*y*x*y*x*y*x*y^-1*x*y^-1>;
M4:=sub<G|y,x*y*x*y*x*y*x*y^-1*x*y*x*y*x*y^-1*x*y*x*y*x*y*x>;
M5:=sub<G|y,x*y*x*y*x*y*x*y*x*y^-1*x*y^-1*x*y*x*y*x*y^-1*x*y*x*y^-1*x>;
M6:=sub<G|x,y*x*y*x*y*x*y^-1*x*y>;
M7:=sub<G|x,y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y>;
M8:=sub<G|x,y^(x*y)>;

M6a:=sub<G|x*y*x*y*x*y*x*y^-1*x*y,y*x*y*x*y*x*y^-1*x*y*x>;
M6b:=sub<G|x,y*x*y*x*y*x*y^-1*x*y*x*y*x*y*x*y*x*y^-1*x*y>;
M6c:=sub<G|x*y*x*y*x*y*x*y^-1*x*y*x,y*x*y*x*y*x*y^-1*x*y>;
M7a:=sub<G|x*y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y*x,y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y>;
M7b:=sub<G|x,y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y*x*y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y,(y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y)^2>;
M7c:=sub<G|x*y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y,y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y*x>;

H1:=sub<G|y,x*y*x*y*x*y^-1*x>;
H2:=sub<G|y,x*y*x*y*x*y*x*y*x*y^-1*x*y*x*y*x*y*x*y*x>;
H3:=sub<G|x,y*x*y^-1*x*y*x*y^-1*x*y,(x,y*x*y)^2>;
H4:=sub<G|x,y*x*y^-1*x*y*x*y^-1*x*y,(x,y*x*y)^2,y*x*y*x*y*x*y*x*y*x*y^-1*x*y*x*y*(x,y*x*y*x*y*x*y*x*y*x*y^-1*x*y*x*y)^2>;
H5:=sub<G|y,x*y*x*y*x*y^-1*x*y*x*y*x*y^-1*x*y*x*y*x>;
H6:=sub<G|y,x^(y*x)>;