/*
Presentations of HN (more-or-less the same).
*/

G<a,b,c,d,t>:=Group<a,b,c,d,t|
a^4,(a^2,b),b^7,(a*b^2)^4,a^-2*(a*b*a*b^3)^3,((a*b)^3*a*b^-3)^2,
c^2*a^2,(a,c),(b*a*b,c),(b*a*b^3*c)^3,
d^2,(a*d)^2,(b,d),d^(c*b*c*b^-1)*(c*d)^3,
t^5,t^a*t^2,t^c*t^-2,(t,b),(d*t)^3
>;

// Copies of 2"HS:2, A12 and A11 respectively.
H:=sub<G|a,b,c,d>;
K:=sub<G|a,b,d,d^(c*b*c),t>;
L:=sub<G|a,b,d,t^(d^(c*b*c))>;
// print Index(G,H:Print:=2,Hard:=true,CosetLimit:=2*10^6,Grain:=10^5);
// print Index(G,K:Print:=2,Hard:=true,CosetLimit:=2*10^6,Grain:=10^5);



G<a,b,c,d,t>:=Group<a,b,c,d,t|
a^4,(a^2,b),b^7,(a*b^2)^4,(a,b^3)^3,((a*b)^3*a*b^-3)^2,
c^2*a^2,(a,c),(b*a*b,c),(b*a*b^3*c)^3,
d^2,(a*d)^2,(b,d),d^(c*b*c*b^-1)*(c*d)^3,
t^5,t^a*t^2,t^c*t^-2,(t,b),(d*t)^3
>;

// Copies of 2"HS:2, A12 and A11 respectively.
H:=sub<G|a,b,c,d>;
K:=sub<G|a,b,d,d^(c*b*c),t>;
L:=sub<G|a,b,d,t^(d^(c*b*c))>;
// print Index(G,H:Print:=2,Hard:=true,CosetLimit:=2*10^6,Grain:=10^5);
// print Index(G,K:Print:=2,Hard:=true,CosetLimit:=2*10^6,Grain:=10^5);