/*
Presentation of HN.
*/

G<a,b,c,d,z,t>:=Group<a,b,c,d,z,t|
z^2,(z,a),(z,b),(z,c),(z,d),
a^2*z,b^7,(a*b^2)^4,(a*b*a*b^3)^3*z,((a*b)^3*a*b^-3)^2,
c^2*z,(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,(z*t)^2,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,z>;
K:=sub<G|a,b,d,d^(c*b*c),z,t>;
L:=sub<G|a,b,d,z,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);