/*
L2(32):5 presented on 4 generators.
a = \eta -> \eta+1.
b = \eta -> w \eta. (where w^31 = 1 \ne w and also w^5 + w^2 + 1 = 0.)
c = \eta -> -1 / \eta.
d = \eta -> \eta^2 (a field automorphism).
*/

G<a,b,c,d>:=Group<a,b,c,d|
a^2,
b^31,
a*b^-2*a*b^-3*a*b^5,
c^2,
(a*c)^3,
(b*c)^2,
d^5,
(a,d),
(c,d),
b^-2*d^-1*b*d
>;

M0:=sub<G|a,b,c>;
M1:=sub<G|a,b,d>;
M2:=sub<G|a,(a*d)^(b^6*a*b*c)>;
M3:=sub<G|b,c,d>;