/*
L2(27) presented on 3 generators.
a = \eta -> \eta + 1.
b = \eta -> w^2 \eta. (where w^3 + 2*w + 1 = 0 = (w^2)^3 + (w^2)^2 + w + 2.)
c = \eta -> -1 / \eta.
[ w is a primitive 26th root of unity in GF(27).]
*/

G<a,b,c>:=Group<a,b,c|
a^3,
b^13,
a^-1*b^-1*a*b^-1*a*b^-1*a*b^3,
(a,a^b),
c^2,
(a*c)^3,
(b*c)^2
>;

M1:=sub<G|a,b>;
M2:=sub<G|c,c^(b*a*b)>;
M3:=sub<G|b,c>;
M4:=sub<G|a,c>;