I am trying to use generators and relations here.
Let M ≤ S_5 be the subgroup generated by two transpositions t_1= (12) and t_2= (34).
Let N = {g ∈S_5| gMg^(-1) = M} be the normalizer of M in S_5.
How should I describe N by generators and relations?
How should I show that N is a semidirect product of two Abelian groups?
How to compute |N|?
How many subgroups conjugate to M are there in S_5 ? Why?
(I think Sylow's theorems should be used here.)