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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.

Describe N by generators and relations.

Show that N is a semidirect product of two Abelian groups.

Compute |N|.

How many subgroups conjugate to M are there in S_5 ? Why？

(I think Sylow's theorems should be used here.)