commutative subgroup of S_n

Hi all,

I try to solve the following pb for several days but I can't reach
the conclusion:

Suppose that G is a commutative subgroup of S_n, where S_n is the
permutation group. Prove that Cardinal(G) <= 3^(n/2).

I tried an induction approach. The small n cases being simple. But this
induction is not that easy. It is straightforward to see that the
elements of G have the same cycles composition. The hard case in the
induction is when every element of G has exactly k d-cycle and k*d=n.
Anyone with a better idea ?

thanx in advance.

.

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