Normalizer of Sylow p-subgroup of simple groups A_n

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what is the order of normalizer of Sylow p-subgroup of simple groups A_n?
 
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So you basically want to count the Sylow p-subgroups of A_n. Isn't this a very hard problem?
 
the order of sylow p-subgroup of A_n is not hard to compute, but the one of normalizer of sylow p-subgroup, how to compute?
 
But my point is if you compute the order of the normalizer of an arbitrary Sylow p-subgroup, then you can count the number of Sylow p-subgroups (because the number of Sylows is the index of the normalizer of anyone of them in the group), which is (as far as I know) very difficult.
 

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