On permutation characters and Sylow p-subgroups of Sn

Let p be an odd prime and let n be a natural number. In this article we determine the irreducible constituents of the permutation module induced by the action of the symmetric group Sn on the cosets of a Sylow p-subgroup Pn. As a consequence, we determine the number of irreducible representations of the corresponding Hecke algebra H(Sn,Pn,1Pn).