On permutation characters and Sylow p-subgroups of Sₙ

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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).