On conjugacy classes of Sn containing all irreducibles

Abstract

It is shown that for the conjugation action of the symmetric group Sn, when n = 6 or n ≥ 8, all Sn-irreducibles appear as constituents of a single conjugacy class, namely, one indexed by a partition λ of n with at least two parts, whose parts are all distinct and taken from the set of odd primes and 1. A simple characterisation of conjugacy classes containing all irreducibles is proved.