Summary: We use the boson-fermion correspondence for \(S\) and \(Q\) functions to establish some interesting properties concerning outer products and plethysms of \(S\)-functions (or \(Q\)-functions) by power sum symmetric functions. The techniques which are developed are also applied to computing the inverse Kostka-Foulkes matrix (which is the transition matrix between Hall-Littlewood symmetric functions and \(S\)-functions) in some simple cases.