A natural permutation
representation for any finite group is the conjugating representation T: for each
g ∈ G, T(g) is the permutation on the set {x∣x ∈ G} given by T(g)(x) = gxg−1.
Frame, Solomon and Gamba have studied some of its properties. This paper
considers the question of which complex irreducible representations occur as
components of T, in particular the conjecture that any such representation whose
kernel contains the center of G is a component of T. This conjecture is verified for a
few special cases and a number of related results are obtained, especially with respect
to the one-dimensional components of T.
