On Character Tables of Wreath Products Original Research Article

The theory of characters of wreath products of finite groups is very well known. The basic fact is that any invariant irreducible character of the base group is extendible to the wreath product, and an extension can be computed explicitly. In this paper we shall study the character table of a wreath product as a whole, rather than single characters. We shall prove that the character table of a wreath product G wreath product A is determined uniquely by the permutation group A and the character table of G. This result provides a powerful tool for increasing the derived length of a group, while keeping its character table under control. We shall employ it in Section 4 to construct pairs (G, H) of groups with identical character tables and derived lengths n and n + 1, for any given natural number n ≥ 2.