ON CHARACTER TABLES OF WREATH-PRODUCTS

The theory of characters of wreath products of finite groups is very w ell known. The basic fact is that any invariant irreducible character of the base group is extendible to the wreath product, and an extensio n can be computed explicitly. In this paper we shall study the charact er table of a wreath product as a whole, rather than single characters . We shall prove that the character table of a wreath product G \ A is determined uniquely by the permutation group A and the character tabl e of G. This result provides a powerful tool for increasing the derive d 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 wi th identical character tables and derived lengths n and n + 1, for any given natural number n greater than or equal to 2. (C) 1995 Academic Press, Inc.