Retrieving information about a group from its character table

This thesis concerns character tables of finite soluble groups. In particular, our main objective is that of showing that the derived length of a soluble group G is not determined by the character table of G. In fact, in Chapters 5 and 6 we shall construct pairs (G, H) of groups which have identical character tables but different derived lengths, namely 2 and 3. A more general result will be proved in Chapter 7, namely that for any natural number n > 2, there exist pairs (G, H) of groups with identical character tables, and derived lengths n and n + 1 respectively. Two by-products of our investigation are a method for comparing character tables in special situations (in Chapter 4), and a description of the character tables of wreath products (in Chapter 7).