A combinatorial approach to the character theory of split metabelian groups (Q1262386)

A finite group G is called metabelian if \(G''=1\). A split metabelian group is a split extension of an abelian group by an abelian group. In this paper the author devises an algorithm for the construction of the character table of any finite split metabelian group. A verification of the algorithm relies heavily on a branch of algebraic combinatorics called association scheme theory. As example the author constructs the character table of the non-abelian group of order 27 and exponent 3.