Thomas Breuer and Götz Pfeiffer,

Finding Possible Permutation Characters.

J. Symbolic Comput. 26 (1998), 343-354.

Abstract.

We describe three different methods to compute all those characters of a finite group that have certain properties of transitive permutation characters. Firstly, a combinatorial approach can be used to enumerate vectors of multiplicities. Secondly, these characters can be found as certain integral solutions of a system of inequalities. Thirdly, they are calculated via Gaussian elimination. The methods are used to determine these characters for some finite groups and runtimes are listed. In the final section, a permutation character of the Lyons group is constructed.

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