Thomas Breuer and Götz Pfeiffer,
Finding Possible Permutation Characters.
J. Symbolic Comput. 26 (1998), 343-354.
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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