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An approach to computing the conjugacy classes of elements of large permutation groups is presented in detail, and a prototype implementation is described. The approach builds on recent efficient algorithms for computing conjugacy classes of p-groups, and for computing Sylow subgroups of large permutation groups. Classes of elements of composite order are determined by recursively analyzing quotients of centralizers of p-elements.

An Inductive Schema for Computing Conjugacy Classes in Permutation Groups