Permutation representations and the subgroup lattice

There is a close correspondence between the set of subgroups of a finite group G and the set of inequivalent transitive permutation representations of G . For many purposes the latter is as useful as the former and more easily calculated. The present paper describes a program which computes a complete set of transitive permutation representations of G (specified by their values on a fixed set of generators of G ) whenever a single faithful permutation representation of G is supplied.