Computing Chief Series, Composition Series and Socles in Large Permutation Groups

We describe the theory and implementation of practical algorithms for computing chief and composition series and socles in large permutation groups. The theory is valid for permutation degrees up to 10 000 000, and the current implementations in the Magma system are practical up to degrees of 1 000 000 for some examples. Several of the techniques involved are based on ideas of Kantor.