Semi-Presentations for the Sporadic Simple Groups

A semi-presentation for a group G is a set of relations which characterises a set of generators of G up to automorphism. We discuss some techniques for finding semi-presentations and illustrate them by exhibiting semi-presentations on standard generators for the 26 sporadic simple groups and their automorphism groups. We then show how these semi-presentations were used to check the data in the World Wide Web Atlas of Group Representations [Wilson et al. 04].