When working with large numbers of graphs, a canonical labelling routine is essential as, after the initial cost of canonically labelling each graph, it permits isomorphism checks to be replaced with identity checks.

Currently I am working with large numbers of transitive permutation groups; the degree is small (40ish) but the size of group can be large, and my programs are gumming up due to having to perform large numbers of - not exactly isomorphism - but *conjugacy* checks. (I need to check each pair of groups to see if they are conjugate in the symmetric group.)

This process would be considerably easier if there was a known way of finding a canonical conjugate of the incoming permutation groups...