Bill, Many thanks for those two messages, and for answering Colin Mallows's question so completely! I have updated the corresponding entry in the OEIS (A154638). Thanks also for the references to the literature and for telling me about Derek Holt's programs. All this was new to me. (I don't suppose you have a student who could run these programs on a bunch of other groups, and add the resulting sequences to the OEIS?) Thanks again for your help. Best regards Neil