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Very interesting how quadigroups make these apperances in combinatorics! One of your cooauthors on this paper actually gave a talk on something similar at my Uni last semester, it was very nice. Either way thank you for letting me know about this nice result
@DaveBenson Unfortunately Oates and Powell don't provide a general construction which is to be expected. It is hard to do in general, I was hoping that given a sufficiently nice description of a group, like finite presentation or as a product of two groups whose finite basis is already known, one would be able to construct the basis for the group at hand. This doesn't seem to be the case however.
