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A (2,*)-group is a group that can be generated by two elements, one of which is an involution. We describe the method we have used to produce a census of all (2,*)-groups of order at most 6,000. Various well-known combinatorial structures are closely related to (2,*)-groups and we also obtain censuses of these as a corollary.

Groups of Order at Most 6,000 Generated by Two Elements, One of Which Is an Involution, and Related Structures