History
The O'Nan group was found by Michael O'Nan (1976) in a study of groups with a Sylow 2-subgroup of "Alperin type", meaning isomorphic to a Sylow 2-Subgroup of a group of type (Z/2nZ ×Z/2nZ ×Z/2nZ).PSL3(F2). For the O'Nan group n=2 and the extension does not split. The only other simple group with a Sylow 2-subgroup of Alperin type with n≥2 is the Higman–Sims group again with n=2, but the extension splits.
Read more about this topic: O'Nan Group
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