On exceptional groups of order p5

J.~R. Britnell, N. Saunders, T. Skyner

Research output: Contribution to journalArticle (Academic Journal)peer-review


A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient. The smallest examples of exceptional p-groups have order p^5. For an odd prime p, we classify all pairs (G,Q) where G has order p^5 and Q is a distinguished quotient. (The case p=2 has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order p^5 with at least one exceptional quotient tends to 1/2.
Original languageEnglish
Publication statusAccepted/In press - 1 Aug 2014


  • Mathematics - Group Theory, 2010 (primary) 20B35, (secondary) 20D15


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