The perfect groups of order up to two million

Hulpke, Alexander

doi:10.1090/mcom/3684

The perfect groups of order up to two million
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Math. Comp. 91 (2022), 1007-1017 Request permission

Abstract:

We enumerate the $15768$ perfect groups of order up to $2\cdot 10^6$, up to isomorphism, thus also completing the missing cases reported by Holt and Plesken [Perfect groups, The Clarendon Press, Oxford University Press, New York, 1989]. The work supplements the by now well-understood computer classifications of solvable groups, illustrating scope and feasibility of the enumeration process for nonsolvable groups.

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