THE PERFECT GROUPS OF ORDER UP TO TWO MILLION

We enumerate the 15768 perfect groups of order up to 2 . 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.

Automated summary

We have enumerated 15768 perfect groups of order up to 2 . 10(6), up to isomorphism, thus completing the missing cases reported by Holt and Plesken. This work supplements the computer classifications of solvable groups, showcasing the scope and feasibility of the enumeration process for nonsolvable groups.