The perfect groups of order up to two million

TL;DR

This paper completes the classification of perfect groups of order up to two million, providing a comprehensive enumeration and demonstrating the process's feasibility for complex nonsolvable groups.

Contribution

It enumerates all perfect groups of order up to two million, filling gaps in previous classifications and showcasing the enumeration method for nonsolvable groups.

Findings

Enumerated 15,768 perfect groups up to order 2 million.

Completed the classification of perfect groups in this order range.

Demonstrated the scope and feasibility of enumeration for nonsolvable groups.

Abstract

We enumerate the 15768 perfect groups of order up to $2\cdot 10^6$, up to isomorphism, thus also completing the missing cases in the prior classification. The work supplements the by now well-understood computer classifications of solvable groups, illustrating scope and feasibility of the enumeration process for nonsolvable groups.