Enumeration of groups whose order factorises in at most 4 primes

TL;DR

This paper derives formulas for counting the number of isomorphism types of groups whose order is a product of at most four primes, expanding understanding of group classifications for such orders.

Contribution

It provides explicit formulas for the enumeration of groups with orders factored into up to four primes, a novel extension in group enumeration.

Findings

Formulas for N(n) when n is a product of up to 4 primes

Enhanced classification of finite groups based on prime factorization

Explicit enumeration results for specific group orders

Abstract

Let $N(n)$ denote the number of isomorphism types of groups of order $n$. We consider the integers $n$ that are products of at most $4$ not necessarily distinct primes and exhibit formulas for $N(n)$ for such $n$.