Enumerating \(p\)-groups. (English) Zbl 0979.20021
Summary: We present a new algorithm which uses a cohomological approach to determine the groups of order \(p^n\), where \(p\) is a prime. We develop two methods to enumerate \(p\)-groups using the Cauchy-Frobenius lemma. As an application we show that there are \(10.494.213\) groups of order \(2^9\).
Online Encyclopedia of Integer Sequences:
Number of groups of order 2^n.Incrementally largest numbers of nonisomorphic finite groups of order n.
Orders of finite groups having the incrementally largest numbers of nonisomorphic forms A046058.
Number of 2-generator groups of order 2^n.
Number of exponent-2 class 2 groups of order 2^n.
Number of exponent-3 class 2 groups of order 3^n.
Number of exponent-5 class 2 groups of order 5^n.
Number of exponent-7 class 2 groups of order 7^n.
