Groups of order 2304

This article gives information about, and links to more details on, groups of order 2304
See pages on algebraic structures of order 2304 | See pages on groups of a particular order

The prime factorization of 56 is $56=2^{8}\cdot 3^{2}$. There are only two prime factors of this number. Order has only two prime factors implies solvable (by Burnside's $p^{a}q^{b}$-theorem) and hence all groups of this order are solvable groups (specifically, finite solvable groups). Another way of putting this is that the order is a solvability-forcing number. In particular, there is no simple non-abelian group of this order.

Statistics at a glance

The reference for the values in this table is here.

Quantity	Value
Total number of groups	15756130
Number of abelian groups	8
Number of nilpotent groups	112184
Number of solvable groups	15756130
Number of simple groups	0