Groups of order 1984

This article gives information about, and links to more details on, groups of order 1984
See pages on algebraic structures of order 1984 | See pages on groups of a particular order

Statistics at a glance

The number 1984 has prime factors 2 and 31. The prime factorization is:

$\!1984=2^{6}\cdot 31=64\cdot 31$

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.

Quantity	Value	Explanation
Number of groups up to isomorphism	1388
Number of abelian groups up to isomorphism	11	Equals the number of unordered integer partitions of $6$ times the number of unordered integer partitions of $1$. See classification of finite abelian groups and structure theorem for finitely generated abelian groups.

See also

• Classification of groups of order sixty-four times a prime