Groups of order 343

This article gives information about, and links to more details on, groups of order 343
See pages on algebraic structures of order 343 | See pages on groups of a particular order

Statistics at a glance

To understand these in a broader context, see
groups of order 7^n|groups of prime-cube order

Since $343=7^{3}$ is a prime power and prime power order implies nilpotent, all groups of this order are nilpotent groups.

Quantity	Value	Explanation
Total number of groups	5	See classification of groups of prime-cube order
Number of abelian groups	3	Equals the number of unordered integer partitions of $3$, which is the exponent term in $7^{3}$. See classification of finite abelian groups and structure theorem for finitely generated abelian groups.