# Groups of order 19683

## Contents

See pages on algebraic structures of order 19683| See pages on groups of a particular order

## Statistics at a glance

To understand these in a broader context, see: groups of order 3^n|groups of prime-ninth order

Since $19683 = 3^9$ 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 up to isomorphism unknown
Number of abelian groups 30 equal to the number of unordered integer partitions of 9. See classification of finite abelian groups
Number of groups of nilpotency class exactly two unknown
Number of groups of nilpotency class exactly three unknown
Number of groups of nilpotency class exactly four unknown
Number of groups of nilpotency class exactly five unknown
Number of groups of nilpotency class exactly six unknown
Number of groups of nilpotency class exactly seven unknown
Number of groups of nilpotency class exactly eight (i.e., maximal class groups) unknown