Groups of order 19683
This article gives information about, and links to more details on, groups of order 19683
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 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 | 5937876645[1] | |
| 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 |
References
- ↑ The number of p-groups of order 19,683 and new lists of p-groups by David Burrell, : Link