Groups of order 6561
This article gives information about, and links to more details on, groups of order 6561
See pages on algebraic structures of order 6561 | 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-eighth 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 | 1396077 | |
| Number of abelian groups | 22 | equal to the number of unordered integer partitions of 8. 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, i.e., maximal class groups | unknown |