Groups of order 243
This article gives information about, and links to more details on, groups of order 243
See pages on algebraic structures of order 243 | See pages on groups of a particular order
Statistics at a glance
Since is a prime power, and prime power order implies nilpotent, all groups of order 243 are nilpotent groups.
| Quantity | Value | Explanation |
|---|---|---|
| Total number of groups up to isomorphism | 67 | |
| Number of abelian groups | 7 | Equals the number of unordered integer partitions of 5, see classification of finite abelian groups |
| Number of groups of nilpotency class exactly two | 28 | |
| Number of groups of nilpotency class exactly three | 26 | |
| Number of groups of nilpotency class exactly four (i.e., maximal class groups) | 6 |