Groups of order 81
The list
| Common name for group | Second part of GAP ID (GAP ID is (p^3, second part)) | Nilpotency class |
|---|---|---|
| Cyclic group:Z81 | 1 | 1 |
| Direct product of Z9 and Z9 | 2 | 1 |
| SmallGroup(81,3) | 3 | 2 |
| Nontrivial semidirect product of Z9 and Z9 | 4 | 2 |
| Direct product of Z27 and Z3 | 5 | 1 |
| Semidirect product of Z27 and Z3 | 6 | 2 |
| Wreath product of Z3 and Z3 | 7 | 3 |
| SmallGroup(81,8) | 8 | 3 |
| SmallGroup(81,9) | 9 | 3 |
| SmallGroup(81,10) | 10 | 3 |
| Direct product of Z9 and E9 | 11 | 1 |
| Direct product of prime-cube order group:U(3,3) and Z3 | 12 | 2 |
| Direct product of semidirect product of Z9 and Z3 and Z3 | 13 | 2 |
| SmallGroup(81,14) | 14 | 2 |
| Elementary abelian group:E81 | 15 | 1 |