Groups of order 18
(Redirected from Order 18)
This article gives information about, and links to more details on, groups of order 18
See pages on algebraic structures of order 18 | See pages on groups of a particular order
The list
| Group | GAP ID |
|---|---|
| dihedral group:D18 | (18,1) |
| cyclic group:Z18 | (18,2) |
| direct product of S3 and Z3 | (18,3) |
| generalized dihedral group for E9 | (18,4) |
| direct product of Z6 and Z3 | (18,5) |
Arithmetic functions
| Function | dihedral group:D18 | cyclic group:Z18 | direct product of S3 and Z3 | generalized dihedral group for E9 | direct product of Z6 and Z3 |
|---|---|---|---|---|---|
| exponent | 18 | 18 | 6 | 6 | 6 |
| derived length | 2 | 1 | 2 | 2 | 1 |
| nilpotency class | -- | 1 | -- | -- | 1 |
| Fitting length | 2 | 1 | 2 | 2 | 1 |
Group properties
| Property | dihedral group:D18 | cyclic group:Z18 | direct product of S3 and Z3 | generalized dihedral group for E9 | direct product of Z6 and Z3 |
|---|---|---|---|---|---|
| cyclic group | No | Yes | No | No | No |
| abelian group | No | Yes | No | No | Yes |
| nilpotent group | No | Yes | No | No | Yes |
| metacyclic group | Yes | Yes | Yes | No | Yes |
| supersolvable group | Yes | Yes | Yes | No | Yes |
| solvable group | Yes | Yes | Yes | Yes | Yes |