Groups of order 18
From Groupprops
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 |
