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 |