Groups of order 2.3^n
This article discusses the groups of order , where varies over nonnegative integers. Note that any such group has a normal 3-Sylow subgroup and a complement to that which is a 2-Sylow subgroup isomorphic to cyclic group:Z2. Thus, the group is either a nilpotent group (a direct product of the 3-Sylow subgroup and cyclic group:Z2) or can be described as the internal semidirect product of a group of order by a group of order two whose non-identity element acts as a non-identity automorphism.
See also groups of order 3^n.
Number of groups of small orders
|Exponent||Value||Value||Number of groups of order||Reason/explanation/list|
|0||1||2||1||cyclic group:Z2, see also equivalence of definitions of group of prime order|
|1||3||6||2||See groups of order 6. The groups are cyclic group:Z6 and symmetric group:S3.|
|2||9||18||5||See groups of order 18.|
|3||27||54||15||See groups of order 54.|
|4||81||162||55||See groups of order 162.|
|5||243||486||261||See groups of order 486.|
|6||729||1458||1798||See groups of order 1458.|