# Changes

## Automorphism group of a group

, 00:51, 25 February 2014
Particular groups
| [[cyclic group:Z7]] || 7 || [[cyclic group:Z6]] || 6 || [[endomorphism structure of cyclic group:Z7]] || In particular, for a prime $p$, the automorphism group of the cyclic group of order $p$ is the cyclic group of order $p - 1$.
|-
| [[cyclic group:Z8]] || 8 || [[cyclic Klein four-group:Z4]] || 4 || [[endomorphism structure of cyclic group:Z8]] || For a [[finite cyclic group]] of order $n$, the automorphism group is of order $\varphi(n)$ where $\varphi$ denotes the [[Euler totient function]]. Further, the automorphism group is cyclic iff $n$ is 2,4, a power of an odd prime, or twice a power of an odd prime.
|-
| [[direct product of Z4 and Z2]] || 8 || [[dihedral group:D8]] || 8 || [[endomorphism structure of direct product of Z4 and Z2]] ||