Automorphism group of cyclic group

This page discusses the automorphism groups of cyclic groups.

Results

• Automorphism group of Zp for p prime is isomorphic to Z(p-1)

Table of examples

The following table lists some small examples.

Cyclic group	Automorphism group of cyclic group
Trivial group	Trivial group
Cyclic group:Z2	Trivial group
Cyclic group:Z3	Cyclic group:Z2
Cyclic group:Z4	Cyclic group:Z2
Cyclic group:Z5	Cyclic group:Z4
Cyclic group:Z6	Cyclic group:Z2
Cyclic group:Z7	Cyclic group:Z6
Cyclic group:Z8	Klein four-group
Cyclic group:Z9	Cyclic group:Z6
Cyclic group:Z10	Cyclic group:Z4