# Order of an automorphism of a finite group

Let G be a finite group of order n. Must every automorphism of G have order less than n?

(David Speyer: I got this question from you long ago, but I don't know whether you knew the answer. I stil don't!)

• Nope, I didn't know the answer. But now I do! – David E Speyer Oct 19 '09 at 0:36