what?!!

read chapter 10 of the book "Finite Groups" written by "Daniel Gorenstein" for a solution to your problem and also if you want to learn more about fixed-point free automorphisms of a finite group.

Let G be a finite group, φ an automorphism of G such that φ3 is the identity automorphism. Suppose further that φ(x)=x if and only if x=e. Prove that for every prime p which divides o(G) the p-Sylow subgroup is normal in G.