# Automorphism of subgroup generated by permutations

In group $$S_5$$ let's take the subgroup $$H$$ generated by permutations $$a=(2\,3\,5)$$ and $$b=(3\,2\,5)$$. Find AutH.

So, I have found out that $$ab=ba=e$$ and $$aa=b$$ and $$bb=a$$. So $$H$$ is $$\{e,a,b\}$$. Is $$\operatorname{Aut}H$$ isomorphic to $$\Bbb Z_3$$? Are there any others isomorphisms? Thanks.