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.


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