How should I Describe automorphism groups $\operatorname{Aut}(\mathbb{Z}_9)$ and $\operatorname{Aut}(\mathbb{Z}_3 \times \mathbb{Z}_3)$ ?
If a group G contains a normal subgroup H of order 9, G is generated by H and an element x not in H of order 3, How should I classify all such groups G?