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There is a clear and more specific answer (with reference moreover!) here, despite the different question: http://math.stackexchange.com/a/18496/84625

In short $\operatorname{Aut}\left(\left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathbb{Z}_p) \right) \cong \operatorname{AGL}(2,p)$ while $\operatorname{Aut}\left(\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p \right) \cong \left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \operatorname{AGL}(1,p)$

where $\operatorname{AGL}(n,p)$ is the General Affine Group .

There is a clear and more specific answer (with reference moreover!) here, despite the different question: https://math.stackexchange.com/a/18496/84625

In short $\operatorname{Aut}\left(\left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathbb{Z}_p) \right) \cong \operatorname{AGL}(2,p)$ while $\operatorname{Aut}\left(\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p \right) \cong \left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \operatorname{AGL}(1,p)$

where $\operatorname{AGL}(n,p)$ is the General Affine Group .

There is a clear and more specific answer (with reference moreover!) here, despite the different question: http://math.stackexchange.com/a/18496/84625

In short $\operatorname{Aut}\left(\left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathbb{Z}_p) \right) \cong \operatorname{AGL}(2,p)$ while $\operatorname{Aut}\left(\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p) \right) \cong \left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \operatorname{AGL}(1,p)$

where $\operatorname{AGL}(n,p)$ is the General Affine Group .

There is a clear and more specific answer (with reference moreover!) here, despite the different question: http://math.stackexchange.com/a/18496/84625

In short $\operatorname{Aut}\left(\left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathbb{Z}_p) \right) \cong \operatorname{AGL}(2,p)$ while $\operatorname{Aut}\left(\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p \right) \cong \left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \operatorname{AGL}(1,p)$

where $\operatorname{AGL}(n,p)$ is the General Affine Group .

There is a clear and more specific answer (with reference moreover!) here, despite the different question: http://math.stackexchange.com/a/18496/84625

In short $\operatorname{Aut}\left(\left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathbb{Z}_p) \right) \cong \operatorname{AGL}(2,p)$ while $\operatorname{Aut}\left(\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p) \right) \cong \left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathsf{AGL}(1,p)$

where $\operatorname{AGL}(n,p)$ is the General Affine Group .

There is a clear and more specific answer (with reference moreover!) here, despite the different question: http://math.stackexchange.com/a/18496/84625

In short $\operatorname{Aut}\left(\left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathbb{Z}_p) \right) \cong \operatorname{AGL}(2,p)$ while $\operatorname{Aut}\left(\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p) \right) \cong \left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \operatorname{AGL}(1,p)$

where $\operatorname{AGL}(n,p)$ is the General Affine Group .