# Questions tagged [dihedral-groups]

For questions on dihedral groups, the group of symmetries of a regular polygon, including both rotations and reflections

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### Finding $N(D_{4})/D_{4}$ for $D_{4}$ in $D_{16}$

I want to find $N(D_{4})/D_{4}$ where $N(D_{4})$ is the normalizer of $D_{4}$ in $D_{16}$. I'm not too clear on what the normalizer of $D_{4}$ in $D_{16}$ Is there a nice way to find $N(D_{4})/D_{4}$?...
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### How to write dihedral group in cycle notation?

Since each symmetry can be thought of as a permutation of the vertices, the elements of $D_n$ can be thought of as elements of $S_n$. So I'm wondering if there's a systematic way that we can always ...
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### About proving that $\operatorname{Aut}(\mathbb {D}_n) \cong \mathbb {Z}_n \rtimes \operatorname{Aut}(\mathbb {Z}_n)$ [closed]

How can I prove that $$\operatorname{Aut}(\mathbb {D}_n) \cong \mathbb {Z}_n \rtimes \operatorname{Aut}(\mathbb {Z}_n),$$ where $\mathbb {D}_n$ is the dihedral group. Can someone help me please? ...