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Let $D_n$, $n\ge 2$, be the dihedral group with $2n$ elements and neutral element $e$. It has the presentation in terms of generators and relators:

$$\langle a,b \mid a^n=b^2=e; \; aba=b^{-1}\rangle$$

1) When $n$ is odd, the conjugacy class of $a^k$ for $k=1,\ldots,n-1$ is
Select Option $\{e, a,\ldots, a^{n-1}\}$$\{a^k\}$$\{a^k,a^{-k}\}$
.
2) When $n$ is even, the conjugacy class of $a^k$ for $k=1,\ldots, n-1$ is
Select Option $\{e, a,\ldots, a^{n-1}\}$$\{a^k\}$$\{a^k, a^{-k}\}$
when $k\not=\cfrac{n}2$. The conjugacy class of $a^{n/2}$ is
Select Option $\{e, a,\ldots, a^{n-1}\}$$\{a^{n/2}\}$
.
3) If $n$ is odd, the conjugacy class of $b$ consists of
Select Option $\{b\}$exactly the $ba^\ell$, $\ell=0,\ldots,n-1$exactly the $ba^{2\ell}$, $\ell=0,\ldots,\cfrac{n-1}{2}$
.
4) If $n$ is even, the conjugacy class of $b$ consists of
Select Option $\{b\}$exactly the $ba^{\ell}$, $\ell=0,\ldots,n-1$exactly the $ba^{2\ell}$, $\ell=0,\ldots,\cfrac{n-2}{2}$
.
5) When $n$ is odd, the group $D_n$ is the disjoint union of
Select Option $\cfrac{n-1}{2}$ +1 $\cfrac{n-1}{2}$ +2$\cfrac{n-1}{2}$ +3
distinct conjugacy classes.
6) When $n$ is even, the group $D_n$ is the disjoint union of
Select Option $\cfrac{n-2}2+2$$\left(\cfrac{n}2\right)+2$$\left(\cfrac{n}2\right)+3$
distinct conjugacy classes.
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