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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}\}$$\{a^{n/2}\} . 3) If n is odd, the conjugacy class of b consists of Select Option \{b\}exactly the ba^\ell, \ell=0,\ldots,n-1exactly the ba^{2\ell}, \ell=0,\ldots,\cfrac{n-1}{2} . 4) If n is even, the conjugacy class of b consists of Select Option \{b\}exactly the ba^{\ell}, \ell=0,\ldots,n-1exactly the ba^{2\ell}, \ell=0,\ldots,\cfrac{n-2}{2} . 5) When n is odd, the group D_n is the disjoint union of Select Option \cfrac{n-1}{2} +1 \cfrac{n-1}{2} +2\cfrac{n-1}{2} +3 distinct conjugacy classes. 6) When n is even, the group D_n is the disjoint union of Select Option \cfrac{n-2}2+2$$\left(\cfrac{n}2\right)+2$$\left(\cfrac{n}2\right)+3$
distinct conjugacy classes.
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