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Show that there exist an injective homomorphism of dihedral group $D_n$ into $G$.

Let $n>2$ and the group $(G,⋅)$. Consider that there existe $a,b∈G$ such that $a^n=b^2=1_G$ and $b⋅a=a^{−1}⋅b$ and $n$ is the smallest $n≥1$ such that $a^n=1_G$. Show that there exist an injective homomorphism of dihedral group $D_n$ into $G$.

I know that the dihedral group $D_n$ has the same properties ($a,b∈G$ such that $a^n=b^2=1_G$ and $b⋅a=a^{−1}⋅b$) as the group $(G,⋅)$.

I can't find a such injective homomorphism of dihedral group $D_n$ into $G$. Does someone could help me?

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