Abstract:

We show that the image of the representation of the modular group $\SL(2, \Z)$ arising from the representation category $\Rep(D(G))$ of the Drinfeld double $D(G)$ is isomorphic to the group $\PSL(2, \Zn) \times S_3$, when $G$ is either the dihedral group of order $2n$ or the dihedral group of order $4n$ for some odd integer $n \geq 3$. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

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