How $G = D_n$ act on $\mathbb{C}^3$?

Question

In particular, given $G = D_n = \langle \kappa, \rho \rangle$, I was wondering what the $3\times 3$ matrix representing $\kappa$ would look like for the action of $G$ on $\mathbb{C}^3$. For this particular basis, I have this matrix for $\rho$: \begin{bmatrix}\cos \theta & -\sin\theta & 0 \\\sin\theta & \cos\theta&0\\ 0 & 0 & -1\end{bmatrix} Any help is much appreciated.