Eigenvalues · Challenge problem

Let $P$ be the $6\times 6$ permutation matrix of the permutation of $\{1, \ldots, 6\}$ with cycles $(1\,2\,3)(4\,5)(6)$ (so $P\mathbf e_1 = \mathbf e_2$, $P\mathbf e_2 = \mathbf e_3$, $P\mathbf e_3 = \mathbf e_1$, $P\mathbf e_4 = \mathbf e_5$, $P\mathbf e_5 = \mathbf e_4$, $P\mathbf e_6 = \mathbf e_6$). Find $\det(P + 2I)$.