In the following paper (Example 1.2) I don't understand how a group action is associated to a certain permutation matrix.
We consider the cyclic group $G = \mathbb{Z}_6$ and for $g \in G$ we define the action on the set $M = \{1,2,3, 4, 5, 6\}$ as $g \cdot m := g-m \, \text{mod 6}$. Then, for $g=\bar{2}$, the following permutation matrix is associated to the group action.
$$2_N = \begin{pmatrix} 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \end{pmatrix}$$
I don't know how such matrix is retrieved, it corresponds to the cycle $(13)(2)(46)(5)$ but I cannot see how it is related to how the group action is defined in this case.