Consider the group of permutation matrices $G =\{I_3, P_1, P_2, P_3, P_4, P_5\}$ For $n=3$ the permutation matrices are $I_3$ and the five matrices are:
\begin{equation*} P_1 = [1,0,0;0,0,1;0,1,0] \\ P_2 = [0,1,0;1,0,0;0,0,1] \\ P_3 = [0,1,0;0,0,1;1,0,0] \\ P_4 = [0,0,1;0,1,0;1,0,0] \\ P_5 = [0,0,1;1,0,0;0,1,0] \end{equation*}
Write out the elements of a group of permutations that is isomorphic to $G$, and exhibit an isomorphism from $G$ to this group!
I think it has to do with Cayley's Theorem. With $f_a:G\to G$ defined by $f_a(x) = ax$ for each $a$ that exists in $G$...
I thought about making a table, but realize I don't know how to since I am dealing with matrices.