The representation of $g \rightarrow xg$ was given to us as Cayley representation. I believe it means that every group element $g \in G$ is mapped to another element $xg$ where $x$ is the same for every element $g$. I'm not sure if $xg$ is a group but I think it is, if $x$ is also in $G$. Please correct me if I'm wrong.
How do I write these permutations in cycle notation?