Let $G$ be a group of size $k\cdot p^n$.
Let $S$ be the set of all subsets of size $p^n$ of $G$.
Define the map $f\colon G \times S \rightarrow S$ by $(g, s) \mapsto gs$ if $s \in S$.
I would like to create the group action table of $f$ with GAP. So in the case of $S_3$ I would get a table with twenty rows ( elements of $S$ ) and six columns ( elements of $S_3$ ) containing $gs$.
Question: How do I create a ( this ) group action table with GAP?