In the package, group_action() gives conjugation, that is, it is the group action
$$\alpha\colon G\times X\longrightarrow X$$
where $X=G$. We have $\alpha(g,x)=g^{-1}xg$ for $g\in G$, $x\in X$; or rewriting, $g\cdot x=g^{-1}xg$. This certainly is a group action, for $e\cdot x=x$ and $(gh)\cdot x=g\cdot(h\cdot x)$. But it is most commonly referred to as conjugation.
In the package,
group_action()gives conjugation, that is, it is the group action$$\alpha\colon G\times X\longrightarrow X$$
where $X=G$. We have $\alpha(g,x)=g^{-1}xg$ for $g\in G$, $x\in X$; or rewriting, $g\cdot x=g^{-1}xg$. This certainly is a group action, for $e\cdot x=x$ and $(gh)\cdot x=g\cdot(h\cdot x)$. But it is most commonly referred to as conjugation.