How to find the inverse of group actions

Question

Let $G$ and $H$ be two groups and let $$\alpha : H~\times~G \rightarrow H$$ be a right action of $G$ on $H$ so that $$\alpha_{g}(h) = h\prime$$ where $g\in G$, $h, h\prime\in H.$ I want to write the inverse of $h\prime$ in terms of $g$ and $h$. Please I want references on where I can get this information.