I have constructed a character table for $A_{4}$ and need to use induced representations to get a character table for $S_{4}$. I'm not very confident with the concept of induced representations, but I am familiar with the definition. In that sense, given a representation $V$ of $G$, and a representation $W$ of a subgroup $H$ of $G$, I understand how I would go about checking whether $V$ is induced by $W$ or not.
But starting with $W$, I don't see how to go about constructing $V$.
Can anyone give me advice on how to approach this problem, or a reference that they think might be helpful?