Constructing character table of subgroup from character table of whole group

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If $\psi : G \to \mathbb C$ is a character and $U \le G$, then $\psi_{|U} : U \to \mathbb C$ is a character, but I guess this might not be irreducible with respect to $U$. But is it possible to construct the character table of $U$ from the character table of $G$?