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Character orthogonality

For irreducible complex characters $\chi,\psi$ of a finite group,
$$
\sum_{g\in G}\chi(g)\overline{\psi(g)}
=|G|\delta_{\chi\psi}.
$$
Equivalently, summing over conjugacy classes $C$ with representatives $c$ gives
$$
\sum_C|C|\chi(c)\overline{\psi(c)}
=|G|\delta_{\chi\psi}.
$$


Row orthogonality relations for a character table

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 19I / Solution

Row orthogonality relations for a character table

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Row orthogonality relations for a character table

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