The character orthogonalities are special cases of the Great Orthogonality. They can be seen directly in all character tables. This is also the chapter where we prove that the character table is square, and that it has an inverse. So perk up.
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McClain, W.M. (2009). Character orthogonalities. In: Symmetry Theory in Molecular Physics with Mathematica. Springer, New York, NY. https://doi.org/10.1007/b13137_34
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DOI: https://doi.org/10.1007/b13137_34
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