State the Great Orthogonality Theorem. Derive the characters of the irreducible representation of the  point group.

The Great Orthogonality Theorem is a fundamental result in Group Theory, particularly in the context of Quantum Chemistry. It states that for any finite group, the irreducible representations (IRs) of the group are orthogonal to each other. Specifically, the rows and columns of the matrix corresponding to an irreducible representation of a group are orthogonal. Mathematically, it can be expressed as:

\[
\sum_{g} \chi^{(i)}(g) \chi^{(j)}(g) = \frac{|G|}{n_i} \delta_{ij}
\]

Where:
- \(\chi^{(i)}(g)\) and \(\chi^{(j)}(g)\) are the characters of the i-th and j-th irreducible representations, respectively, for each group element \(g\).
- \(|G|\) is the order of the group ____ _________ ____ ________ ____.
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