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

The Great Orthogonality Theorem (GOT) is a fundamental result in group theory that applies to the irreducible representations (irreps) of a finite group. It states that the rows (or columns) of the character table of a group form an orthogonal set with respect to the standard inner product. Mathematically, for two irreducible representations R1R_1 and R2R_2 of a group GG, the orthogonality condition is given by:

∑g∈GχR1(g)χR2(g)‾=∣G∣δR1,R2\sum_{g \in G} \chi_{R_1}(g) ____ _________ _______ __________ __________ ____.
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