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Maschke's Theorem

Fundamental to the study of group representations.
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The statement of the theorem

Every representation of a finite group GG over a field of characteristic 00 (like C\mathbb{C}) decomposes into a direct sum of irreducible representations.\nVW1W2WkV \cong W_1 \oplus W_2 \oplus \cdots \oplus W_k
Source: Wikipedia