## Regular representation always direct sum of irreducible representations? [closed]

Hi, is the regular representation of a finite group $G$ over $K$ always a direct sum of irreducible representations, even if I take a general field $K$ (which must NOT be algebraically closed) but has $char(K) \nmid |G|$ ? If this is true, I whould try to use Maschke's theorem to proof it.

Regards, James

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 Take a look at the answer to math.stackexchange.com/q/151347/33256 (you should be able to figure it out). – Someone Aug 2 at 10:48 This question is likely to be closed as too elementary for mathoverflow, which is for research level questions. Maschke's theorem states that every representation is a direct sum of irreducible representations, and so is the regular one. – F. Ladisch Aug 2 at 12:40