I know that every irreducible representations of $S_n$ can be found in $\mathbb{C}S_n$. I wonder how can I prove that irreducible representations of a finite groups $G$ can be found in $\mathbb{C}G$. I thought to use the embedding of $G$ in $S_n$, but then I don't know how to go on. Could any of you help me, please?
Maybe I got it: I know that the character of the regular representation can be viewed as the sum of the characters of the irreducible representations with coefficients their dimension, so they are in the decomposition of the regular representation. Am I right?