For example if "G" is a finite group and "K" is the complex number field, the regular representation is a direct sum of irreducible representations, in number at least the number of conjugacy classes of "G".
For example if "G" is a finite group and "K" is the complex number field, the regular representation decomposes as a direct sum of irreducible representations, with each irreducible representation appearing in the decomposition with multiplicity its dimension. The number of these irreducibles is equal to the number of conjugacy classes of "G".