每日定理13

Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(2.5)

The number $k$ of similarity classes of irreducible representations of $G$ is equal to the number of conjugacy classes of $G$.

Pf:

• The $K_i$ form a basis for $\mathbf{Z}(\mathbb{C}[G])$ and $dim(\mathbf{Z}(A))=|\mathcal{M}(A)|$.