A finite group is its center plus its noncentral conjugacy classes.Suggest a slogan
Let \(G\) be a finite group with center \(Z(G)\), and for \(g\in G\) let \(Z(g) = \theset{h\in G \st hgh^{-1} = g}\) be the centralizer of \(g\). Let \(g_1, \ldots, g_r\) be representatives of the conjugacy classes of \(G\) that have more than one element. Then \[ \size G = \size Z(G) + \sum_{i=1}^{r} [G : Z(g_i)], \] where \([G:Z(g_i)]\) is the index of \(Z(g_i)\) in \(G\).