  Let $G$ be a finite group. Let $X_1(G)$ be the first column of the ordinary
character table of $G.$ In this paper, we will show that if $X_1(G)=X_1(S_n),$
then $G\cong S_n.$ As a consequence, we show that $S_n$ is uniquely determined
by the structure of the complex group algebra $\C S_n.$
