  Let $k$ be a number field, $K/k$ a finite Galois extension with Galois group
$G$, $\chi$ a faithful character of $G$. We prove that the Artin L-function
$L(s,\chi,K/k)$ determines the Galois closure of $K$ over $\Q$. In the special
case $k=\Q$ it also determines the character $\chi$.
