If $X$ is a proper scheme over $k$, is $X/G$ separated?

Question

Let $X$ a proper scheme over a field $k$ and let $G$ a finite group of its automorphism (as $k$-scheme).

Let suppose that the quotient $X/G$ exists, is it is separated? How to prove it?

If the general case is false, is true with additional ipotesis? For example is true if $X$ is a proper 1-dimensional $k$ scheme?

Thank you