Let $G=Hol(C_8)$. In addition let $f(x)\in \mathbb{Q}[x]$ be an irreducible polynomial of degree $8$, $L$ a splitting field of $f(x)$ over $\mathbb{Q}$ and suppose that $Gal(L/\mathbb{Q})\cong G$
How to show that there is a subgroup of $S_8$ isomorphic to $G$
Thanks.