Here's the standard example. I found it in Lang's Algebraic Number Theory where he attributes it to Artin. Let $K$ be the splitting field of $X^5-X+1$ over $\mathbb{Q}$. Then $K$ has Galois group $S_5$ over $\mathbb{Q}$ and $A_5$ over $L=\mathbb{Q}(sqrt{2869})$. L=\mathbb{Q}(\sqrt{2869})$. Also$K$is unramified over$L$. 1 Here's the standard example. I found it in Lang's Algebraic Number Theory where he attributes it to Artin. Let$K$be the splitting field of$X^5-X+1$over$\mathbb{Q}$. Then$K$has Galois group$S_5$over$\mathbb{Q}$and$A_5$over$L=\mathbb{Q}(sqrt{2869})$. Also$K$is unramified over$L\$.