Let $H=\{\beta \in S_5\mid\beta(1)=1\}$ and $K=\{\beta \in S_5\mid\beta(2)=2\}$. Prove that $H$ is isomorphic to $K$. Let $H=\{\beta \in S_5\mid\beta(1)=1\}$ and $K=\{\beta \in S_5\mid\beta(2)=2\}$. Prove that $H$ is isomorphic to $K$.
$H$ is the group of permutations fixing $1$ and $K$ is the group of permutations fixing $2$. I don't know how to write the isomorphism $\phi$.

Hint: $H$ is conjugated to $K$ by the transposition $(1,2)$.
