I found the following exercise in my algebra syllabus:
Prove $\mathrm{Aut}(\mathbb{H})\cong S_4$.
Here $\mathrm{Aut}(\cdot)$ denotes the set of group automorphisms.
I assume this is a typo, since $\mathrm{Aut}(Q_8)\cong S_4$, and proofs for this are managable and can be found on this site. However, before I found out this is most likely a typo, I was thinking about how to find $\mathrm{Aut}(\mathbb{H})$, but I didn't find a way to solve this. Is there anything known about $\mathrm{Aut}(\mathbb{H})$? I couldn't find anything on the internet. I would be glad with either a reference or an answer.