TITLE: Is $ \mathrm{Aut}(\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})) $ known?
QUESTION [5 upvotes]: Following my previous question about the outer automorphism group, I would like to know if the structure of the automorphism group of the absolute Galois group of the rationals is known. Specifically, is it isomorphic to the cyclic group with two elements ?

REPLY [5 votes]: By the Neukirch–Uchida theorem , Aut(Gal($\mathbb{\bar{Q}/Q}$))= Gal($\mathbb{\bar{Q}/Q}$).