Is the next claim about automorphism group ${\rm \mathit Aut} _\mathbb{Q} (\mathbb{C})$ correct?

Question

Let $G={\rm \mathit Aut} _\mathbb{Q} (\mathbb{C})$ be the automorphism group.

$K \subset \mathbb{C}$ is defined as $K =\ \bigr\{ \alpha \in \mathbb{C} \ |\ \sigma(\alpha) = \alpha \ ( \forall \sigma \in G)\bigl\}$ .

Then $K= \mathbb{Q} \ $ is true??