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This is a common exercise:

Sketch the lattice of subfields of $F = \mathbb{Q} ( \mathbb{e^{\frac{2 \pi i}{p}}})$ be a cyclotomic extension over $\mathbb{Q}$ (where $p$ is an odd prime).

It got me wondering, what's the easiest way of writing/listing down the elements of the Galois group $Aut_{\mathbb{Q}} F$?

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