Let $L/\mathbb Q$ be a (finite) Galois extension of degree $n$ with Galois group $\Gamma$. We know that there is a primitive element or generator $\alpha$ of this extension.
Is the number of Galois conjugates of $\alpha$ (i.e. the length of the orbit of $\alpha$ under $\Gamma$) smaller than or equal to the order of the Galois group?
And under which conditions are they the same?