Galois group of a polynomial
I have to find a splitting field of the polynomial over and the galois group and all intermediate fields of the algebraic extension .
I found out, that is irreducible, the roots of are:
and that is a splitting field of .
Furthermore I find out, that the three homomorphisms
have order 2, so the galois group is isomorph to .
But now I don't know how to find the fixed fields, which belongs to the homomorphisms.
For example: Which fixed field belongs to the homomorphism ?
The definition says:
...and this don't help me, because I need a description of the fixed field like this: (with suitable ).
I hope, you can help me.