1. The problem statement, all variables and given/known data Describe the structure of the Galois group for G(Q(c):Q) where c is a 14th primitive root of unity 2. Relevant equations 3. The attempt at a solution the minimal polynomial for c over Q is f(x)=x^6-x^5+x^4-x^3+x^2-x+1. Is the galois group isomorphic to Z*_14? Or maybe that's only true for prime numbers? Anyway, c has order 6, so c^1,.....,c^6=1 will all be roots of it's minimal polynomial f(x). The galois group will have a map b(1)=c^i for each 0>i>6. A part of me wants to say the galois group is the cyclic group of order 6, but the alternating polynomial makes me think it's a bit trickier than that. Could the galois group be some sort of alternating cyclic group? If that makes any sense... Thanks PF!