P<x>:=PolynomialRing(Rationals());
SetClassGroupBounds("GRH");

for i in [1..20] do
  if IsPrime(i) then
    K<w>:=NumberField(x^i-i);
    O:=MaximalOrder(K);
    Factorization(Discriminant(O));
    GaloisGroup(K);
   end if;
end for;