GaloisType( L )
Galois( f )
The first version returns the number of the permutation isomorphism type of the Galois group of the normal closure of L, considered as a transitive permutation group of the roots of the defining polynomial (see The Transitive Groups Library). The second version returns the Galois type of the splitting field of f. Identification is done by factoring appropriate Galois resolvents as proposed in MS85. This function is provided for rational polynomials of degree up to 15. However, it may be not feasible to call this function for polynomials of degree 14 or 15, as the involved computations may be enormous. For some polynomials of degree 14, a complete discrimination is not yet possible, as it would require computations, that are not feasible with current factoring methods.
gap> GaloisType(e);
2
gap> TransitiveGroup(e.degree,2);
E(4) = 2[x]2
GAP 3.4.4