Closed G2-structures with a Transitive Reductive Group of Automorphisms

We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G2-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is one-dimensional and the manifold is the Riemannian product of a flat factor and a non-compact homogeneous six-dimensional manifold endowed with an invariant strictly symplectic half-flat SU(3)-structure.