  Due to seminal works of Weinberg, Cachazo and Strominger we know that tree
level quantum gravity amplitudes satisfy three factorization constraints.
Building on previous works which relate two of these constraints to symmetries
of quantum gravity at null infinity, we present rather strong evidence that the
third constraint is also equivalent to a new set of symmetries of
(perturbative) quantum gravity. Our analysis implies that the symmetry group of
quantum gravity may be even richer than the BMS group (or infinite dimensional
extension thereof) previously considered.
