Mild pro-p-groups with 4 generators

Let p be an odd prime and S a finite set of primes ≡1 mod p. We give an effective criterion for determining when the Galois group G=GS(p) of the maximal p-extension of Q unramified outside of S is mild when |S|=4 and the cup product H1(G,Z/pZ)⊗H1(G,Z/pZ)→H2(G,Z/pZ) is surjective.