  Generalizing results of Morishita and Vogel, an explicit description of the
triple Massey product for the Galois group $G_S(2)$ of the maximal 2-extension
of $\mathbb{Q}$ unramified outside a finite set of prime numbers $S$ containing
2 is given in terms of R\'edei symbols. We show that mild pro-2-groups with
Zassenhaus invariant 3 occur as Galois groups of the form $G_S(2)$.
Furthermore, a non-analytic mild fab pro-2-group having only 3 generators is
constructed .
