  The p-class tower $F_p^\infty(k)$ of a number field k is its maximal
unramified pro-p extension. It is considered to be known when the p-tower
group, that is the Galois group $G:=Gal(F_p^\infty(k)/k)$, can be identified by
an explicit presentation. The main intention of this article is to characterize
assigned finite 3-groups uniquely by abelian quotient invariants of subgroups
of finite index, and to provide evidence of actual realizations of these groups
by 3-tower groups G of real quadratic fields $K=Q(\sqrt{d})$ with
3-capitulation type (0122) or (2034).
