  For a prime number $p$ and a free profinite group $S$ on the basis $X$, let
$S_{(n,p)}$, $n=1,2,\ldots,$ be the $p$-Zassenhaus filtration of $S$. For
$p>n$, we give a word-combinatorial description of the cohomology group
$H^2(S/S_{(n,p)},\mathbb{Z}/p)$ in terms of the shuffle algebra on $X$. We give
a natural linear basis for this cohomology group, which is constructed by means
of unitriangular representations arising from Lyndon words.
