If M is a simplicial module over a field K of characteristic p , the homology of the symmetric algebra Sd of M depends only on H [M] and it is the universal envelopping coalgebra U [V] of a vector space V. An explicit description of this Hopf algebra with divided powers is given. The proof is done in such a way thst it is possible to see what are the contributions of a generator of H [M] to H [S M].If n ⩽ 2p, Hn[S M]is computed as in characteristic zero. This is no more true in higher dimensions: for instance a genera-tor of H3[M] yields a generator of H2p+1[SM].