  We give a classification of minimal algebras generated in degree 1, defined
over any field $\bk$ of characteristic different from 2, up to dimension 6.
This recovers the classification of nilpotent Lie algebras over $\bk$ up to
dimension 6. In the case of a field $\bk$ of characteristic zero, we obtain the
classification of nilmanifolds of dimension less than or equal to 6, up to
$\bk$-homotopy type. Finally, we determine which rational homotopy types of
such nilmanifolds carry a symplectic structure.
