  In this paper, two things are done. First, we analyze the compatibility of
Dirac fermions with the hidden duality symmetries which appear in the toroidal
compactification of gravitational theories down to three spacetime dimensions.
We show that the Pauli couplings to the p-forms can be adjusted, for all simple
(split) groups, so that the fermions transform in a representation of the
maximal compact subgroup of the duality group G in three dimensions. Second, we
investigate how the Dirac fermions fit in the conjectured hidden overextended
symmetry G++. We show compatibility with this symmetry up to the same level as
in the pure bosonic case. We also investigate the BKL behaviour of the
Einstein-Dirac-p-form systems and provide a group theoretical interpretation of
the Belinskii-Khalatnikov result that the Dirac field removes chaos.
