  Using a generalization of Cayley's hyperdeterminant as a new measure of
tripartite fermionic entanglement we obtain the SLOCC classification of
three-fermion systems with six single particle states. A special subclass of
such three-fermion systems is shown to have the same properties as the
well-known three-qubit ones. Our results can be presented in a unified way
using Freudenthal triple systems based on cubic Jordan algebras. For systems
with an arbitrary number of fermions and single particle states we propose the
Pl\"ucker relations as a sufficient and necessary condition of separability.
