  Freyd's generating hypothesis, interpreted in the stable module category of a
finite p-group G, is the statement that a map between finite-dimensional
kG-modules factors through a projective if the induced map on Tate cohomology
is trivial. We show that Freyd's generating hypothesis holds for a non-trivial
finite p-group G if and only if G is either C_2 or C_3. We also give various
conditions which are equivalent to the generating hypothesis.
