  The basic ingredients of the `consistent histories' approach to quantum
theory are a space $\UP$ of `history propositions' and a space $\D$ of
`decoherence functionals'. In this article we consider such history quantum
theories in the case where $\UP$ is given by the set of projectors $\P(\V)$ on
some Hilbert space $\V$. Using an analogue of Wigner's Theorem in the context
of history quantum theories proven earlier, we develop the notion of a
`symmetry of a decoherence functional' and prove that all such symmetries form
a group which we call `the symmetry group of a decoherence functional'. We
calculate---for the case of history quantum mechanics---some of these
symmetries explicitly and relate them to some discussions that have appeared
previously.
