  We show that some hypergeometric monodromy groups in Sp(4,Z) split as free or
amalgamated products and hence by cohomological considerations give examples of
Zariski dense, non-arithmetic monodromy groups of real rank 2. In particular,
we show that the monodromy of the natural quotient of the Dwork family of
quintic threefolds in P^{4} splits as Z*Z/5. As a consequence, for a smooth
quintic threefold X we show that a certain group of autoequivalences of the
bounded derived category of coherent sheaves is an Artin group of dihedral
type.
