  It is one of the wonderful ``coincidences'' of the theory of finite groups
that the simple group G of order 25920 arises as both a symplectic group in
characteristic 3 and a unitary group in characteristic 2. These two
realizations of G yield two G-covers of the moduli space of configurations of
six points on the projective line modulo PGL_2, via the 3- and 2-torsion of the
Jacobians of the double and triple cyclic covers of P^1 branched at those six
points. Remarkably these two covers are isomorphic. This was proved over C by
transcendental methods by Hunt and Weintraub. We give an algebraic proof valid
over any field not of characteristic 2 or 3 that contains the cube roots of
unity. We then explore the connection between this $G$-cover and the elliptic
surface $y^2 = x^3 + sextic(t), whose Mordell-Weil lattice is E_8 with
automorphisms by a central extension of G.
