  We construct a family of quantum Hall Hamiltonians whose ground states, at
least for small system sizes, give correlators of the S3 conformal field
theories. The ground states are considered as trial wavefunctions for quantum
Hall effect of bosons at filling fraction nu=3/4 interacting either via delta
function interaction or delta function plus dipole interaction. While the S3
theories can be either unitary or nonunitary, we find high overlaps with exact
diagonalizations only for the nonunitary case, suggesting that these
wavefunctions may correspond to critical points, possibly analogous to the
previously studied Gaffnian wavefunction. These wavefunctions give an explicit
example which cannot be fully characterized by their thin-torus limit or by
their pattern of zeros.
