  We investigate the accuracy of several schemes to calculate ground-state
correlation energies using the generator coordinate technique. Our test-bed for
the study is the $sd$ interacting boson model, equivalent to a 6-level
Lipkin-type model. We find that the simplified projection of a triaxial
generator coordinate state using the $S_3$ subgroup of the rotation group is
not very accurate in the parameter space of the Hamiltonian of interest. On the
other hand, a full rotational projection of an axial generator coordinate state
gives remarkable accuracy. We also discuss the validity of the simplified
treatment using the extended Gaussian overlap approximation (top-GOA), and show
that it works reasonably well when the number of boson is four or larger.
