  High precision spectroscopy of the $^1S_0$-to-${^1}D_2$ clock transition of
$^{176}$Lu is reported. Measurements are performed with Hertz level precision
with the accuracy of the hyperfine-averaged frequency limited by the
calibration of an active hydrogen maser to the SI definition of the second via
a GPS link. The measurements also provide accurate determination of the $^1D_2$
hyperfine structure. Hyperfine structure constants associated with the magnetic
octupole and electric hexadecapole moments of the nucleus are considered, which
includes a derivation of correction terms from third-order perturbation theory.
