  The Wigner function of a finite-dimensional system can be constructed via
dual pairing of a density matrix with the Stratonovich-Weyl kernel. Following
Kenfack and $\dot{\text{Z}}$yczkowski, we consider the indicator of
nonclassicality of a finite-dimensional quantum system which depends on the
volume of the negative part of the Wigner function. This indicator is defined
over the unitary non-equivalent classes of quantum states, i.e. represents an
invariant, but since for a given quantum system there is no unique Wigner
function it turns to be sensitive to the choice of representations for the
Wigner function. Based on the explicit parameterization of the moduli space of
the Wigner functions, we compute the corresponding
Kenfack-$\dot{\text{Z}}$yczkowski indicators of a 3-level system for
degenerate, unitary non-equivalent Stratonovich-Weyl kernels.
