  It is commonly accepted that a deviation of the Wigner quasiprobability
distribution of a quantum state from a proper statistical distribution
signifies its nonclassicality. Following this ideology, we introduce the global
indicator $\mathcal{Q}_N$ for quantification of "classicality-quantumness"
correspondence in the form of the functional on the orbit space
$\mathcal{O}[\mathfrak{P}_N]$ of the $SU(N)$ group adjoint action on the state
space $\mathfrak{P}_N$ of an $N$-dimensional quantum system. The indicator
$\mathcal{Q}_{N}$ is defined as a relative volume of a subspace
$\mathcal{O}[\mathfrak{P}^{(+)}_N] \subset \mathcal{O}[\mathfrak{P}_N]\,,$
where the Wigner quasiprobability distribution is positive. An algebraic
structure of $\mathcal{O}[\mathfrak{P}^{(+)}_N]$ is revealed and exemplified by
a single qubit $(N=2)$ and single qutrit $(N=3)$. For the Hilbert-Schmidt
ensemble of qutrits the dependence of the global indicator on the moduli
parameter of the Wigner quasiprobability distribution has been found.
