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.
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