  The orientational order of nematic liquid crystals is traditionally studied
by means of the second-rank ordering tensor $\mathbb{S}$. When this is
calculated through experiments or simulations, the symmetry group of the phase
is not known \emph{a-priori}, but needs to be deduced from the numerical
realisation of $\mathbb{S}$, which is affected by numerical errors. There is no
generally accepted procedure to perform this analysis. Here, we provide a new
algorithm suited to identifying the symmetry group of the phase. As a by
product, we prove that there are only five phase-symmetry classes of the
second-rank ordering tensor and give a canonical representation of $\mathbb{S}$
for each class. The nearest tensor of the assigned symmetry is determined by
group-projection. In order to test our procedure, we generate uniaxial and
biaxial phases in a system of interacting particles, endowed with $D_{\infty
h}$ or $D_{2h}$, which mimic the outcome of Monte-Carlo simulations. The actual
symmetry of the phases is correctly identified, along with the optimal choice
of laboratory frame.
