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The analytical canonical NLT partition function of a quasi-one dimensional (q1D) system of hard disks [J. Chem Phys. v.153, 144111 (2020)] provides a direct analytical description of the thermodynamics and ordering in this system (a pore) as a function of the linear density N/L both for finite and infinite systems. It is alternative to the well-developed transfer matrix method based on the isobaric NPT ensemble. We derive the analytical formulae for the actual distance dependence of the translational pair distribution function (PDF) and the DF of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for the whole range of the q1D pore widths and different densities shows a non-monotonic dependence with a maximum at the density N/L=1 and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length L is equal exactly to N disk diameters. We introduce an orientational order parameter that accounts for the local quality of the crystalline zigzag formed by disks and is related to its structural element. This parameter is maximum in the densely packed state and vanishes for a very low density. Due to specific quasi-one dimensional geometry, this macroscopic order parameter is constant along the pore so that the macroscopic orientational order is of a liquid crystalline type.