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We have studied a nearly stoichiometric insulating Y$_{0.97(2)}$Cr$_{0.98(2)}$O$_{3.00(2)}$ single crystal by performing measurements of magnetization, heat capacity, and neutron diffraction. Albeit that the YCrO$_3$ compound behaviors like a soft ferromagnet with a coersive force of $\sim$ 0.05 T, there exist strong antiferromagnetic (AFM) interactions between Cr$^{3+}$ spins due to a strongly negative paramagnetic Curie-Weiss temperature, i.e., -433.2(6) K. The coexistence of ferromagnetism and antiferromagnetism may indicate a canted AFM structure. The AFM phase transition occurs at $T_\textrm{N} =$ 141.5(1) K, which increases to $T_\textrm{N}$(5T) = 144.5(1) K at 5 T. Within the accuracy of the present neuron-diffraction studies, we determine a G-type AFM structure with a propagation vector \textbf{k} = (1 1 0) and Cr$^{3+}$ spin directions along the crystallographic \emph{c} axis of the orthorhombic structure with space group \emph{Pnma} below $T_\textrm{N}$. At 12 K, the refined moment size is 2.45(6) $μ_\textrm{B}$, $\sim$ 82\% of the theoretical saturation value 3 $μ_\textrm{B}$. The Cr$^{3+}$ spin interactions are probably two-dimensional Ising like within the reciprocal (1 1 0) scattering plane. Below $T_\textrm{N}$, the lattice configuration (\emph{a}, \emph{b}, \emph{c}, and \emph{V}) deviates largely downward from the Gr$\ddot{\textrm{u}}$neisen law, displaying an anisotropic magnetostriction effect and a magnetoelastic effect. Especially, the sample contraction upon cooling is enhanced below the AFM transition temperature. There is evidence to suggest that the actual crystalline symmetry of YCrO$_3$ compound is probably lower than the currently assumed one. Additionally, we compared the $t_{2\textrm{g}}$ YCrO$_3$ and the $e_\textrm{g}$ La$_{7/8}$Sr$_{1/8}$MnO$_3$ single crystals for a further understanding of the reason for the possible symmetry lowering.