The Cosmology Large Angular Scale Surveyor (CLASS) is mapping the polarization of the cosmic microwave background (CMB) at large angular scales (2 < ℓ lesssim 200) in search of a primordial gravitational wave B-mode signal down to a tensor-to-scalar ratio of r ≈ 0.01. The same data set will provide a near sample-variance-limited measurement of the optical depth to reionization. Between 2016 June and 2018 March, CLASS completed the largest ground-based Q-band CMB survey to date, covering over 31,000 square-degrees (75% of the sky), with an instantaneous array noise-equivalent temperature sensitivity of $32\,\mu {{\rm{K}}}_{\mathrm{cmb}}\sqrt{{\rm{s}}}$. We demonstrate that the detector optical loading (1.6 pW) and noise-equivalent power (19 $\mathrm{aW}\sqrt{{\rm{s}}}$) match the expected noise model dominated by photon bunching noise. We derive a 13.1 ± 0.3 K pW−1 calibration to antenna temperature based on Moon observations, which translates to an optical efficiency of 0.48 ± 0.02 and a 27 K system noise temperature. Finally, we report a Tau A flux density of 308 ± 11 Jy at 38.4 ± 0.2 GHz, consistent with the Wilkinson Microwave Anisotropy Probe Tau A time-dependent spectral flux density model.