The Cosmology Large Angular Scale Surveyor (CLASS) is mapping the polarization of the cosmic microwave background (CMB) at large angular scales (2 < l less than or similar to 200) in search of a primordial gravitational wave B-mode signal down to a tensor-to-scalar ratio of r approximate to 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 K-cmb root s. We demonstrate that the detector optical loading (1.6 pW) and noise-equivalent power (19 aW root 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.