We present the first comprehensive study of a giant, approximate to 70 kpc-scale nebula around a radio-quiet quasar at z<1. The analysis is based on deep integral field spectroscopy with MUSE of the field of HE0238-1904, a luminous quasar at z=0.6282. The nebula emits strongly in [OII], H beta, and [OIII], and the quasar resides in an unusually overdense environment for a radio-quiet system. The environment likely consists of two groups which may be merging, and in total have an estimated dynamical mass of M-dyn approximate to 4x10(13) to 10(14) M-circle dot. The nebula exhibits largely quiescent kinematics and irregular morphology. The nebula may arise primarily through interaction-related stripping of circumgalactic and interstellar medium (CGM/ISM) of group members, with some potential contributions from quasar outflows. The simultaneous presence of the giant nebula and a radio-quiet quasar in a rich environment suggests a correlation between such circum-quasar nebulae and environmental effects. This possibility can be tested with larger samples. The upper limits on the electron number density implied by the [OII] doublet ratio range from log(ne,[OII]/cm(-3))<1.2 to 2.8. However, assuming a constant quasar luminosity and negligible projection effects, the densities implied from the measured line ratios between different ions (e.g., [OII], [OIII], and [NeV]) and photoionization simulations are often 10-400 times larger. This large discrepancy can be explained by quasar variability on a timescale of approximate to 10(4)-10(5) years.