The physical characteristics of a two-dimensional electron gas located in the GaN layer near the AlN/GaN interface of AlGaN/AlN/GaN heterostructures have been studied for decades. According to the currently accepted concepts, its symmetry coincides with that of the nonsymmorphic space group C⁴_6v in the bulk of GaN. However, this is incorrect. Indeed, the only nonsymmorphic element of this group—the rotation of the system about the [0001] axis normal to the interface plane, with a simultaneous shift along this axis by half a period of the GaN crystal lattice—is forbidden for a two-dimensional gas owing to the confinement potential, which, therefore, reduces its symmetry to the symmetry of the trigonal point group C_3v. This fact has been confirmed in this work by ab initio density functional calculations and by electrophysical data.