Catalyzes the reversible conversion of L-glutamate to 2-oxoglutarate. H2O + L-glutamate + NAD(+) = 2-oxoglutarate + H(+) + NADH + NH4(+) Activity is inhibited by unphosphorylated GarA. Interacts with (unphosphorylated) GarA. Belongs to the Glu/Leu/Phe/Val dehydrogenases family.