NAD(+)-dependent glutamate dehydrogenase which degrades glutamate to ammonia and alpha-ketoglutarate. H2O + L-glutamate + NAD(+) = 2-oxoglutarate + H(+) + NADH + NH4(+) Homotetramer. Belongs to the Glu/Leu/Phe/Val dehydrogenases family.