Catalyzes the reversible cyclization of carbamoyl aspartate to dihydroorotate. (S)-dihydroorotate + H2O = H(+) + N-carbamoyl-L-aspartate Binds 1 Zn(2+) ion per subunit (PubMed:15381710, PubMed:15826652, PubMed:19128030, PubMed:24314009). Fully functional with a mononuclear metal center. Does not require a second metal for activity, although the conservation of the second metal-binding site during evolution leaves open the possibility that a second ion might bind in vivo (PubMed:24314009). The monomer has very low activity by itself. Activated several thousandfold by formation of a complex with PyrB aspartate carbamoyltransferase (ATCase). Pyrimidine metabolism; UMP biosynthesis via de novo pathway; (S)-dihydroorotate from bicarbonate: step 3/3. Monomer. Forms a 1:1 stoichiometric complex with PyrB. The complex exists as an equilibrium mixture of heterohexamers, composed of 3 PyrC and 3 PyrB subunits, and dodecamers. The complex has both DHOase and ATCase activities. Belongs to the metallo-dependent hydrolases superfamily. DHOase family. Class I DHOase subfamily.