Involved in the biosynthesis of the tyvelose, a 3,6-dideoxyhexose found in the O-antigen of the surface lipopolysaccharides. It catalyzes the transfer of a CMP moiety from CTP to glucose 1-phosphate (By similarity). alpha-D-glucose 1-phosphate + CTP + H(+) = CDP-D-glucose + diphosphate Binds 1 Mg(2+) ion per subunit. Nucleotide-sugar biosynthesis; CDP-3,6-dideoxy-D-mannose biosynthesis; CDP-3,6-dideoxy-D-mannose from CTP and alpha-D-glucose 1-phosphate: step 1/5. Bacterial outer membrane biogenesis; LPS O-antigen biosynthesis. Homohexamer. Catalysis proceeds via a sequential rather than a ping-pong bi-bi reaction mechanism. Belongs to the glucose-1-phosphate cytidylyltransferase family.