Catalyzes the transfer of the cytidylyl group of CTP to sn-glycerol 3-phosphate so the activated glycerol 3-phosphate can be used for teichoic acid synthesis, via incorporation into both the linkage unit and the teichoic acid polymer by TagB and TagF. CTP + H(+) + sn-glycerol 3-phosphate = CDP-glycerol + diphosphate Inhibited by the divalent cations cadmium, mercury, tin, copper and zinc. Optimum pH is 6.5-9.5. Optimum temperature is 50 degrees Celsius. Cell wall biogenesis; poly(glucopyranosyl N-acetylgalactosamine 1-phosphate) teichoic acid biosynthesis. Cell wall biogenesis; poly(glycerol phosphate) teichoic acid biosynthesis. Homodimer. Positively regulated by WalR. Mainly expressed during exponential growth and rapidly shut off as cells enter the stationary phase. Proceeds via a random order reaction mechanism where there is negative cooperativity in the binding of substrates but not in catalysis. Belongs to the cytidylyltransferase family.