Prenyltransferase that catalyzes the transfer of the geranylgeranyl moiety of geranylgeranyl diphosphate (GGPP) to the C3 hydroxyl of sn-glycerol-1-phosphate (G1P). This reaction is the first ether-bond-formation step in the biosynthesis of archaeal membrane lipids. To a much lesser extent, is also able to use heptaprenyl pyrophosphate (HepPP; 35 carbon atoms) as the prenyl donor. (2E,6E,10E)-geranylgeranyl diphosphate + sn-glycerol 1-phosphate = diphosphate + sn-3-O-(geranylgeranyl)glycerol 1-phosphate Membrane lipid metabolism; glycerophospholipid metabolism. Homodimer. Belongs to the GGGP/HepGP synthase family. Group I subfamily.