There are two kinds of factions, in game, and online. They do not transfer. The online factions are very official, usally important, and technically better. The ingame factions are the ones that do stuff, like homebases and faction tags. This isnt Eve, and therefore you dont need to belong to an online faction to do faction stuff. Hit \"H\", hit \"Create New Faction\", then name it \"Syndicate\" or \"The Syndicate\" Whichever you prefer.