Your Y-Ties? :P
You cannot make a new faction while IN a faction. At the very least, you will have to leave your current faction in order to create a faction. Since you also need at least 5 people to start a faction, my suggestion is to find 6, and make one of them your nominee and Leader of that new faction. Have them makeover ownership of the faction to you and then it's your faction, you're still in your current faction.