There's little chance you can tell which variety it is by just looking at it. You may be able to narrow it down to a turban or purple stripe by some distinguishing feature but it's often a huge challenge even for those that grow a lot of garlic.
Maybe try calling the stores produce department and asking them for their source. If you're lucky they might have gotten it locally from a farm you can contact. If it's through a distributor they won't be much help as it may have come all the way from China.
Check the Gourmet garlic website or maybe Filaree farm. They both have some great photos.