I know you can make it so that no one can find you in a search and that you can block individual people, but I don’t think you can block a whole group (of people that aren’t your friends). You can block people that are already your friends and in a specific group from certain information though. To do that, go to privacy settings, then go to customize settings under sharing on facebook. Then you can select customize (in the drop down box) for each area and block the specific groups (as in the groups that you put your friends into) by typing the group name in the box that says to block from these people (or something like that). If they aren’t your friend, I think you would have to block each person individually.