Global Goups

Every pc on the network has a global group called Tech Support that has been added to the local admin group. We have 300 users that need to be added to the Tech Support group so they will have sufficient rights to connect to a site that will automatically update their software. They will do updates once a month, then they must be removed from Tech Support.
Is there an easy way to add and remove these users from Tech Support. I can create Global Group for them, but I assume a Global Group cannot be added to Tech Support, which is already a Global Group.
We’re using NT 4 servers.
Any help would be greatly appreciated.