If you ever wondered if there is a cooler or faster way to update a computer's group membership without having to reboot: well there is. If you delete or "purge" the kerberos tickets on the machine and then perform a gpupdate, the client is going to retrieve a new kerberos ticket with the new group membership.

Here are the two (well, if have never heard of gpupdate /force):

klist -lh 0 -li 0x3e7 purge

gpupdate /force