Matthew McGiffen shows us a way to test if an account is a member of an Active Directory group:
As part of my job I manage a bunch of SQL instances for Development and Test.
Access is managed though Active Directory groups, so I rarely have to do anything regards managing permissions. Nonetheless I often get requests from people to give them access. This is usually for a new starter or someone who has moved from one team to another.
Of course, the answer is usually that they just need adding to the right AD group. Rather than assume though, I always get them to check before I pass the request on to the AD team. You never know, there could be something else wrong.
You can also use xp_logininfo if you want to go the other way and get all of the members of a particular group.