While some group URLs come in the format of www.facebook.com/groups/%ID%/ other come in the format of www.facebook.com/groups/%SOME_STRING%/. For example http://www.facebook.com/groups/2261122614/ vs. http://www.facebook.com/groups/fbdevelopers/.
In the former case it's very easy to programmatically extract the Graph API ID from the URL. How can that be done for URLs of the latter case?
Just figured this out! Do this:
http://graph.facebook.com/search?q=[ALIAS]&type=group