"user group" or "users group"?

I'm organizing a database user group (formerly Oracle user group) at my work place. One trivial question comes up. Should it be "Database User Group" or "Database Users Group" with plural "Users"? While people are making comments with respect to English grammar, I thought it would be helpful to check how most people say on the Internet. So here it is my email to them:

"users group" or "user group"? Here's Google exact word search hit count (when you search, enclose the words in double quotes):

user group: 7,950,000
users group: 3,580,000
oracle user group: 80,400
oracle users group: 70,100
unix user group: 32,100
unix users group: 50,600
linux user group: 566,000
linux users group: 2,800,000
mac user group: 53,400
mac users group: 43,300
java user group: 82,700
java users group: 36,800

Although how people say on the Internet doesn't mean it's grammatical, it's at least statistically more popular. So we can use that as a reference. It looks like more people prefer the singular "user group". When it's broken down to a specific type of user group, all that I checked except Linux and UNIX people prefer singular. (No wonder UNIX and especially Linux people are the most likely associated with geeks in this society.) My conclusion of this search: the geekier and less coherent the members are, the more likely they prefer plural, "users group".