I'm interested in this girl from my class, but I am not sure on what to do.

I'm in university, and one of the modules I'm taking this semester is a compulsory one for all faculties. The class is tutorial group sized i.e 25 people, and we were separated into groups from the first lesson. I'm in a group with the girl, 2 other girls and another guy, and we have to sit at the same table every class for activities. Yes, this sounds like grade school all over again, and yes this does give me more opportunities for conversation but wait. Even though I mentioned this was similar to a tutorial group, the teacher just goes on as if it's a lecture, and everyone just keeps silent throughout the class. It's pretty obvious when someone's talking since the class size is small so no one really bothers to. The group activities are 10 minutes out of the entire hour and thirty, so I've gotten chances to talk to her here and there but it's really not a lot. After class, she makes her way off with a friend from another group and I'm also kind of forced to leave with my friend.

The class is conducted fortnightly, and next week is the last class. How should I go about trying for something? I don't have her number, and I can't ask her that in private - there are no opportunities and everyone else will be looking.

Also, some other questions. If I approach first, does it mean that I'll be in the weaker position of power? To clarify, I'm not developing oneitis (at least, I hope not). I'm interested in her but given a lack of experience I am really unsure of what to do. I also cannot tell what she's thinking - she hasn't really shown any kind of interests. I am pretty well built (no troll), fit and social but this was all after self improvement over a period of 2 years before university. Prior to that, I had no experience at all. I would genuinely appreciate any helpful advice. Cheers.