The first possibility is that she will happen to approach you one day and you'll be able to talk to her then.  Although this is probably the solution you're hoping for, it's not guaranteed to happen.  In my opinion, it's not doing you much good to sit around and wait for this girl to approach you and start talking to you.  It's time to be proactive.

There are a few ways you could go about approaching her.  First, do you only see her in that one class?  If not, maybe it would be easier to approach her some other time during the school day when she's less busy with her friends.  Just make small talk.  Start by talking about things relevant to the class you have together, and then move on from there.

If you only see her during this one class, you might have to try to squeeze into the picture.  Either wait and see if she's ever not talking to her friends, and then go talk to her, or try to talk to them all as a group.  I understand that a group of girls you don't know can be pretty intimidating, but if you're nice and just make small talk I don't see why they wouldn't include you.

Whatever you decide on, know that nothing is going to happen overnight.  It takes time to get to know someone, so just take the opportunities that you get and try to get to know her better.

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Around and around and around we spin,
With feet of lead and wings of tin