<human>: Summarize the given text in a few sentences.

So I've been spending time with a group of friends I stumbled into recently and as much fun as that is there's quite a cute lady who hangs out with us and who's taken my interest. We usually sit next to each other, though it's neither of our choice exactly, and when we talk I definitely get an "interested" vibe.

Problem is this is the only contact we have. We see each other once a week for two hours max. She always shows up late and leaves early so short of waiting around outside of our friend's houses there's no opportunity to get her alone. These are all open layout, everyone is right next to each other, homes. I can't catch her alone by he fridge or outside of the bathroom, everyone can still see and hear us.

Second problem is she's hooking up with a guy in our group. It's nothing serious and I know she's still available but come on you don't just ask a girl out in front of her entire crowd of friends AND the dude she's doing. It's rude and I refuse to initiate a beef with a guy in this cool group of people. This pretty much leaves me with one option:

Email. It's lame and it sucks but I don't know what else to do. I just want to ask her out for coffee but I don't have a phone number or anything, the only reason I even have her email is because we're on our big group email for our hangout nights. There are never other events or nights out, let alone one where she would be there and let alone still without the guy she's "seeing." What do I even do here?
<bot>: I only ever see an ostensibly interested girl when there are several other people around, including her FWB, no matter what. Is an email a viable option in this situation or will it come across as weird?