I'll give you a very, very good advice
asking for the phone is as difficult as you make it to be, so I'll give you the easy way and the hard way, but regardless, there is a specially important detail that you'll do:
easy way (beginner style)
while chatting her in isolation (you and her alone, remember), and making sure she has no eye contact with the group (you position yourself against the group, so she is facing you) you just talk about hobbiesand such, and after a bit, tell her how awesome it would be to spend some time together, see her reaction. If everything is going alright, she'll be positive, then cool, give her your phone and tell her to write her phone, and explain her that you'll make a call and now she'll have your number. Now you both have phones. DO NOT LEAVE NOW, keep chatting and make her comfortable again, avoid the issue of the phone and act natural, and just reinforce her with her hobbies. that's it
if you don't see a positive reaction, you do the same but only when you return to the group, and then do the same but with other girl, usually the ugly one... then the whole group will do it, and you'll have her phone number the same way by social pressure
the most important thing is that YOU give her the phone, YOU tell her to write the number (in fact you don't even tell her "give me your phone", you don't need to say anything, she'll understand it and you'll comunicate it without saying it), and SHE won't be able to give a fake number, because that way she'll be caught in that same instant. Also, that way she can add you in that moment, and then moment you use that phone number she won't have to remember who you are, but instead, read it in the phone
hard way... you just make her so interested that she'll ask for it, usually happens when you isolated her. It's not so difficult but it takes a bit more practice, because you'll have to mnow how to manage a conversation at this point and how to harness interest and such