Why is she jealouse and betrayed ?

Just because she broke up with you, doesn't mean that her feelings are just gone. Typically it takes both people a little while to completely adjust to not being together, regardless who broke up with who. And because of that shes probably not used you going out without her, especially with her friends.. even if you were friends with them too. It's dumb, i know but girls are strange like that. I think that if you two are serious about not being together then you need to talk to her and tell her that you're not going to just stop being friends with these people because she's not included. That's part of breaking up. Good Luck.