It sounds like the group dynamic doesn't work for you but seeing a few of these people one on one is okay. Could you avoid group activities with them? It sounds like they may have a different conversational style than you do, and when all of you are together, there are more people with their style than yours.

I've been struggling for a solution to a similar problem for a year now. I've thought about saying something like 'I'm sorry, I was talking' when interrupted, but it seems pointless when she is so obviously not interested in what I'm saying. I've decided that I am better off letting this friendship go and pursuing a more enjoyable friendship with someone else.