I think it comes down to how your friend makes an introduction of you to the others present. I have thought further on my initial reply. I remain thinking that her invitation is an act of kindness but it occurs to me that as her guest, she has a responsibility to try to make you feel comfortable. It is up to her to welcome you to the rest of the group and to make efforts to include you. This starts with a proper introduction to the others. Is a failure to do this perhaps causing you to feel less than welcome?