Of course this isn’t your fault Katerina! Long established groups can fall prey to becoming insular and it seems like the group you’ve joined has let itself slip into such a state. It is common in long established groups such as yours, sadly I’m not sure that any of my ideas will work but you should decide if any of these are worth trying. Also, my comment is going to be very long and all over the place, I’m sorry about that!
In order to better meld with the members, could you attempt to add something to the group without changing the core purpose and activities that take place? Such as, if their is a new member, holding a 10 minute ‘welcome to the group meet and let’s give you a rundown so you are up to speed’ before the group starts. That’s something you could put to the group, maybe saying that you have had a hard time becoming a cohesive member and you think that in the future, this will help others who join who may feel the same. Stress that this addition would not detract from, but add too the group.
However, do consider that this group may be far too closed off for anyone to be able to fit in, or only a specific type of persons. They may be accepting new members but really their minds are so closed off to the possibility that they will not accept someone actually trying to join. Also consider that the members possibly are just not nice people? You could always bring up how you feel directly to the group obviously in a polite way so that future relations won’t be soured, but again, the group may not respond well, or they could respond fabulously and welcome you with open arms! Think about possibly lightly probing the group about your feelings and see what they say.
Other ideas are maybe there is another group of the same subject that you could join or you could even start a new one - if the group is a book club, start one that is for book club beginners or for much shorter novels than those that the long established group reads. Who knows, there may be more people who faced the same issues as you are, others who joined the group and left because they also were not able to fit in the the conversation.
If none of that sounds appealing, I’d say stick it out in the group for a bit more, but have low expectations: that you won’t be able to join in the discussion, you’ll still feel like you’re on the outside looking in, and that it will take time for anything to change. If you have low expectations then you will be protecting yourself (more so than before) from further disappointment. And hopefully after a while of being in the group you will learn more (if it is a group for learning an activity, that is) and be able to participate much more fluently.
So no, this is absolutely common and not to do with you. I would pull up some studies about this phenomenon (of groups becoming closed off to new members) but I already wrote you a book and a half. 
Keep your chin up, set your sights on becoming a valuable source of discussion to the group, and after getting the hang of things, try to add on to the conversation and do it with confidence! I hope it turns out wonderfully for you Katerina1, I’ll be thinking of you.
