Groups only plugin?

Hello. I was recently deleted from goodreads for not being in favor of white genocide (no, I am not kidding!) and I would like to make a different book club on my wordpress website for those who were in my club! I only have a few days. Any help as to how to do this is a relatively straightforward, but if possible feature rich, way would be much appreciated. I basically just want to be able to have a chat about books with our group, for members only if possible so that they can feel more comfortable. Is there anything like this out there that would work, a plugin or some instructions somewhere? Thanks very much!
Oh and the site is odinist.org although there is not much that one can see that would help.