BuddyPress.org

“the function where by if your are member it just displays the group or if you are the admin of the group it displays the group setting and so on”
That’s how it is already set up actually. If I didn’t get what you meant though, you can also use https://wordpress.org/extend/plugins/buddypress-restrict-group-creation/ or check source code for more info.

edit – too slow mercime