They aren't really a group they're the same person but split into 3 different host bodies.
They may dress the same but if an outsider of their clan wears clothes that even resemble theirs in the slightest way then they're going to get an earful of abuse.
The begs are the eyes and the ears of the illumitani so beware of what you say around them!
Girl 1: AAH THE ILLUMITANI! Don't absorb my natural beauty!
Girl 2: don't trust her she's a minion of the ringleader of the illumitani
Ringleader: HOW DARE YOU WEAR THEM SHOES! I HAVE ONES SIMILAR TO THEM!