Also the clique that everyone thinks about isn't really what the group is today. The regulars of olde were more involved in the forum affairs, but nowadays the regulars of the group don't have much to do with the forum beyond posting occasionally and working on projects sometimes.
Since you asked who's in it, some regulars include Trogtor, Kobewarrior, AlexFrost, Acorncake, Legoboss, Gatysh, Jam Jar, Magus, Zharthon, Rockinboy, Jayce, Charles Barkley, Mcjob and Maxwell. The older regulars who aren't around as much as they were are GumbaJonny, Nal, Squartle, Momentum, DrenDran and a few other people whom I forget completely.
why don't they have a clan page
Imagine this: You make a group for your friends who are all mutually friends with each other. You eventually accumulate enough friends that it becomes a pretty active group, and since you all share a common community you're in (The BLF), your group's presence becomes pretty obvious.
The clique contest thing was mostly a joke and thing about
getting people in the group to contribute art towards as a project. Beyond that, opening the group would be strange and having a public thing would also be strange. The group's tight-knit enough that anyone who doesn't know anyone in the group personally would have a hard time fitting into the group.