The Club has existed for centuries. It originated from the realization by ultra-privileged individuals that despite their differences they had one common goal - to maintain their power and wealth. So, they decided to set up regular meetings where they try to find new and better ways to get ever more powerful and increase their vast fortunes.
The Club first turns up at the end of Geek Addiction and then briefly in Penny and the Silver key #1, when Takagi's reasons for being at Dr Lem's rehab clinic are revealed. Very little is shown both times, but it's clear someone has an interest in Tim. Then, in Penny and the Silver Key #2, Penny spends some time trying to escape their headquarters. She also finds a list of club activities that appear to be limited to orgies with the occasional world domination plotting. The people she sees at the Club are:
TOM
When she first sees him, Penny thinks he's Tim, but she soon finds out that he's very much the opposite of the brave, helpful, self-sacrificing monster slayer.
LADY KATRINA
She's with Tom, and has a (literally) fiery personality.
DR SVENSON
While looking for the way out, Penny overhears a conversation between Dr Svenson and Takagi.
INSPIRATION
Marvel's Helfire Club, the Freemasonry, and secret societies in general.