Empyreal Seat

There are, in my opinion, very few ways to more easily indicate that one is compensating for something than to term one's opponents as "underground cryptozoological entities", thus supposedly declaring that they are hidden but more literally stating that they are beneath you. The only real way to top it is to put one's secret base in space.
Therefore, the Epoch Society is, logically, more pretentious than any other such organization in the history of the world.

But Why Space?

Because when they made it up there, they were relatively unique and there weren't a lot of things that could stop them. As an organization of scientists, aligned with several powerful secret organizations, and more than a few warlords, they were able to construct something that survived fairly well and was modular enough to be adapted into the modern era.

Influences

The station itself periodically becomes defunct when the interests of Epoch move to a less theoretical sphere, forcing their attentions on the ground. But the Empyreal Seat remains as a core part of their infrastructure.

What's Up There

I don't know. They wouldn't be stupid enough to let me up there to find out how to destroy their precious station. They really don't let a lot of people up there in the modern era. What little data we have is usually gleaned from past iterations and the occasional defector. These people are frightening in their superiority complex. Normally their arrogance should be enough to cause their downfall, but the unfettered science has allowed them to produce some truly gnarly defenses, sometimes purely by accident.

A Literal Seat of Power

There is, at some point within the station, a literal seat of powers. Or rather, the ability to grant powers. It apparently works in very limited capacity and mostly just kills those who sit in it, but regardless it does lend further importance to the station.

Type

Starbase