The correct term, and it is important to understand it, is class instance. Not Class.
The question is how to get a reference to the right class instance. There could be million class instances running at the same time. Each client is managed by its own instance.
Do you want to send to all of them? To a few? How will you distinguish between the clients?
The way to do it, and it is demonstrated in some of the examples, is with a concurrent map that holds all the live connections.