Since we do not want to restrict ourselves to values in traditional number systems...
Each remarquable/exceptional finite algebraic structure, graph, can be described/encoded as a specific value in a numbering system. For instance as a series of generating matrices, multiplication table, representation tables, etc.
We can consider each sporadic group as a remarquable constant. To me the Monster Group is a mathematical attraction point that can be compared to $\pi$ or $e$. And it is well hidden in the armies of soluble groups around it.
