Monster group

The monster group is the largest of the 26 "sporadic groups," which are one of the classifications of the finite simple groups. Its order is approximately \(8 \cdot 10^{53}\), with a full decimal expansion of 808017424794512875886459904961710757005754368000000000.

Conway and Guy suggest that the order of the monster group is the "largest undeflatable number" (in comparison to Graham's number and Skewes' number which are upper bounds). Arguably, numbers such as TREE(3) discredit this claim, but the order of the monster group is still interesting in that it is a naturally occurring large number, and there does not appear to be any obvious way to generalize the value.