## FANDOM

10,027 Pages

The monster group is the largest of the 26 sporadic groups, which are one of the classes in the classification of the finite simple groups. Its order is approximately $$8 \cdot 10^{53}$$, with a full decimal expansion of:

808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000

.

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.

## Approximations in other notations Edit

Notation Lower bound Upper bound
Scientific notation $$8.08\times10^{53}$$ $$8.081\times10^{53}$$
Arrow notation $$43\uparrow33$$ $$3\uparrow113$$
Steinhaus-Moser Notation 34[3] 35[3]
Copy notation 7[54] 8[54]
Taro's multivariable Ackermann function A(3,176) A(3,177)
Pound-Star Notation #*(7,3,5)*15 #*(4,7,6,4,0,2)*6
BEAF {43,33} {3,113}
Hyper-E notation 8E53 E[3]113
Hyperfactorial array notation 43! 44!
Fast-growing hierarchy $$f_2(171)$$ $$f_2(172)$$
Hardy hierarchy $$H_{\omega^2}(171)$$ $$H_{\omega^2}(172)$$
Slow-growing hierarchy $$g_{\omega^{32}5}(46)$$ $$g_{\omega^{\omega2+9}10}(17)$$