*Here is a group that truly lives up to its name! The order of the Monster (for that really is what it is called) is:
808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000,
that is, 2 46 × 3 20 × 5 9 × 7 6 × 11 2 × 13 3 × 17 × 19 × 23 × 29 × 31 × 41 × 47 × 59 × 71.*
*This integer is approximately 8.08 × 10 53, meaning that the Monster has more elements than there are atoms on planet Earth, whose number is estimated at 1.33 × 10 50.*
*This group is the largest of the sporadic groups (see the article "The classification of finite simple groups"). What is remarkable, as with many of these groups, is that its existence was conjectured long before it was constructed. In 1973, two mathematicians independently predicted its existence: Bernd Fischer from Germany and Robert Griess from the United States.*
The properties expected of such a group made its existence necessary. But it was not until 1980 that Griess constructed it as a group of special rotations in a space of 196,883 dimensions! This number is no coincidence: it is the product of the three largest prime factors of the Monster’s order (196,883 = 47 × 59 × 71).
