A001228 Orders of sporadic simple groups.

7920, 95040, 175560, 443520, 604800, 10200960, 44352000, 50232960, 244823040, 898128000, 4030387200, 145926144000, 448345497600, 460815505920, 495766656000, 42305421312000, 64561751654400, 273030912000000, 51765179004000000, 90745943887872000, 4089470473293004800, 4157776806543360000, 86775571046077562880, 1255205709190661721292800, 4154781481226426191177580544000000, 808017424794512875886459904961710757005754368000000000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• nice
• full

Comments

Numbers of divisors: A174601(n) = A000005(a(n)); squarefree kernels: A174848(n) = A007947(a(n)). - Reinhard Zumkeller, Apr 02 2010

By historical convention, the Tits group is often excluded from the list of sporadic simple groups. It could be inserted as a(7) = 17971200 giving this sequence 27 rather than 26 elements. - Charles R Greathouse IV, Jul 09 2020

Examples

			The first term is 7920 because the order of the sporadic group M_{11} is 7920, the smallest order of any sporadic group.
		

References

• J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 296.
• Martin Gardner, "The Last Recreations", 1997, chap 9, p. 153.

Links

• David Madore, Table of sporadic simple groups.
• Grant Sanderson, Group theory and 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000, 3Blue1Brown video (2020)
• Eric Weisstein's World of Mathematics, Sporadic Group
• Index entries for sequences related to groups

Crossrefs

Cf. A001034, A005180.

Extensions

Entries checked by Pab Ter (pabrlos(AT)yahoo.com), May 29 2004