A001228 - OEIS

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

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OFFSET

1,1

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

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

Table of n, a(n) for n=1..26.

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

EXAMPLE

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

CROSSREFS

Cf. A001034, A005180.