A001228
Orders of sporadic simple groups.
Original entry on oeis.org
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
The first term is 7920 because the order of the sporadic group M_{11} is 7920, the smallest order of any sporadic group.
- 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.
- 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
Entries checked by Pab Ter (pabrlos(AT)yahoo.com), May 29 2004
A002267
The 15 supersingular primes: primes dividing order of Monster simple group.
Original entry on oeis.org
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71
Offset: 1
- 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].
- A. P. Ogg, Modular functions, in The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), pp. 521-532, Proc. Sympos. Pure Math., 37, Amer. Math. Soc., Providence, R.I., 1980.
- J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
- T. Gannon, Postcards from the edge, or Snapshots of the theory of generalised Moonshine, arXiv:math/0109067 [math.QA], 2001.
- Alan W. Reid, Arithmetic hyperbolic manifolds, slides of a talk, Cornell University, June 2014,
- G. K. Sankaran, A supersingular coincidence, arXiv:2009.11379 [math.NT], 2020.
- J. G. Thompson, Finite groups and modular functions, Bulletin of the London Mathematical Society 11.3 (1979): 347-351. See page 350.
- Eric Weisstein's World of Mathematics, Supersingular Prime
- Index entries for sequences related to groups
-
FactorInteger[GroupOrder[MonsterGroupM[]]][[All, 1]] (* Jean-François Alcover, Oct 03 2016 *)
-
A002267=vecextract(primes(20),612351) \\ bitmask 2^20-1-213<<11: remove primes # 12, 14, 16, 18 and 19. - M. F. Hasler, Nov 10 2017
A321224
Sporadic numbers: n is defined to be sporadic if the set of groups G not in {A_n, S_n} and having a core-free maximal subgroup of index n is nonempty and contains only sporadic simple groups.
Original entry on oeis.org
266, 506, 759, 1045, 1288, 1463, 3795
Offset: 1
- The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.9.3, 2018. gap-system.org.
-
IsSporadic:=function(G)
if not IsSimple(G) then
return false;
else
return IsomorphismTypeInfoFiniteSimpleGroup(G).series="Spor";
fi;
end;;
SporadicNumbers:=function(b1,b2)
local L,i,n,a,j,G;
L:=[];
for i in [b1..b2] do
n:=NrPrimitiveGroups(i);
if n>2 then
a:=0;
for j in [1..n] do
G:=PrimitiveGroup(i,j);
if not G=SymmetricGroup(i) and not G=AlternatingGroup(i) and not IsSporadic(G) then
a:=1;
break;
fi;
od;
if a=0 then
Add(L,i);
fi;
fi;
od;
return L;
end;;
SporadicNumbers(1,4095);
# gives: [ 266, 506, 759, 1045, 1288, 1463, 3795 ]
Showing 1-3 of 3 results.
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