A005180 Orders of simple groups. (Formerly M0651)

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 60, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 168, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset

1,2

Comments

Officially the group of order 1 is not considered to be simple - see for example Rotman, Group Theory.

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].

M. Hall, Jr., A search for simple groups of order less than one million, pp. 137-168 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Michael Aschbacher, Review of "Classification of the finite simple groups, No. 2" by D. Gorenstein, R. Lyons, and R. Solomon, Bull. Amer. Math. Soc. 34 (1997), 39-41.

Rashid Barket, Enrico Grimaldi, Yacoub Hendi, Edward Hirst, Adam Onus, and Harmeet Singh, Learning the Graphical Nature of Symmetries, arXiv:2607.12026 [stat.ML], 2026. See p. 8.

Craig Cato, The orders of the known simple groups as far as one trillion, Math. Comp. 31 (1977), 574-577.

Dept. of Pure Math., Univ. Sheffield, The Classification of Finite Simple Groups, 1999.

Daniel Gorenstein, Richard Lyons, and Ronald Solomon, The Classification of the Finite Simple Groups, AMS Books Online, Providence RI, 1994. (Bookstore link).

Daniel Gorenstein, Richard Lyons, and Ronald Solomon, The Classification of the Finite Simple Groups, Number 2, AMS Books Online, Providence RI, 1996. (Bookstore link).

Richard K. Guy and N. J. A. Sloane, Correspondence, 1988.

Ronald Solomon, A Brief History Of The Classification Of The Finite Simple Groups, Bull. Amer. Math. Soc. 38 (2001), 315-352.

Index entries for sequences related to groups

Mathematica

(* Recomputation from A001034. *)
maxOrder = 7789;
A001034 = Select[Cases[Import["https://oeis.org/A001034/b001034.txt", "Table"], {_, _}][[All, 2]], # <= maxOrder&];
Union[{1}, Prime[Range[PrimePi[maxOrder]]], A001034] (* Jean-François Alcover, Aug 19 2019 *)

Crossrefs

Cf. A000001, A001228. Union of {1}, A000040 and A001034.

Sequence in context: A054403 A092579 A171028 * A118848 A390097 A316903

Adjacent sequences: A005177 A005178 A005179 * A005181 A005182 A005183

Keyword

nonn,nice,easy,changed

Author

N. J. A. Sloane, R. K. Guy

Status

approved