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A000679 Number of groups of order 2^n.
(Formerly M1470 N0581)
22
1, 1, 2, 5, 14, 51, 267, 2328, 56092, 10494213, 49487367289 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
James Gleick, Faster, Vintage Books, NY, 2000 (see pp. 259-261).
M. Hall, Jr. and J. K. Senior, The Groups of Order 2^n (n <= 6). Macmillan, NY, 1964.
Newman, M. F. (1990). Groups of prime-power order. In Groups—Canberra 1989 (pp. 49-62). Springer, Berlin, Heidelberg. See Table 1.
Newman, M. F. and O'Brien, E. A.; A CAYLEY library for the groups of order dividing 128. Group theory (Singapore, 1987), 437-442, de Gruyter, Berlin-New York, 1989.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Hans Ulrich Besche and Bettina Eick, Construction of finite groups, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 387-404.
Hans Ulrich Besche and Bettina Eick, The groups of order at most 1000 except 512 and 768, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 405-413.
Hans Ulrich Besche, Bettina Eick and E. A. O'Brien, The groups of order at most 2000, Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 1-4.
David Burrell, On the number of groups of order 1024, Communications in Algebra, 2021, 1-3.
Hans Ulrich Besche, The Small Groups library
Bettina Eick and E. A. O'Brien, Enumerating p-groups. Group theory. J. Austral. Math. Soc. Ser. A 67 (1999), no. 2, 191-205.
R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
Rodney James and John Cannon, Computation of isomorphism classes of p-groups, Mathematics of Computation 23.105 (1969): 135-140.
R. James, M. F. Newman, and E. A. O'Brien, The Groups of Order 128, J. Algebra 129, 136-158, 1990.
G. A. Miller, Determination of all the groups of order 64, Amer. J. Math., 52 (1930), 617-634.
E. A. O'Brien, The Groups of Order 256 J. Algebra 143, 219-235, 1991.
E. Rodemich, The groups of order 128, J. Algebra 67 (1980), no. 1, 129-142.
Eric Weisstein's World of Mathematics, Finite Group
M. Wild, The groups of order 16 made easy, Amer. Math. Monthly, 112 (No. 1, 2005), 20-31.
FORMULA
a(n) = 2^((2/27)n^3 + O(n^(8/3))).
EXAMPLE
G.f. = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 51*x^5 + 267*x^6 + 2328*x^7 + ...
MAPLE
seq(GroupTheory:--NumGroups(2^n), n=0..10); # Robert Israel, Oct 15 2017
MATHEMATICA
Join[{1}, FiniteGroupCount[2^Range[10]]] (* Vincenzo Librandi, Mar 28 2018 *)
PROG
(GAP) A000679 := List([0..8], n -> NumberSmallGroups(2^n)); # Muniru A Asiru, Oct 15 2017
CROSSREFS
Sequence in context: A049338 A306892 A115275 * A266932 A243787 A275825
KEYWORD
nonn,hard,more,nice
AUTHOR
EXTENSIONS
a(9) and a(10) found by Eamonn O'Brien
a(10) corrected by David Burrell, Jun 06 2022
STATUS
approved

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Last modified February 28 17:13 EST 2024. Contains 370400 sequences. (Running on oeis4.)