A073043 Number of nonisomorphic (finite) groups with n conjugacy classes.

1, 1, 2, 4, 8, 8, 12, 21, 26, 37, 35, 51, 53, 93

Offset

1,3

References

E. K. Annavaddar, Determination of the Finite Groups Having Eight Conjugacy Classes. Ph.D. Diss., Arizona State Univ., 1971.

I. M. Isaacs, Algebra, Brooks/Cole, 1994; pp. 48-49 (for n = 4).

T. Y. Lam, Exercises in Classical Ring Theory, Springer, 1995; pp. 92-93 (for n=1,2,3).

A. Vera-López and J. Vera-López, Classification of finite groups according to the number of conjugacy classes, Israel J. Math. 51 (1985), 305-338.

A. Vera-López and J. Vera-López, Classification of finite groups according to the number of conjugacy classes II, Israel J. Math. 56 (1986), 188-221.

A. Vera-López and J. Sangroniz, The finite groups with thirteen and fourteen conjugacy classes, Math. Nachr. 280 (2007), No. 5-6, 676-694.

Links

Table of n, a(n) for n=1..14.

LMFDB, Abstract group search results

J. Poland, Finite groups with a given number of conjugate classes<, Canad. J. Math. 20 1968 456-464 (for n <= 7).

SmallClassNr, github repository

J. Sondow and K. MacMillan, Primary pseudoperfect numbers, arithmetic progressions, and the Erdős-Moser equation, Amer. Math. Monthly, 124 (2017) 232-240 (see page 232); arXiv:math/1812.06566 [math.NT], 2018.

Antonio Vera Lopez and Juan Vera Lopez, Classification of finite groups according to the number of conjugacy classes, Israel Journal of Mathematics, 51 (1985), No. 4.

Index entries for sequences related to groups

Formula

Equals A003061 + A000688.

Example

n=1: C_1; n=2: C_2; n=3: A_3 or S_3; n=4: C_2 X C_2, C_4, A_4, D_10.

Crossrefs

Cf. A109230, A003061, A002319, A006379, A000688.

Sequence in context: A260514 A123263 A008218 * A083542 A181533 A263981

Adjacent sequences: A073040 A073041 A073042 * A073044 A073045 A073046

Keyword

nonn,nice,more,hard

Author

N. J. A. Sloane, Aug 30 2002

Extensions

Corrected and extended by A. S. Muktibodh (amukti2000(AT)yahoo.com), Nov 07 2006

a(10), a(12) corrected and a(13)-a(14) added by Benjamin Sambale, Jun 08 2024

a(14) corrected by Sean A. Irvine, Dec 31 2024

Status

approved