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

1, 1, 2, 4, 8, 8, 12, 21, 26, 38, 35, 32

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).

Links

Table of n, a(n) for n=1..12.

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

Benjamin Sambale, On a theorem of Ledermann and Neumann, arXiv:1909.13220 [math.GR], 2019.

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

Status

approved