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
Examples
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.
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
- 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
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