A073043 - OEIS

%I #41 Jul 01 2024 14:34:18

%S 1,1,2,4,8,8,12,21,26,37,35,51,53,92

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

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

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

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

%D 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.

%D 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.

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

%H LMFDB, <a href="https://beta.lmfdb.org/Groups/Abstract/?number_conjugacy_classes=10">Abstract group search results</a>

%H J. Poland, <a href="http://dx.doi.org/10.4153/CJM-1968-042-9">Finite groups with a given number of conjugate classes<</a>, Canad. J. Math. 20 1968 456-464 (for n <= 7).

%H SmallClassNr, <a href="https://github.com/stertooy/SmallClassNr/tree/main">github repository</a>

%H J. Sondow and K. MacMillan, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.124.3.232">Primary pseudoperfect numbers, arithmetic progressions, and the Erdős-Moser equation</a>, Amer. Math. Monthly, 124 (2017) 232-240 (see page 232); <a href="http://arxiv.org/abs/1812.06566">arXiv:math/1812.06566 [math.NT]</a>, 2018.

%H Antonio Vera Lopez and Juan Vera Lopez, <a href="http://dx.doi.org/10.1007/BF02764723">Classification of finite groups according to the number of conjugacy classes</a>, Israel Journal of Mathematics, 51 (1985), No. 4.

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%F Equals A003061 + A000688.

%e 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.

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

%K nonn,nice,more,hard

%O 1,3

%A _N. J. A. Sloane_, Aug 30 2002

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

%E a(10), a(12) corrected and a(13)-a(14) added by _Benjamin Sambale_, Jun 08 2024