A124678 Number of conjugacy classes in PSL_2(p), p = prime(n).

3, 4, 5, 6, 8, 9, 11, 12, 14, 17, 18, 21, 23, 24, 26, 29, 32, 33, 36, 38, 39, 42, 44, 47, 51, 53, 54, 56, 57, 59, 66, 68, 71, 72, 77, 78, 81, 84, 86, 89, 92, 93, 98, 99, 101, 102, 108, 114, 116, 117, 119, 122, 123, 128, 131, 134, 137, 138, 141, 143, 144, 149, 156, 158

Offset: 1

Author

N. J. A. Sloane, Dec 25 2006

Keywords

• nonn

Comments

A great deal is known about the number of conjugacy classes in the classical linear groups. See for example Dornhoff, Section 38, or Green.

References

• Dornhoff, Larry, Group representation theory. Part A: Ordinary representation theory. Marcel Dekker, Inc., New York, 1971.

Links

• Robin Visser, Table of n, a(n) for n = 1..10000 (terms n = 1..270 from Klaus Brockhaus).
• J. A. Green, The characters of the finite general linear groups, Trans. Amer. Math. Soc., 80 (1955), 402-447.

Crossrefs

Cf. A000040, A000702, A006951, A124679, A124681.

Programs

Magma

[ NumberOfClasses(PSL(2,p)) : p in [2,3,5,7,11,13,17,19,23,29,31,37] ];

Formula

a(n) = (prime(n) + 5)/2 for all n > 1. - Robin Visser, Sep 24 2023

Extensions

More terms from Klaus Brockhaus, Dec 26 2006