A045515 Number of conjugacy classes of elements of order n in 2.E_7(C).

0, 1, 3, 5, 11, 21, 35, 63, 97, 153, 229, 351, 474, 714, 957, 1329, 1760, 2430, 3061, 4159, 5176, 6774, 8413, 10879, 13075, 16774, 20116, 25107, 29897, 37144, 43329, 53503, 62216, 75309, 87370, 105163, 120143, 144209, 164317, 194184, 220622, 260129, 292134

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Arjeh M. Cohen and Robert L. Griess Jr., On finite simple subgroups of the complex Lie group of type E_8, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), 367-405, Proc. Sympos. Pure Math., 47, Part 2, Amer. Math. Soc., Providence, RI, 1987.

Crossrefs

Cf. A045514.

Formula

a(n) = Sum_{d|n} mu(n/d) * [x^d*z^0] b(x,z), n > 0, where b(x,z) = 1 / ((1-x) * (1-x^2)^2 * (1-x^3) * (1-x^4) * (1-z*x) * (1-z*x^2) * (1-z*x^3)) with z^2=1. - Sean A. Irvine, Mar 13 2021

Extensions

More terms from Sean A. Irvine, Mar 13 2021