A346848 Number of conjugacy classes of the symplectic group Sp(2n, 2) over the field with 2 elements

1, 3, 11, 30, 81, 198, 477, 1089, 2451, 5358, 11567, 24537, 51577, 107205, 221378, 453900, 926395, 1882152, 3812232, 7699191, 15518112, 31220991, 62733296, 125911851, 252516626, 506082933, 1013780968, 2029989807, 4063678159, 8132877129, 16274093175

Offset

0,2

Comments

Sp(2n, 2) is isomorphic to the orthogonal group O(2n+1, 2) over the field with 2 elements, and is a simple and complete group for n>=3.

Links

Jan Kristian Haugland, Table of n, a(n) for n = 0..1000

G. E. Wall, On the conjugacy classes in the unitary, symplectic and orthogonal groups, J. Aust. Math. Soc., 3 (1963), 1-62.

Example

a(2)=11, and Sp(4, 2) is isomorphic to the symmetric group S_6 which has 11 conjugacy classes.

Crossrefs

Discrete convolution of A070933 and A098613. A003923 gives the order of the group.

Sequence in context: A295144 A167375 A098150 * A372480 A330148 A085376

Adjacent sequences: A346845 A346846 A346847 * A346849 A346850 A346851

Keyword

nonn

Author

Jan Kristian Haugland, Aug 06 2021

Status

approved