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

Author

Jan Kristian Haugland, Aug 06 2021

Keywords

• nonn

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.

Examples

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

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.

Crossrefs

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