A346848 - OEIS

%I #10 Aug 06 2021 08:09:39

%S 1,3,11,30,81,198,477,1089,2451,5358,11567,24537,51577,107205,221378,

%T 453900,926395,1882152,3812232,7699191,15518112,31220991,62733296,

%U 125911851,252516626,506082933,1013780968,2029989807,4063678159,8132877129,16274093175

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

%C 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.

%H Jan Kristian Haugland, <a href="/A346848/b346848.txt">Table of n, a(n) for n = 0..1000</a>

%H G. E. Wall, <a href="https://doi.org/10.1017/S1446788700027622">On the conjugacy classes in the unitary, symplectic and orthogonal groups</a>, J. Aust. Math. Soc., 3 (1963), 1-62.

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

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

%K nonn

%O 0,2

%A _Jan Kristian Haugland_, Aug 06 2021