A225933 Number of conjugacy classes in adjoint Chevalley group E_6(q) as q runs through the prime powers.
180, 1269, 5940, 20454, 140470, 304548, 605685, 1965462, 5261278, 17967252, 25736406, 49799782, 155060070, 254724622, 402876885, 616803846, 918048406, 1109465220, 2638932670, 4871761782, 6475385158, 11018543046, 14135549422, 22598655270, 42920128086
Offset: 1
Keywords
Links
- Eric M. Schmidt, Table of n, a(n) for n = 1..1000
- Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.
Programs
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Sage
def A225933(q) : return q^6 + q^5 + 2*q^4 + 2*q^3 + [9*q^2 + 9*q + 22, 6*q^2 + 4*q + 4, 7*q^2 + 5*q + 3, 8*q^2 + 8*q + 20, 7*q^2 + 5*q + 4][q%6-1]
Formula
Let q be the n-th prime power.
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 9q^2 + 9q + 22 if q == 1 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 6q^2 + 4q + 4 if q == 2 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 7q^2 + 5q + 3 if q == 3 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 8q^2 + 8q + 20 if q == 4 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 7q^2 + 5q + 4 if q == 5 (mod 6).