A225935 Number of conjugacy classes in adjoint twisted Chevalley group 2E6(q) as q runs through the prime powers.
266, 1389, 6102, 20934, 141262, 306062, 607533, 1968990, 5266030, 17975982, 25748166, 49814254, 155087838, 254757166, 402919341, 616857990, 918109966, 1109537246, 2639036782, 4871910150, 6475547950, 11018764446, 14135789614, 22598970438, 42920560350
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 A225935(q) : return q^6 + q^5 + 2*q^4 + 4*q^3 + [11*q^2 + 11*q + 16, 12*q^2 + 14*q + 30, 11*q^2 + 11*q + 15, 10*q^2 + 10*q + 14, 13*q^2 + 15*q + 34][q%6-1]
Formula
Let q be the n-th prime power.
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 11q^2 + 11q + 16 if q == 1 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 12q^2 + 14q + 30 if q == 2 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 11q^2 + 11q + 15 if q == 3 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 10q^2 + 10q + 14 if q == 4 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 13q^2 + 15q + 34 if q == 5 (mod 6).