A225934 Number of conjugacy classes in simply connected twisted Chevalley group 2E6(q) as q runs through the prime powers.
346, 1389, 6102, 21182, 141262, 306574, 607533, 1969886, 5266030, 17975982, 25750142, 49814254, 155091326, 254757166, 402919341, 616863422, 918109966, 1109543806, 2639036782, 4871920766, 6475547950, 11018778302, 14135789614, 22598987966, 42920581982
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 A225934(q) : return q^6 + q^5 + 2*q^4 + 4*q^3 + [11*q^2 + 11*q + 16, 18*q^2 + 26*q + 62, 11*q^2 + 11*q + 15, 10*q^2 + 10*q + 14, 19*q^2 + 27*q + 72][q%6-1]
Formula
Let q be the n-th prime power.
a(n) = q^6 + q^5 + 2q^4 + 11q^2 + 11q + 16 if q == (1 mod 6).
a(n) = q^6 + q^5 + 2q^4 + 18q^2 + 26q + 62 if q == (2 mod 6).
a(n) = q^6 + q^5 + 2q^4 + 11q^2 + 11q + 15 if q == (3 mod 6).
a(n) = q^6 + q^5 + 2q^4 + 10q^2 + 10q + 14 if q == (4 mod 6).
a(n) = q^6 + q^5 + 2q^4 + 19q^2 + 27q + 72 if q == (5 mod 6).