A225932 Number of conjugacy classes in simply connected Chevalley group E_6(q) as q runs through the prime powers.

180, 1269, 6116, 20454, 140886, 304548, 605685, 1965462, 5262486, 17969012, 25736406, 49802214, 155060070, 254728710, 402876885, 616803846, 918054582, 1109465220, 2638941366, 4871761782, 6475396806, 11018543046, 14135564454, 22598655270, 42920128086

Offset

1,1

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.

Formula

Let q be the n-th prime power.

a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 15q^2 + 21q + 60 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 + 14q^2 + 20q + 52 if q == 4 (mod 6).

a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 7q^2 + 5q + 4 if q == 5 (mod 6).

Prog

(Sage) def A225932(q) : return q^6 + q^5 + 2*q^4 + 2*q^3 + [15*q^2 + 21*q + 60, 6*q^2 + 4*q + 4, 7*q^2 + 5*q + 3, 14*q^2 + 20*q + 52, 7*q^2 + 5*q + 4][q%6-1]

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Sequence in context: A251255 A251204 A225933 * A081380 A115184 A154672

Adjacent sequences: A225929 A225930 A225931 * A225933 A225934 A225935

Keyword

nonn

Author

Eric M. Schmidt, May 21 2013

Status

approved