A225928 -id:A225928 - cp's OEIS frontend

A225938 Number of conjugacy classes in Chevalley group E_8(q) as q runs through the prime powers (A246655).

1156, 12825, 97154, 519071, 6906102, 19543486, 49150839, 238045722, 889575240, 4600759094, 7439557452, 17980383618, 82034207430, 159213167411, 293713437009, 518754968088, 882274298862, 1136129443366, 3612770425152, 8189556710532, 11973138177210, 24340206797502

Offset: 1

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.
Index entries for sequences related to groups

Cf. A188161, A224790, A225928-A225937.

A225938 := proc(n)
    local q ;
    q := A246655(n) ;
    if modp(q,2) = 0 then
        q^8 + q^7 + 2*q^6 + 3*q^5 +  9*q^4 + 14*q^3 + 32*q^2 + 47*q +  70;
    elif modp(q,3) = 0 then
        q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 39*q^2 + 65*q + 102 ;
    elif modp(q,5) = 0 then
        q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 111 ;
    else
        q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 112 ;
    end if;
end proc: # R. J. Mathar, Jan 09 2017

qmax = 100;
Reap[For[q = 2, q < qmax, q++, If[PrimePowerQ[q], cc = q^8 + q^7 + 2 q^6 + 3 q^5 + Which[Mod[q, 2] == 0, 9 q^4 + 14 q^3 + 32 q^2 + 47 q + 70, Mod[q, 3] == 0, 10 q^4 + 16 q^3 + 39 q^2 + 65 q + 102, Mod[q, 5] == 0, 10 q^4 + 16 q^3 + 40 q^2 + 67 q + 111, True, 10 q^4 + 16 q^3 + 40 q^2 + 67 q + 112]; Sow[cc]]]][[2, 1]] (* Jean-François Alcover, Mar 24 2020 *)

def A225938(q) : return q^8 + q^7 + 2*q^6 + 3*q^5 + (9*q^4 + 14*q^3 + 32*q^2 + 47*q + 70 if q%2==0 else 10*q^4 + 16*q^3 + 39*q^2 + 65*q + 102 if q%3==0 else 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 111 if q%5==0 else 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 112)

Let q be the n-th prime power. Then a(n) is
q^8 + q^7 + 2q^6 + 3q^5 +  9q^4 + 14q^3 + 32q^2 + 47q +  70, q==0(mod 2);
q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 39q^2 + 65q + 102, q==0(mod 3);
q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 40q^2 + 67q + 111, q==0(mod 5);
q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 40q^2 + 67q + 112, otherwise.

A225929 Number of conjugacy classes in Chevalley group G_2(q) as q runs through the prime powers.

Original entry on oeis.org

16, 23, 32, 44, 72, 88, 107, 152, 204, 296, 332, 408, 584, 684, 791, 908, 1032, 1096, 1452, 1772, 1944, 2312, 2508, 2924, 3608, 3852, 4232, 4632, 5192, 5484, 6408, 6731, 7064, 8108, 9612, 10412, 10824, 11672, 12108, 13004, 14892, 15884, 16392, 16648, 17432

Offset: 1

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A188161, A224790, A225928 - A225938.

def A225929(q) : return q^2 + 2*q + (9 if q%6 in [1,5] else 8)

Let q be the n-th prime power. Then a(n) = q^2 + 2q + c, where c = 9 if q == 1, 5 (mod 6) and c = 8 otherwise.

A225937 Number of conjugacy classes in adjoint Chevalley group E_7(q) as q runs through the prime powers.

Original entry on oeis.org

531, 4569, 24553, 105644, 992834, 2447517, 5477205, 21674822, 68494004, 287617189, 437805224, 946620206, 3567305234, 6369359984, 10879403385, 17889596996, 28462405562, 35505127221, 97646355404, 199751157632, 278452165094, 517886829194, 692659723976

Offset: 1

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A188161, A224790, A225928 - A225938.

def A225937(q) : return q^7 + q^6 + 2*q^5 + (4*q^4 + 10*q^3 + 15*q^2 + 25*q + 21 if q%2==0 else 5*q^4 + 13*q^3 + 24*q^2 + 46*q + 57 if q%3==0 else 5*q^4 + 13*q^3 + 24*q^2 + 47*q + 59)

Let q be the n-th prime power. Then, a(n) is
q^7 + q^6 + 2q^5 + 4q^4 + 10q^3 + 15q^2 + 25q + 21 if q == 0 (mod 2);
q^7 + q^6 + 2q^5 + 5q^4 + 13q^3 + 24q^2 + 46q + 57 if q == 0 (mod 3);
q^7 + q^6 + 2q^5 + 5q^4 + 13q^3 + 24q^2 + 47q + 59 otherwise.

A225930 Number of conjugacy classes in twisted Chevalley group 3D4(q) as q runs through the prime powers.

Original entry on oeis.org

35, 126, 345, 786, 2806, 4685, 7386, 16110, 30946, 69909, 88746, 137566, 292566, 406906, 551886, 732546, 954310, 1082405, 1926226, 2896410, 3500206, 4985766, 5884906, 8042226, 12326286, 14076610, 17043525, 20456446, 25774710, 28792666, 39449446, 43584810, 48037086

Offset: 1

Eric M. Schmidt, May 21 2013

nonn

Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Eric M. Schmidt)
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A000961 (without 1), A188161, A224790, A225928-A225938.

Map[(#^2 + 1)*(# + 1)*# + 5 + Mod[#, 2] &, Select[Range[100], PrimePowerQ]] (* Paolo Xausa, Jan 16 2025 *)

apply(x->(x^4 + x^3 + x^2 + x + 5 + (x%2)), select(isprimepower, [1..100])) \\ Michel Marcus, Jan 16 2025

Let q be the n-th prime power. Then, a(n) = q^4 + q^3 + q^2 + q + c, where c = 5 if q is even and c = 6 if q is odd.

A225931 Number of conjugacy classes in Chevalley group F_4(q) as q runs through the prime powers.

Original entry on oeis.org

95, 273, 539, 1156, 3566, 5603, 8751, 18346, 34364, 75443, 95656, 146882, 308254, 426656, 576345, 762412, 990326, 1120595, 1985636, 2976016, 3591434, 5103526, 6017672, 8208724, 12553402, 14326796, 17326739, 20785106, 26163886, 29214704, 39981062, 44156775

Offset: 1

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A188161, A224790, A225928 - A225938.

def A225931(q) : return q^4 + 2*q^3 + (6*q^2 + 10*q + 19 if q%2==0 else 7*q^2 + 15*q + 30 if q%3==0 else 7*q^2 + 15*q + 31)

Let q be the n-th prime power.
a(n) = q^4 + 2q^3 + 6q^2 + 10q + 19 if q == 0 mod 2.
a(n) = q^4 + 2q^3 + 7q^2 + 15q + 30 if q == 0 mod 3.
a(n) = q^4 + 2q^3 + 7q^2 + 15q + 31 otherwise.

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

Original entry on oeis.org

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

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A188161, A224790, A225928 - A225938.

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]

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).

A225933 Number of conjugacy classes in adjoint Chevalley group E_6(q) as q runs through the prime powers.

Original entry on oeis.org

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

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A188161, A224790, A225928 - A225938.

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]

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).

A225934 Number of conjugacy classes in simply connected twisted Chevalley group 2E6(q) as q runs through the prime powers.

Original entry on oeis.org

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

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A188161, A224790, A225928 - A225938.

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]

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).

A225935 Number of conjugacy classes in adjoint twisted Chevalley group 2E6(q) as q runs through the prime powers.

Original entry on oeis.org

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

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A188161, A224790, A225928 - A225938.

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]

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).

A225936 Number of conjugacy classes in simply connected Chevalley group E_7(q) as q runs through the prime powers.

Original entry on oeis.org

531, 5052, 24553, 107833, 999759, 2447517, 5494392, 21711067, 68562129, 287617189, 437995549, 946912755, 3567919999, 6370211253, 10880553708, 17891119105, 28464383127, 35505127221, 97650322329, 199757104357, 278459342139, 517897029319, 692671751805

Offset: 1

Eric M. Schmidt, May 21 2013

nonn

Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.

Cf. A188161, A224790, A225928 - A225938.

def A225936(q) : return q^7 + q^6 + 2*q^5 + (4*q^4 + 10*q^3 + 15*q^2 + 25*q + 21 if q%2==0 else 7*q^4 + 17*q^3 + 35*q^2 + 70*q + 99 if q%3==0 else 7*q^4 + 17*q^3 + 35*q^2 + 71*q + 103)

Let q be the n-th prime power. Then, a(n) is
q^7 + q^6 + 2q^5 + 4q^4 + 10q^3 + 15q^2 + 25q + 21 if q == 0 (mod 2);
q^7 + q^6 + 2q^5 + 7q^4 + 17q^3 + 35q^2 + 70q + 99 if q == 0 (mod 3);
q^7 + q^6 + 2q^5 + 7q^4 + 17q^3 + 35q^2 + 71q + 103 otherwise.

cp's OEIS Frontend

A225938 Number of conjugacy classes in Chevalley group E_8(q) as q runs through the prime powers (A246655).

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Maple

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Sage

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A225929 Number of conjugacy classes in Chevalley group G_2(q) as q runs through the prime powers.

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Sage

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A225937 Number of conjugacy classes in adjoint Chevalley group E_7(q) as q runs through the prime powers.

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Sage

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A225930 Number of conjugacy classes in twisted Chevalley group 3D4(q) as q runs through the prime powers.

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Mathematica

PARI

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A225931 Number of conjugacy classes in Chevalley group F_4(q) as q runs through the prime powers.

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Sage

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

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Sage

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A225933 Number of conjugacy classes in adjoint Chevalley group E_6(q) as q runs through the prime powers.

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Sage

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A225934 Number of conjugacy classes in simply connected twisted Chevalley group 2E6(q) as q runs through the prime powers.

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Sage

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A225935 Number of conjugacy classes in adjoint twisted Chevalley group 2E6(q) as q runs through the prime powers.

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