A003932 -id:A003932 - cp's OEIS frontend

A003931 Order of universal Chevalley group B_2(q), q = prime power.

720, 51840, 979200, 9360000, 276595200, 1056706560, 3443212800, 25721308800, 137037962880, 1095199948800, 2008994088960, 6114035779200, 41348052472320, 95214600000000, 205608315669120, 420206392771200, 818774509363200, 1124799322521600, 4805069329111680, 13414669637644800

Offset: 1

N. J. A. Sloane

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Robin Visser, Table of n, a(n) for n = 1..10000
Index entries for sequences related to groups.

Cf. A000961, A003920, A003932, A003933, A003934, A003935, A003936, A003937.

[#SymplecticGroup(4,q) : q in [2..50] | IsPrimePower(q)];  // Robin Visser, Aug 06 2023

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[q, 2], {q, Select[Range[50], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

a(n) = B(A000961(n + 1), 2) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

More terms from Robin Visser, Aug 06 2023

A003937 Order of universal Chevalley group B_8(q), q = prime power.

Original entry on oeis.org

59980383884075203672726385914533642240000, 67806677896800158816511248022114282163091244291914415200010240000, 7084630453281025440882493116981310890142026281589018852388680249504694272000000000

Offset: 1

N. J. A. Sloane

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Sean A. Irvine, Table of n, a(n) for n = 1..10
Index entries for sequences related to groups.

Cf. A000961, A003920, A003931, A003932, A003933, A003934, A003935, A003936.

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[q, 8], {q, Select[Range[10], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

a(n) = B(A000961(n + 1), 8) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

a(3) from Sean A. Irvine, Sep 22 2015

A003933 Order of universal Chevalley group B_4(q), q = prime power.

Original entry on oeis.org

47377612800, 131569513308979200, 4408780839651901440000, 13946558535000000000000000, 2596509480922336727312302080000, 319368723699461283992462111539200, 22246837484597339860644476682240000

Offset: 1

N. J. A. Sloane

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Index entries for sequences related to groups.

Cf. A000961, A003920, A003931, A003932, A003934, A003935, A003936, A003937.

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[q, 4], {q, Select[Range[10], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

a(n) = B(A000961(n + 1), 4) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

a(7) from Sean A. Irvine, Sep 22 2015

A003934 Order of universal Chevalley group B_5(q), q = prime power.

Original entry on oeis.org

24815256521932800, 152915585868239728626892800, 1211875293642881119668928512000000, 266009466302345390625000000000000000000, 29597339316082819652234687848790174733434880000, 46025883638628966977843321053405598530493271244800

Offset: 1

N. J. A. Sloane

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Index entries for sequences related to groups.

Cf. A000961, A003920, A003931, A003932, A003933, A003935, A003936, A003937.

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[q, 5], {q, Select[Range[10], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

a(n) = B(A000961(n + 1), 5) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

a(5)-a(6) from Sean A. Irvine, Sep 22 2015

A003935 Order of universal Chevalley group B_6(q), q = prime power.

Original entry on oeis.org

208114637736580743168000, 14395932257291877030764312963579904000, 85278137430613949474674174708223909560320000000, 3171079936179764469273010253906250000000000000000000000

Offset: 1

N. J. A. Sloane

H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.

Index entries for sequences related to groups.

Cf. A000961, A003920, A003931, A003932, A003933, A003934, A003936, A003937.

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[q, 6], {q, Select[Range[10], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

a(n) = B(A000961(n + 1), 6) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

A003936 Order of universal Chevalley group B_7(q), q = prime power.

Original entry on oeis.org

27930968965434591767112450048000, 109777561863482259035023554842176139436811616256000, 1536234346098532793158147848149455029037710018156586598400000000, 23626386639924457166562360847447514533996582031250000000000000000000000000

Offset: 1

N. J. A. Sloane

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Index entries for sequences related to groups.

Cf. A000961, A003920, A003931, A003932, A003933, A003934, A003935, A003937.

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[q, 7], {q, Select[Range[10], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

a(n) = B(A000961(n + 1), 7) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

a(3)-a(4) from Sean A. Irvine, Sep 22 2015

A364783 Order of the symplectic group of 6 X 6 matrices over Z_n.

Original entry on oeis.org

1, 1451520, 9170703360, 3044058071040, 457002000000000, 13311459341107200, 546914437209907200, 6383852471797678080, 95928796265538862080, 663347543040000000000, 7338585441586912128000, 27916153580121646694400, 245593958671812227742720, 793857243898924498944000

Offset: 1

Robin Visser, Aug 07 2023

Let M be any fixed nonsingular skew-symmetric 6 X 6 matrix over the integers mod n. Then a(n) is the number of invertible 6 X 6 matrices A over the integers mod n such that A^T * M * A = M, where A^T denotes the transpose of A.

E. Artin, Geometric Algebra, Wiley Classics Library. John Wiley & Sons, Inc., New York, 1988. Reprint of the 1957 original, A Wiley-Interscience Publication.
Larry C. Grove, Classical Groups and Geometric Algebra, Grad. Stud. Math., 39 American Mathematical Society, Providence, RI, 2002. x+169 pp.

Cf. A364771, A364782.

f[p_, e_] := p^(21*e - 12)*(p^2 - 1)*(p^4 - 1)*(p^6 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 15] (* Amiram Eldar, Aug 08 2023 *)

def a(n):
    return product([p^(21*n.valuation(p) - 12)*(p^2 - 1)*(p^4 - 1)*(p^6 - 1)
        for p in n.prime_factors()])

a(n) = Product_{primes p dividing n} p^(21*v_p(n) - 12)*(p^2 - 1)*(p^4 - 1)*(p^6 - 1), where v_p(n) is the largest power k such that p^k divides n.
For primes p : a(p) = A003932(n), where A246655(n) = p.
Sum_{k=1..n} a(k) ~ c * n^22 / 22, where c = Product_{p prime} (1 - 1/p^3 - 1/p^5 + 1/p^9 + 1/p^11 - 1/p^13) = 0.8006965549... . - Amiram Eldar, Aug 08 2023

cp's OEIS Frontend

A003931 Order of universal Chevalley group B_2(q), q = prime power.

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A003937 Order of universal Chevalley group B_8(q), q = prime power.

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A003933 Order of universal Chevalley group B_4(q), q = prime power.

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A003934 Order of universal Chevalley group B_5(q), q = prime power.

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A003935 Order of universal Chevalley group B_6(q), q = prime power.

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A003936 Order of universal Chevalley group B_7(q), q = prime power.

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A364783 Order of the symplectic group of 6 X 6 matrices over Z_n.

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