A003932 Order of universal Chevalley group B_3(q), q = prime power.

1451520, 9170703360, 4106059776000, 457002000000000, 546914437209907200, 9077005607176765440, 108051462804999168000, 7338585441586912128000, 245593958671812227742720, 19266960106724096212992000, 68852034247000426560552960, 712225595693024258315904000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• 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.

Links

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

Crossrefs

Cf. A000961, A003920, A003931, A003933, A003934, A003935, A003936, A003937.

Programs

Magma

[#SymplecticGroup(6, q) : q in [2..50] | IsPrimePower(q)];  // Robin Visser, Aug 07 2023

Mathematica

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[q, 3], {q, Select[Range[20], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = B(A000961(n + 1), 3) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

Extensions

More terms from Robin Visser, Aug 07 2023