A003837 Order of (usually) simple Chevalley group D_n (3).

1, 144, 6065280, 4952179814400, 1289512799941305139200, 6762844700608770238252960972800, 11470635634813395742481912276441576767488000, 393736985584514548835738283681336315795223487793070080000

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

• Index entries for sequences related to groups.

Crossrefs

Cf. A003830, A003838, A003839, A003840.

Programs

Mathematica

d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}] / GCD[4, q^n-1]; Table[d[3, n], {n, 1, 8}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = d(3,n) where d(q,n) = D(q,n) / gcd(4, q^n-1) and D(q,n) as defined in A003830. - Sean A. Irvine, Sep 17 2015

Extensions

Fixed offset, one more term, and formula from Sean A. Irvine, Sep 17 2015