A003830 Order of universal Chevalley group D_n (3).

2, 576, 12130560, 19808719257600, 2579025599882610278400, 27051378802435080953011843891200, 22941271269626791484963824552883153534976000, 1574947942338058195342953134725345263180893951172280320000

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

• Robert Israel, Table of n, a(n) for n = 1..32
• Robert Steinberg, Lectures on Chevalley Groups, Dept. of Mathematics, Yale University, 1967, pp. 130-131.
• Index entries for sequences related to groups.

Crossrefs

Cf. A003831, A003832, A003834, A003835, A003836, A132037.

Programs

Maple

f:= n -> 3^(n*(n-1))*(3^n-1)*mul(3^(2*k)-1,k=1..n-1):
map(f, [$1..10]); # Robert Israel, Sep 22 2015

Mathematica

f[m_, n_] := m^(n (n - 1)) (m^n - 1) Product[m^(2 k) - 1, {k, n - 1}];
f[3, #] & /@ Range@ 8 (* Michael De Vlieger, Sep 17 2015 *)

PARI

a(n,q=3) = q^(n*(n-1)) * (q^n-1) * prod(k=1,n-1,q^(2*k)-1); \\ Michel Marcus, Sep 17 2015

Formula

a(n) = D(3,n) where D(q,n) = q^(n*(n-1)) * (q^n-1) * Product_{k=1..n-1}(q^(2*k)-1). - Sean A. Irvine, Sep 17 2015

a(n) ~ c * 3^(n*(2*n-1)), where c = A132037. - Amiram Eldar, Jul 07 2025

Extensions

a(8) and formula from Sean A. Irvine, Sep 17 2015