A003850 Order of simple Chevalley group D_4(q), q = prime power.

174182400, 4952179814400, 67010895544320000, 8911539000000000000, 112554991177798901760000, 19031213036231093492121600, 129182006871144805294080000, 35749625435272978955066880000

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. A000961, A003808, A003837, A003848, A003851, A003852, A003853, A003854.

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[q, 4], {q, Select[Range[20], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = d(A000961(n+1),4) where d(q,n) is defined in A003837. - Sean A. Irvine, Sep 17 2015