A003835 Order of universal Chevalley group D_n (8).

7, 254016, 34558531338240, 19031213036231093492121600, 42863636354909175368011800612065142374400, 395357821818670720302212111102866352228895870285434270515200

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, A003831, A003832, A003834, A003836.

Programs

Mathematica

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

Formula

a(n) = D(8,n) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015

a(n) ~ c * 8^(n*(2*n-1)), where c = Product_{k>=1} (1 - 1/8^(2*k)) = 0.984130860306... . - Amiram Eldar, Jul 08 2025