A003924 Order of universal Chevalley group B_n (7).

336, 276595200, 546914437209907200, 2596509480922336727312302080000, 29597339316082819652234687848790174733434880000, 810042101621990387485449491667484171676631766280916065845248000000

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. A003920, A003921, A003922, A003925, A003926.

Programs

Mathematica

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[7, n], {n, 1, 6}] (* Amiram Eldar, Jun 23 2025 *)

Formula

a(n) = B(7,n) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

a(n) ~ c * 7^(2*n^2+n), where c = Product_{k>=1} (1-1/49^k) = 0.979175347148... . - Amiram Eldar, Jul 09 2025

Extensions

a(6) from Sean A. Irvine, Sep 22 2015

Offset corrected by Amiram Eldar, Jun 23 2025