A003841 Order of universal Chevalley group D_2(q), q = prime power.

36, 576, 3600, 14400, 112896, 254016, 518400, 1742400, 4769856, 16646400, 23970816, 46785600, 147476736, 243360000, 386358336, 593409600, 885657600, 1071645696, 2561979456, 4744454400, 6314527296

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers given so far divided by 36 (except the first) are all members of A014796. - Ralf Stephan, Feb 07 2004

Is a(n) = A007531( A000961(n)+1 )^2? - Ralf Stephan, Feb 08 2004 [Answer: Yes. This is equivalent to the first formula below. - Amiram Eldar, Jun 24 2025]

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, A003801, A003830, A003843, A003844, A003845, A003846, A003847, A007531, A014796.

Programs

Mathematica

d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[q, 2], {q, Select[Range[50], PrimePowerQ]}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(A000961(n+1),2) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015