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Order of simple Chevalley group A_2(q), q = prime power.
2

%I #19 Jun 14 2024 22:31:08

%S 168,5616,20160,372000,1876896,16482816,42456960,212427600,270178272,

%T 1425715200,6950204928,5644682640,78156525216,50778000000,

%U 282027786768,499631102880,283991644800,1098404364288

%N Order of simple Chevalley group A_2(q), q = prime power.

%D 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.

%D H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

%F a(n) = a(A000961(n+1),2) where a(q,n) is defined in A003793. - _Sean A. Irvine_, Sep 18 2015

%t f[m_, n_] := Block[{g, x, y}, g[x_, y_] := x^(y (y + 1)/2) Product[x^k - 1, {k, 2, y + 1}]; g[m, n]/GCD[n + 1, m - 1]]; f[#, 2] & /@ Select[Range[2, 36], PrimePowerQ] (* _Michael De Vlieger_, Sep 18 2015 *)

%Y Cf. A000961.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_