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Order of simple Chevalley group A_5(q), q = prime power.
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%I #19 Jun 14 2024 22:31:08

%S 20158709760,21032402889738240,361310134959341568000,

%T 1383059427750000000000000,61637759336805268655956377600,

%U 39841906041871272087686291128320,1234219157861100568481165377536000,1392357762553459444742198951136000000,161092184393918097496815608751014338560

%N Order of simple Chevalley group A_5(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),5) 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[#, 5] & /@ Select[Range[2, 13], PrimePowerQ] (* _Michael De Vlieger_, Sep 18 2015 *)

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E a(8)-a(9) from _Michael De Vlieger_, Sep 18 2015