A360389 - OEIS

%I #11 Feb 19 2023 12:18:00

%S 24,120,360,720,2520,5040,7920,20160,40320,95040,181440,362880,

%T 1814400,3628800,10200960,19958400,39916800,239500800,244823040,

%U 479001600,3113510400,6227020800,43589145600,87178291200,653837184000,1307674368000

%N The orders of 4-transitive permutation groups.

%C The 4-transitive permutation groups are either: 1) symmetric groups of degree k for k >= 4, with order k! = A000142(k); 2) alternating groups of degree k for k >= 6, with order k!/2 = A001710(k); or 3) Mathieu groups of degree 11, 12, 23, or 24, with order A001228(k), where k = 1, 2, 6, or 9 respectively.

%H Hal M. Switkay, <a href="/A360389/b360389.txt">Table of n, a(n) for n = 1..44</a>

%H Shreeram S. Abhyankar, <a href="https://doi.org/10.1090/S0273-0979-1992-00270-7">Galois Theory on the Line in Non-Zero Characteristic</a>, Bulletin of the AMS, 27 (1992), 68-133.

%Y Cf. A000142, A001228, A001710.

%K nonn

%O 1,1

%A _Hal M. Switkay_, Feb 05 2023