A360389 The orders of 4-transitive permutation groups.

24, 120, 360, 720, 2520, 5040, 7920, 20160, 40320, 95040, 181440, 362880, 1814400, 3628800, 10200960, 19958400, 39916800, 239500800, 244823040, 479001600, 3113510400, 6227020800, 43589145600, 87178291200, 653837184000, 1307674368000

Offset: 1

Author

Hal M. Switkay, Feb 05 2023

Keywords

• nonn

Comments

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.

Links

• Hal M. Switkay, Table of n, a(n) for n = 1..44
• Shreeram S. Abhyankar, Galois Theory on the Line in Non-Zero Characteristic, Bulletin of the AMS, 27 (1992), 68-133.

Crossrefs

Cf. A000142, A001228, A001710.