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

1,1

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.

Sequence in context: A114200 A229567 A069074 * A059775 A372497 A052762

Adjacent sequences: A360386 A360387 A360388 * A360390 A360391 A360392

Keyword

nonn

Author

Hal M. Switkay, Feb 05 2023

Status

approved