A066085 Orders of non-supersolvable groups.

12, 24, 36, 48, 56, 60, 72, 75, 80, 84, 96, 108, 112, 120, 132, 144, 150, 156, 160, 168, 180, 192, 196, 200, 204, 216, 224, 225, 228, 240, 252, 264, 276, 280, 288, 294, 300, 312, 320, 324, 336, 348, 351, 360, 363, 372, 375, 384, 392, 396, 400, 405, 408, 420

Offset

1,1

Comments

A finite group is supersolvable if it has a normal series with cyclic factors. Huppert showed that a finite group is supersolvable iff the index of any maximal subgroup is prime.

All multiples of non-supersolvable orders are non-supersolvable orders. - Des MacHale, Dec 22 2003

Links

Table of n, a(n) for n=1..54.

B. Huppert, Über das Produkt von paarweise vertauschbaren zyklischen Gruppen, Math. Z. 58 (1954).

Des MacHale and J. Manning, Converse Lagrange Theorem Orders and Supersolvable Orders, Journal of Integer Sequences, 2016, Vol. 19, #16.8.7.

Example

a(1)=12 is in the sequence since the alternating group on 4 elements is the smallest group which is not supersolvable.

Crossrefs

Cf. A000001, A066083, A340511.

For primitive terms see A340517.

Sequence in context: A059691 A097060 A336657 * A340511 A094529 A270571

Adjacent sequences: A066082 A066083 A066084 * A066086 A066087 A066088

Keyword

nonn

Author

Reiner Martin, Dec 29 2001

Extensions

More terms from Des MacHale, Dec 22 2003

Status

approved