A340512 Order of a smallest group G with a conjugacy class of size n.

1, 6, 6, 12, 10, 24, 14, 24, 18, 40, 22, 48, 26, 56, 30, 48, 34, 72, 38, 60, 42, 88, 46, 96, 50, 104, 54, 84, 58, 120, 62, 96, 66, 136, 70, 144, 74, 152, 78, 160, 82, 168, 86, 176, 90, 184, 94, 192, 98, 150, 102, 156, 106, 216, 110, 168, 114, 232, 118, 240, 122, 248, 126, 192, 130

Offset

1,2

Comments

By Lagrange's theorem, a(n) is always a multiple of n, and it is likely this multiple is always 2, 3, or 4 for n>1.

Because of dihedral groups, a(2k+1) = 4k+2.

Links

Bob Heffernan, Table of n, a(n) for n = 1..191

Example

a(4) = 12 because the smallest finite group with a conjugacy class of size 4 has order 12 (A_4).

Crossrefs

Cf. A340513 for the number of groups of this order.

Sequence in context: A124508 A028317 A220435 * A338992 A055665 A168328

Adjacent sequences: A340509 A340510 A340511 * A340513 A340514 A340515

Keyword

nonn

Author

Bob Heffernan and Des MacHale, Feb 02 2021

Status

approved