A340512 - OEIS

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

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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.