A340513 -id:A340513 - cp's OEIS frontend

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

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Bob Heffernan and Des MacHale, Feb 02 2021

nonn

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.

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

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

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

cp's OEIS Frontend

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

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