A340512 - OEIS

%I #21 Feb 03 2021 01:09:35

%S 1,6,6,12,10,24,14,24,18,40,22,48,26,56,30,48,34,72,38,60,42,88,46,96,

%T 50,104,54,84,58,120,62,96,66,136,70,144,74,152,78,160,82,168,86,176,

%U 90,184,94,192,98,150,102,156,106,216,110,168,114,232,118,240,122,248,126,192,130

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

%C 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.

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

%H Bob Heffernan, <a href="/A340512/b340512.txt">Table of n, a(n) for n = 1..191</a>

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

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

%K nonn

%O 1,2

%A _Bob Heffernan_ and _Des MacHale_, Feb 02 2021