cp's OEIS Frontend

A341293 Smallest order of a non-abelian group with a commutator subgroup of index n.

%I A341293 #27 Feb 11 2021 23:27:09
%S A341293 60,6,12,8,55,18,56,16,27,30,253,24,351,42,60,32,1020,54,1140,40,84,
%T A341293 66,1081,48,125,78,81,56,1711,90,992,64,132,102,280,72,2220,114,156,
%U A341293 80,2460,126,2580,88,135,138,2820,96,343,150,204,104,3180,162,605,112,228,174,3540,120,3660
%N A341293 Smallest order of a non-abelian group with a commutator subgroup of index n.
%C A341293 By Lagrange's Theorem a(n) is a multiple of n.
%H A341293 Bob Hefferman, <a href="/A341293/b341293.txt">Table of n, a(n) for n = 1..255</a>
%e A341293 Examples for small n:
%e A341293 n a(n) group
%e A341293 1  60  A5
%e A341293 2  6  S3
%e A341293 3  12  A4
%e A341293 4  8  D8
%e A341293 5  55  C11 : C5
%e A341293 6  18  C3 x S3
%e A341293 7  56  (C2 x C2 x C2) : C7
%e A341293 8  16  (C4 x C2) : C2
%e A341293 9  27  (C3 x C3) : C3
%e A341293 10  30  C5 x S3
%e A341293 11  253  C23 : C11
%e A341293 12  24  C3 x D8
%Y A341293 Cf. A001034, A340518.
%K A341293 nonn
%O A341293 1,1
%A A341293 _Bob Heffernan_ and _Des MacHale_, Feb 05 2021