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

60, 6, 12, 8, 55, 18, 56, 16, 27, 30, 253, 24, 351, 42, 60, 32, 1020, 54, 1140, 40, 84, 66, 1081, 48, 125, 78, 81, 56, 1711, 90, 992, 64, 132, 102, 280, 72, 2220, 114, 156, 80, 2460, 126, 2580, 88, 135, 138, 2820, 96, 343, 150, 204, 104, 3180, 162, 605, 112, 228, 174, 3540, 120, 3660

Offset: 1

Author

Bob Heffernan and Des MacHale, Feb 05 2021

Keywords

• nonn

Comments

By Lagrange's Theorem a(n) is a multiple of n.

Examples

			Examples for small n:
n a(n) group
1  60  A5
2  6  S3
3  12  A4
4  8  D8
5  55  C11 : C5
6  18  C3 x S3
7  56  (C2 x C2 x C2) : C7
8  16  (C4 x C2) : C2
9  27  (C3 x C3) : C3
10  30  C5 x S3
11  253  C23 : C11
12  24  C3 x D8
		

Links

• Bob Hefferman, Table of n, a(n) for n = 1..255

Crossrefs

Cf. A001034, A340518.