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

1,1

Comments

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

Links

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

Example

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

Crossrefs

Cf. A001034, A340518.

Sequence in context: A016532 A075080 A202561 * A373240 A133000 A386251

Adjacent sequences: A341290 A341291 A341292 * A341294 A341295 A341296

Keyword

nonn

Author

Bob Heffernan and Des MacHale, Feb 05 2021

Status

approved