A389994 Second smallest order m > 0 for which there are n nonisomorphic finite groups of order m, or 0 if no such order exists.

2, 6, 363, 30, 12, 78, 605, 690, 532, 132, 364, 152, 60, 36, 54, 126, 3267, 342, 5145, 1220, 3249, 9075, 1014, 798, 8450, 3450, 2660, 2244, 2820, 396, 25886, 1170

Offset

1,1

Links

Table of n, a(n) for n=1..32.

John H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica, The Mathematical Intelligencer, Volume 30, Issue 2 (2008), pp 6-15, DOI:10.1007/BF02985731.

Max Horn, Numbers of isomorphism types of finite groups of given order.

Example

a(1) = 2 because A000001(1) = 1 and A000001(2) = 1.
a(2) = 6 because A000001(4) = 2 and A000001(6) = 2, and no other values of A000001 below 6 are equal to 2.

Crossrefs

Cf. A000001, A046057 (smallest order), A389995 (third smallest order).

Sequence in context: A321571 A092024 A252741 * A069261 A053608 A199239

Adjacent sequences: A389991 A389992 A389993 * A389995 A389996 A389997

Keyword

nonn,hard,more

Author

Robin Jones, Oct 21 2025

Status

approved