A139669 Number of isomorphism classes of finite groups of order 11*2^n.

1, 2, 4, 12, 42, 195, 1387, 19324, 1083472

Offset

0,2

Comments

This appears to be the smallest possible number of groups of order q*2^n for an odd number q.

Apparently, a(n) is also the number of isomorphism classes of finite groups of order 19*2^n and, more generally, of order p*2^n for primes p such that p is congruent to 3 modulo 4 and p+1 is not a power of 2.

References

J. H. Conway et al., The Symmetries of Things, Peters, 2008, p. 206.

Links

Table of n, a(n) for n=0..8.

John H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica.

Formula

a(n) = A000001(11*2^n). - Max Alekseyev, Apr 26 2010

Example

a(2) is the number of groups of order 11*2^2=44, which is 4 and also the number of groups of order 19*2^2=76, 23*2^2=92, etc.

Maple

A139669 := n -> GroupTheory[NumGroups](11*2^n);

Crossrefs

Sequence in context: A200222 A063179 A096802 * A179973 A275780 A334272

Adjacent sequences: A139666 A139667 A139668 * A139670 A139671 A139672

Keyword

hard,more,nonn

Author

Anthony D. Elmendorf (aelmendo(AT)calumet.purdue.edu), Jun 12 2008

Extensions

a(8) from Max Alekseyev, Dec 24 2014

Status

approved