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A139669 Number of isomorphism classes of finite groups of order 11*2^n. 1

%I

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

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

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

%C 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.

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

%H John H. Conway, Heiko Dietrich and E. A. O'Brien, <a href="http://www.math.auckland.ac.nz/~obrien/research/gnu.pdf">Counting groups: gnus, moas and other exotica</a>.

%F a(n) = A000001(11*2^n). - _Max Alekseyev_, Apr 26 2010

%e 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.

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

%K hard,more,nonn

%O 0,2

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

%E a(8) from _Max Alekseyev_, Dec 24 2014

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Last modified November 27 16:35 EST 2021. Contains 349394 sequences. (Running on oeis4.)