A341823 Number of finite groups G with |Aut(G)| = 2^n.

2, 3, 4, 7, 11, 19, 34, 70

Offset

0,1

Comments

This sequence is infinite, but the amount of computation needed to consider the large number of groups of order 2^8 suggests it may be hard to find the next term.

Links

Table of n, a(n) for n=0..7.

J. Flynn, D. MacHale, E. A. O'Brien and R. Sheehy, Finite Groups whose Automorphism Groups are 2-groups, Proc. Royal Irish Academy, 94A, (2) 1994, 137-145.

Example

a(3) = 7, because there are seven finite groups G with |Aut(G)| = 8. Four cyclic groups: Aut(C_15) = Aut(C_16) = Aut(C_20) = Aut(C_30) ~~ C_4 x C_2, also Aut(C_4 x C_2) = Aut(D_4) ~~ D_4, with D_4 is the dihedral group of the square, finally Aut(C_24) ~~ C_2 x C_2 x C_2 = (C_2)^3 where ~~ stands for “isomorphic to". - Bernard Schott, Mar 04 2021

Crossrefs

Cf. A341824, A341825.

Subsequence of A340521.

Sequence in context: A226161 A188624 A327010 * A339548 A256994 A107481

Adjacent sequences: A341820 A341821 A341822 * A341824 A341825 A341826

Keyword

nonn,more

Author

Des MacHale, Feb 20 2021

Extensions

Offset modified by Bernard Schott, Mar 04 2021

Status

approved