A341823 - OEIS

%I #27 Mar 07 2021 18:04:43

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

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

%C 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.

%H J. Flynn, D. MacHale, E. A. O'Brien and R. Sheehy, <a href="https://www.jstor.org/stable/20489479">Finite Groups whose Automorphism Groups are 2-groups</a>, Proc. Royal Irish Academy, 94A, (2) 1994, 137-145.

%e 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

%Y Cf. A341824, A341825.

%Y Subsequence of A340521.

%K nonn,more

%O 0,1

%A _Des MacHale_, Feb 20 2021

%E Offset modified by _Bernard Schott_, Mar 04 2021