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A340521 List of possible orders of automorphism groups of finite groups. 4
1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 36, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The terms shown here match the initial terms of all of A002174, A002202, A049225, but this is a strictly different sequence since it is known that it contains 3^7 = 2187 (which is the smallest odd term greater than 1), whereas for the other three sequences all terms greater than 1 are even.

This is a supersequence of A002202 since |Aut(Z/nZ)| = phi(n). - Jianing Song, Feb 05 2021

John Bray has produced a group G of order 3^2*19 = 171 such that |Aut G| = 1026 = 2.3^3.19. So 1026 is in the present sequence but is not in A002202. So the present sequence contains both odd and even terms not in A002202. - Des MacHale, Feb 10 2021

For more about this problem, see the references in A137315.

LINKS

Table of n, a(n) for n=1..26.

D. MacHale and R. Sheehy, Finite groups with few automorphisms, Mathematical Proceedings of the Royal Irish Academy, Vol. 104A, No. 2 (December 2004), 231-238.

CROSSREFS

Cf. A002174, A002202, A049225, A137315.

Sequence in context: A011860 A259278 A049445 * A002174 A002202 A049225

Adjacent sequences:  A340518 A340519 A340520 * A340522 A340523 A340524

KEYWORD

nonn,more

AUTHOR

Des MacHale, Feb 05 2021

STATUS

approved

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Last modified May 11 03:49 EDT 2021. Contains 343784 sequences. (Running on oeis4.)