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A372011
Orders of finite groups for which there is at least one group G such that |Aut(G)| = |G|.
0
1, 6, 8, 12, 16, 20, 24, 32, 36, 40, 42, 48, 54, 64, 72, 80, 84, 96, 108, 110, 120, 126, 128, 144, 156, 160, 162, 168, 192, 216, 220, 240, 252, 256, 272, 288, 312, 320, 324, 336, 342, 378, 384, 432, 440, 468, 480, 486, 500, 504, 506, 512, 544, 550, 576, 624, 640, 648, 660, 672
OFFSET
1,2
COMMENTS
Contains A341298 as a subsequence.
Every symmetric group S_n of order n! is a member for every n not equal to 2 or 6 since every such S_n is complete.
FORMULA
|Out(G)|<=|G| for every entry.
EXAMPLE
a(2) = 6 since the symmetric group of order 6 has 6 automorphisms.
PROG
(GAP)
for n in [1..32] do
for i in [1..NrSmallGroups(n)] do
if Size(AutomorphismGroup(SmallGroup(n, i))) = n then
Print(n, ", ", " ");
break;
fi;
od;
od;
CROSSREFS
Cf. A341298 (orders of complete groups).
Sequence in context: A194409 A115166 A050992 * A090259 A089241 A280270
KEYWORD
nonn
AUTHOR
Miles Englezou, Apr 19 2024
STATUS
approved