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A075094 Triangle of the sorted orders of graph automorphism groups for the simple graphs.

%I A075094 #19 Feb 16 2025 08:32:47
%S A075094 1,2,2,2,2,6,6,2,2,2,4,4,6,6,8,8,24,24,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,
%T A075094 4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120,1,1,1,1,1,1,1,1,2,
%U A075094 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A075094 Triangle of the sorted orders of graph automorphism groups for the simple graphs.
%C A075094 For n>1 row n ends with n!,n! since the automorphism group of the empty graph and the complete graph is the symmetric group.  - _Geoffrey Critzer_, Aug 09 2016
%H A075094 Sean A. Irvine, <a href="/A075094/b075094.txt">Table of n, a(n) for n = 1..13598</a>
%H A075094 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphAutomorphism.html">Graph Automorphism</a>
%e A075094 From _Geoffrey Critzer_, Aug 09 2016: (Start)
%e A075094 Triangle begins:
%e A075094   1;
%e A075094   2, 2;
%e A075094   2, 2, 6, 6;
%e A075094   2, 2, 2, 4, 4, 6, 6, 8, 8, 24, 24;
%e A075094   ... (End)
%t A075094 a = {1, 2, 4, 11, 34, 156, 1044};
%t A075094 Table[Sort[Table[GraphData[{n, i}, "AutomorphismCount"], {i, 1, a[[n]]}]], {n,1, 7}] // Grid (* _Geoffrey Critzer_, Aug 09 2016 *)
%Y A075094 Cf. A003400, A000088 (row lengths).
%K A075094 nonn,tabf
%O A075094 1,2
%A A075094 _Eric W. Weisstein_, Aug 31 2002