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%I #20 Mar 09 2024 20:30:15
%S 60,120,168,336,360,504,660,720,1092,1320,1440,1512,2184,2448,2520,
%T 3420,4080,4896,5040,5616,6048,6072,6840,7800,7920,8160,9828,11232,
%U 12096,12144,12180,14880,15600,16320,19656,20160,24360,25308,25920,29120,29484,29760,31200,32736,34440
%N Orders of almost simple groups.
%C A group G is almost simple if there exists a (non-abelian) simple group S for which S <= G <= Aut(S).
%H Sébastien Palcoux, <a href="/A371037/b371037.txt">Table of n, a(n) for n = 1..113</a>
%H T. Connor and D. Leemans, <a href="https://leemans.dimitri.web.ulb.be/atlaslat/">An atlas of subgroup lattices of finite almost simple groups</a>.
%H GroupNames, <a href="https://people.maths.bris.ac.uk/~matyd/GroupNames/AS.html">Almost simple groups</a>.
%H Groupprops, <a href="https://groupprops.subwiki.org/wiki/Almost_simple_group">Almost simple group</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Almost_simple_group">Almost simple group</a>.
%e For n = 1, 2, 3, 4 the values a(n) = 60, 120, 168, 336 correspond to the groups A5, S5, PSL(2,7), PGL(2,7), respectively.
%o (GAP)
%o m := 100000;;
%o L := [];;
%o it := SimpleGroupsIterator(2, m);;
%o for g in it do
%o ag := AutomorphismGroup(g);;
%o iag := InnerAutomorphismsAutomorphismGroup(ag);;
%o Inter := IntermediateSubgroups(ag, iag).subgroups;;
%o LL := [Order(ag), Order(iag)];;
%o for h in Inter do
%o Add(LL, Order(h));;
%o od;
%o for o in LL do
%o if o <= m and (not o in L) then
%o Add(L, o);;
%o fi;
%o od;
%o od;
%o Sort(L);;
%o Print(L);;
%Y Cf. A001034.
%K nonn
%O 1,1
%A _Sébastien Palcoux_, Mar 08 2024
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