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A371037 Orders of almost simple groups.

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