%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