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A371037
Orders of almost simple groups.
1
60, 120, 168, 336, 360, 504, 660, 720, 1092, 1320, 1440, 1512, 2184, 2448, 2520, 3420, 4080, 4896, 5040, 5616, 6048, 6072, 6840, 7800, 7920, 8160, 9828, 11232, 12096, 12144, 12180, 14880, 15600, 16320, 19656, 20160, 24360, 25308, 25920, 29120, 29484, 29760, 31200, 32736, 34440
OFFSET
1,1
COMMENTS
A group G is almost simple if there exists a (non-abelian) simple group S for which S <= G <= Aut(S).
EXAMPLE
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.
PROG
(GAP)
m := 100000;;
L := [];;
it := SimpleGroupsIterator(2, m);;
for g in it do
ag := AutomorphismGroup(g);;
iag := InnerAutomorphismsAutomorphismGroup(ag);;
Inter := IntermediateSubgroups(ag, iag).subgroups;;
LL := [Order(ag), Order(iag)];;
for h in Inter do
Add(LL, Order(h));;
od;
for o in LL do
if o <= m and (not o in L) then
Add(L, o);;
fi;
od;
od;
Sort(L);;
Print(L);;
CROSSREFS
Cf. A001034.
Sequence in context: A056866 A098136 A060793 * A334761 A169823 A309842
KEYWORD
nonn
AUTHOR
Sébastien Palcoux, Mar 08 2024
STATUS
approved