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).
LINKS
Sébastien Palcoux, Table of n, a(n) for n = 1..113
T. Connor and D. Leemans, An atlas of subgroup lattices of finite almost simple groups.
GroupNames, Almost simple groups.
Groupprops, Almost simple group.
Wikipedia, Almost simple group.
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
KEYWORD
nonn
AUTHOR
Sébastien Palcoux, Mar 08 2024
STATUS
approved