A371037 Orders of almost simple groups.

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

Author

Sébastien Palcoux, Mar 08 2024

Keywords

• nonn

Comments

A group G is almost simple if there exists a (non-abelian) simple group S for which S <= G <= Aut(S).

Examples

			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.
		

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.

Crossrefs

Cf. A001034.

Programs

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);;