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

1,1

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

Cf. A001034.

Sequence in context: A056866 A098136 A060793 * A334761 A169823 A309842

Adjacent sequences: A371034 A371035 A371036 * A371038 A371039 A371040

Keyword

nonn

Author

Sébastien Palcoux, Mar 08 2024

Status

approved