Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C47×#543 ⋊ C2 |
| Sylow | C47 ⋊ #2029 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13093993 |
| commutator | C24×C47 | C23 |
| Frattini | C24 | C22×D47 |
| Fitting | C47×#543 | C2 |
| socle | C22×C47 | #120 |
| hypercenter | #543 | D47 |
| hypocenter | C47 | #2029 |
| LCS | G ▷ C24×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #543 | |
466 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^c=h^46532 conjugacy classes — view the full character table.
| maximal subgroup of | #26128993, #26128998, #26129010, … |
| maximal normal subgroup of | #26128993, #26128998, #26129010, … |
| maximal quotient of | #26119245, #26119250, #26119265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 5673);