Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #444×D47 |
| Fitting | C47×#444 ⋊ C2 |
| Sylow | C47 ⋊ C2×#444 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D47 |
| commutator | C4×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#444 | C2 |
| socle | C2×C47 | C2×C4×D4 |
| hypercenter | #444 | D47 |
| hypocenter | C47 | C2×#444 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ #444 | |
464 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2180, D47×AGL(1,ℤ/16), #26369723, … |
| maximal normal subgroup of | D47×#2180, D47×AGL(1,ℤ/16), #26369723, … |
| maximal quotient of | D47×SD16⋊C8, D47×#1579, D47×#1580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13402);