Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×C47⋊C32 |
| derived, Sylow | C47 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D47 |
| commutator, hypocenter | C47 | C4×C32 |
| Frattini | C2×C16 | C2×D47 |
| Fitting | C4×C16×C47 | C2 |
| socle | C22×C47 | C2×C16 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C4×C16 | |
72 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C47⋊C8, C8×C47⋊C32, #26103605, … |
| maximal normal subgroup of | C32×C47⋊C8, C8×C47⋊C32, #26103605, … |
| maximal quotient of | C8×C47⋊C32, #26103609, #26103965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2642);