Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#15689002 |
| Fitting | C24×C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ C2×#386 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D47 |
| commutator | C22×C47 | C23×C4 |
| Frattini | C23 | C23×D47 |
| Fitting | C24×C4×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C24×C4 | D47 |
| hypocenter | C47 | C2×#386 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
1576 conjugacy classes of subgroups.
1528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26111647, #26111649, #26111667, … |
| maximal normal subgroup of | #26111647, #26111649, #26111667, … |
| maximal quotient of | C2×#20241611, C2×#20241621, C2×#20241626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6928);