Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×C47⋊#338 |
| unambiguous semidirect product | (C2×C47)⋊#338 |
| Sylow | C47 ⋊ C2×#338 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic47 |
| commutator | C4×C47 | C2×C42 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C22×M16×C47 | C2 |
| socle | C22×C47 | #95 |
| hypercenter | C22×M16 | D47 |
| hypocenter | C47 | C2×#338 |
| LCS | G ▷ C4×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
372 conjugacy classes of subgroups.
964 conjugacy classes — view the full character table.
| maximal subgroup of | #26103412, #26103414, #26103418, … |
| maximal normal subgroup of | #26103412, #26103414, #26103418, … |
| maximal quotient of | C2×#20241218, C2×#20241219, #26105696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4213);