Finite Group DatabasebetaFinite Group Databasebeta| order | 6042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1007 |
| unambiguous semidirect product | C53⋊(C3×D19) |
| Fitting, socle, Hall | C3×C19×C53 ⋊ C2 |
| derived, Hall | C19×C53 ⋊ C2×C3 |
| Hall | C3×C53 ⋊ D19 |
| Hall | C3×C19 ⋊ D53 |
| Sylow | C53 ⋊ C3×D19 |
| Sylow | C19 ⋊ C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1007 |
| commutator, hypocenter | C19×C53 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C53 | C2 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
1515 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D19×D53, D3×D1007, D57⋊D53, … |
| maximal normal subgroup of | C3×D19×D53, D3×D1007, D57⋊D53, … |
| maximal quotient of | C3×Dic1007, C2×C3×D1007, C9×D1007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6042, 5);