Finite Group DatabasebetaFinite Group Databasebeta| order | 4902 |
| isoclinism | isoclinic class of D43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D43⋊C3 |
| unambiguous semidirect product | D43⋊(C3×C19) |
| unambiguous semidirect product | (C43⋊C3)⋊(C2×C19) |
| Fitting, socle, Hall | C19×C43 ⋊ C2×C3 |
| derived, Sylow | C43 ⋊ C2×C3×C19 |
| Hall | C19×C43⋊C3 ⋊ C2 |
| Hall | C19×D43 ⋊ C3 |
| Hall | C43⋊C3 ⋊ C2×C19 |
| Hall | D43 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D43⋊C3 |
| commutator, hypocenter | C43 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C43 | C2×C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4902, 13);