Finite Group DatabasebetaFinite Group Databasebeta| order | 5418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×(C43⋊C3)⋊D7 |
| unambiguous semidirect product | (C43⋊C3)⋊(C3×D7) |
| Fitting, socle | C3×C7×C43 ⋊ C2×C3 |
| derived, Hall | C7×C43 ⋊ C2×C32 |
| Hall | C3×C7×C43⋊C3 ⋊ C2 |
| Hall | D301 ⋊ C32 |
| Hall | C3×C43⋊C3 ⋊ D7 |
| Sylow | C43 ⋊ C32×D7 |
| Sylow | C7 ⋊ C3×D43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C43⋊C3)⋊D7 |
| commutator, hypocenter | C7×C43 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C43 | C2×C3 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5418, 56);