Finite Group DatabasebetaFinite Group Databasebeta| order | 5418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D387 |
| unambiguous semidirect product | C9⋊(C7×D43) |
| Fitting, Hall | C7×C9×C43 ⋊ C2 |
| derived, Hall | C9×C43 ⋊ C2×C7 |
| Hall | C7×C43 ⋊ D9 |
| Hall | C7×C9 ⋊ D43 |
| Sylow | C43 ⋊ C7×D9 |
| Sylow | C9 ⋊ C7×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D387 |
| commutator, hypocenter | C9×C43 | C2×C7 |
| Frattini | C3 | C7×D129 |
| Fitting | C7×C9×C43 | C2 |
| socle | C3×C7×C43 | D3 |
| LCS | G ▷ C9×C43 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
1365 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D9×D43, D7×D387, D63⋊D43, … |
| maximal normal subgroup of | C7×D9×D43, D7×D387, D63⋊D43, … |
| maximal quotient of | C7×Dic387, C2×C7×D387, C5×C7×D387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5418, 28);