Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×Dic43⋊C7 |
| unambiguous semidirect product | Dic43⋊C72 |
| unambiguous semidirect product | (C43⋊C7)⋊(C4×C7) |
| unambiguous semidirect product | (C7×Dic43)⋊C7 |
| derived, Sylow | C43 ⋊ C4×C72 |
| Hall | C7×C43⋊C7 ⋊ C4 |
| Hall | Dic43 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D43⋊C7 |
| commutator, hypocenter | C43 | C4×C72 |
| Frattini | C2 | C7×D43⋊C7 |
| Fitting, socle | C2×C7×C43 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C7 | |
60 conjugacy classes of subgroups.
238 conjugacy classes — view the full character table.
| maximal subgroup of | C7×((C43⋊C3)⋊C4)⋊C7, #16813401⋊C7, #16813400⋊C7, … |
| maximal normal subgroup of | C7×((C43⋊C3)⋊C4)⋊C7, #16813401⋊C7, #16813400⋊C7, … |
| maximal quotient of | C3×C7×Dic43⋊C7, C7×C3⋊(Dic43⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 15);