Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C4×C43⋊C49 |
| unambiguous semidirect product | (C4×C43)⋊C49 |
| derived, Sylow | C43 ⋊ C4×C49 |
| Hall | C4×C43 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C7 | C43⋊C7 |
| commutator, hypocenter | C43 | C4×C49 |
| Frattini | C2×C7 | C2×C43⋊C7 |
| Fitting | C4×C7×C43 | C7 |
| socle | C2×C7×C43 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C4×C7 | |
18 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(C43⋊C3)⋊C49, Dic3×C43⋊C49, C3×C4×C43⋊C49 |
| maximal normal subgroup of | C4×(C43⋊C3)⋊C49, C3×C4×C43⋊C49 |
| maximal quotient of | Dic3×C43⋊C49, C3×C4×C43⋊C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 3);