Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×D7×C43⋊C7 |
| unambiguous semidirect product | C7⋊(C22×C43⋊C7) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C43⋊C7) |
| unambiguous semidirect product | (C2×D7×C43)⋊C7 |
| Fitting, socle | C2×C7×C43 ⋊ C2×C7 |
| derived | C7×C43 ⋊ C22×C7 |
| Hall | C7×C43⋊C7 ⋊ C22 |
| Sylow | C43 ⋊ C2×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D7×C43⋊C7 |
| commutator, hypocenter | C7×C43 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C43 | C2×C7 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C2 | |
52 conjugacy classes of subgroups.
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 28);