Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×D43⋊C49 |
| unambiguous semidirect product | D43⋊(C2×C49) |
| unambiguous semidirect product | (C2×D43)⋊C49 |
| unambiguous semidirect product | (C43⋊C49)⋊C22 |
| unambiguous semidirect product | (C2×C43⋊C49)⋊C2 |
| derived, Sylow | C43 ⋊ C22×C49 |
| Hall | C43⋊C49 ⋊ C22 |
| Hall | C2×D43 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D43⋊C7 |
| commutator, hypocenter | C43 | C22×C49 |
| Frattini | C7 | C2×D43⋊C7 |
| Fitting, socle | C2×C7×C43 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C7 | |
30 conjugacy classes of subgroups.
238 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D43⋊C3)⋊C49, D3×D43⋊C49, C2×C3×D43⋊C49, … |
| maximal normal subgroup of | C2×(D43⋊C3)⋊C49, C2×C3×D43⋊C49 |
| maximal quotient of | D3×D43⋊C49, C2×C3×D43⋊C49, C2×C3⋊(D43⋊C49) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 8);