Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic43⋊C49 |
| unambiguous semidirect product | (C43⋊C49)⋊C4 |
| derived, Sylow | C43 ⋊ C4×C49 |
| Hall | C43⋊C49 ⋊ C4 |
| Hall | Dic43 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C7 | D43⋊C7 |
| commutator, hypocenter | C43 | C4×C49 |
| Fitting, socle | C2×C7×C43 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C7 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,43,2,7|a^2=d,b^7=e,c^a=c^42,c^b=c^41238 conjugacy classes — view the full character table.
| maximal subgroup of | ((C43⋊C3)⋊C4)⋊C49, C3×Dic43⋊C49, C3⋊(Dic43⋊C49) |
| maximal normal subgroup of | ((C43⋊C3)⋊C4)⋊C49, C3×Dic43⋊C49 |
| maximal quotient of | C3×Dic43⋊C49, C3⋊(Dic43⋊C49) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 2);