Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(Dic43⋊C7) |
| unambiguous semidirect product | (C43⋊C7)⋊Dic7 |
| unambiguous semidirect product | Dic301⋊C7 |
| derived | C7×C43 ⋊ C4×C7 |
| Hall | C7×C43⋊C7 ⋊ C4 |
| Sylow | C43 ⋊ C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(D43⋊C7) |
| commutator, hypocenter | C7×C43 | C4×C7 |
| Fitting, socle | C2×C7×C43 | C2×C7 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,7^2,43,2|a^2=e,c^a=c^6,d^a=d^42,d^b=d^41112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 16);