Finite Group DatabasebetaFinite Group Databasebeta| order | 8246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D589 |
| unambiguous semidirect product | C19⋊(C7×D31) |
| unambiguous semidirect product | C31⋊(C7×D19) |
| Fitting, socle, Hall | C7×C19×C31 ⋊ C2 |
| derived, Hall | C19×C31 ⋊ C2×C7 |
| Hall | C7×C31 ⋊ D19 |
| Hall | C7×C19 ⋊ D31 |
| Sylow | C31 ⋊ C7×D19 |
| Sylow | C19 ⋊ C7×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D589 |
| commutator, hypocenter | C19×C31 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C31 | C2 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
2072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D19×D31, D7×D589, D133⋊D31, … |
| maximal normal subgroup of | C7×D19×D31, D7×D589, D133⋊D31, … |
| maximal quotient of | C7×Dic589, C2×C7×D589, C3×C7×D589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8246, 4);