Finite Group DatabasebetaFinite Group Databasebeta| order | 7714 |
| isoclinism | isoclinic class of D133 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D133 |
| unambiguous semidirect product | C7⋊(C29×D19) |
| unambiguous semidirect product | C19⋊(D7×C29) |
| Fitting, socle, Hall | C7×C19×C29 ⋊ C2 |
| derived, Hall | C7×C19 ⋊ C2×C29 |
| Hall | C19×C29 ⋊ D7 |
| Hall | C7×C29 ⋊ D19 |
| Sylow | C19 ⋊ D7×C29 |
| Sylow | C7 ⋊ C29×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D133 |
| commutator, hypocenter | C7×C19 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C29 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
1972 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D133, D7×C29×D19, D133⋊D29, … |
| maximal normal subgroup of | D29×D133, D7×C29×D19, D133⋊D29, … |
| maximal quotient of | C29×Dic133, C2×C29×D133, C3×C29×D133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7714, 8);