Finite Group DatabasebetaFinite Group Databasebeta| order | 7714 |
| isoclinism | isoclinic class of D29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D29⋊C7 |
| unambiguous semidirect product | D29⋊(C7×C19) |
| unambiguous semidirect product | (C29⋊C7)⋊(C2×C19) |
| unambiguous semidirect product | (C19×D29)⋊C7 |
| Fitting, socle, Hall | C19×C29 ⋊ C2×C7 |
| derived, Sylow | C29 ⋊ C2×C7×C19 |
| Hall | C19×C29⋊C7 ⋊ C2 |
| Hall | C19×D29 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C2×C19 |
| Hall | D29 ⋊ C7×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D29⋊C7 |
| commutator, hypocenter | C29 | C2×C7×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C29 | C2×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
304 conjugacy classes — view the full character table.
| maximal subgroup of | C19×AGL(1,𝔽29), C19⋊AGL(1,𝔽29), D19×D29⋊C7, … |
| maximal normal subgroup of | C19×AGL(1,𝔽29), C19⋊AGL(1,𝔽29), D19×D29⋊C7, … |
| maximal quotient of | C19×Dic29⋊C7, C2×C19×D29⋊C7, C3×C19×D29⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7714, 10);