Finite Group DatabasebetaFinite Group Databasebeta| order | 9614 |
| isoclinism | isoclinic class of D253 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D253 |
| unambiguous semidirect product | C11⋊(C19×D23) |
| unambiguous semidirect product | C23⋊(C19×D11) |
| Fitting, socle, Hall | C11×C19×C23 ⋊ C2 |
| derived, Hall | C11×C23 ⋊ C2×C19 |
| Hall | C19×C23 ⋊ D11 |
| Hall | C11×C19 ⋊ D23 |
| Sylow | C23 ⋊ C19×D11 |
| Sylow | C11 ⋊ C19×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D253 |
| commutator, cosocle, hypocenter | C11×C23 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C11×C19×C23 | C2 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
2432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×D11×D23, D19×D253, D209⋊D23, … |
| maximal normal subgroup of | C19×D11×D23, D19×D253, D209⋊D23, … |
| maximal quotient of | C19×Dic253, C2×C19×D253, C3×C19×D253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9614, 7);