Finite Group DatabasebetaFinite Group Databasebeta| order | 10868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C19⋊#261 |
| unambiguous semidirect product | C19⋊(C11×#261) |
| Fitting, socle, Hall | C11×C13×C19 ⋊ C4 |
| derived, Hall | C13×C19 ⋊ C4×C11 |
| Hall | C11×C19 ⋊ #261 |
| Hall | C11×C13 ⋊ Dic19 |
| Sylow | C19 ⋊ C11×#261 |
| Sylow | C13 ⋊ C11×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C19⋊#261 |
| commutator, hypocenter | C13×C19 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C19 | C4 |
| prime radical | C11×C19×D13 | C2 |
| cosocle | C19×D13 | C2×C11 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
869 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#15688300, C11×#15688301, C11×#15688304, … |
| maximal normal subgroup of | C11×#15688300, C11×#15688301, C11×#15688304, … |
| maximal quotient of | C3×C11×C19⋊#261, C11×C3⋊(C19⋊#261) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10868, 11);