Finite Group DatabasebetaFinite Group Databasebeta| order | 10846 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C29 · Schur multiplier (H2) = C1 |
| direct product | C11×C29×D17 |
| unambiguous semidirect product | C17⋊(C2×C11×C29) |
| Fitting, socle, Hall | C11×C17×C29 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C11×C29 |
| Hall | C17×C29 ⋊ C2×C11 |
| Hall | C11×C17 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C29 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C11×C29 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C29 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C11×C29 | |
16 conjugacy classes of subgroups.
3190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C29×#595, C11×#14520309, C11×D17×D29, … |
| maximal normal subgroup of | C11×C29×#595, C11×#14520309, C11×D17×D29, … |
| maximal quotient of | C11×C29×Dic17, C2×C11×C29×D17, C3×C11×C29×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10846, 3);