Finite Group DatabasebetaFinite Group Databasebeta| order | 10846 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D493 |
| unambiguous semidirect product | C17⋊(C11×D29) |
| unambiguous semidirect product | C29⋊(C11×D17) |
| Fitting, socle, Hall | C11×C17×C29 ⋊ C2 |
| derived, Hall | C17×C29 ⋊ C2×C11 |
| Hall | C11×C29 ⋊ D17 |
| Hall | C11×C17 ⋊ D29 |
| Sylow | C29 ⋊ C11×D17 |
| Sylow | C17 ⋊ C11×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D493 |
| commutator, cosocle, hypocenter | C17×C29 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C29 | C2 |
| LCS | G ▷ C17×C29 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
2728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#14520308, C11×#14520307, C11×D17×D29, … |
| maximal normal subgroup of | C11×#14520308, C11×#14520307, C11×D17×D29, … |
| maximal quotient of | C11×Dic493, C2×C11×D493, C3×C11×D493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10846, 4);