Finite Group DatabasebetaFinite Group Databasebeta| order | 10846 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D319 |
| unambiguous semidirect product | C11⋊(C17×D29) |
| unambiguous semidirect product | C29⋊(C17×D11) |
| Fitting, socle, Hall | C11×C17×C29 ⋊ C2 |
| derived, Hall | C11×C29 ⋊ C2×C17 |
| Hall | C17×C29 ⋊ D11 |
| Hall | C11×C17 ⋊ D29 |
| Sylow | C29 ⋊ C17×D11 |
| Sylow | C11 ⋊ C17×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D319 |
| commutator, cosocle, hypocenter | C11×C29 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C29 | C2 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
2737 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D11×D29, D17×D319, D187⋊D29, … |
| maximal normal subgroup of | C17×D11×D29, D17×D319, D187⋊D29, … |
| maximal quotient of | C17×Dic319, C2×C17×D319, C3×C17×D319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10846, 6);