Finite Group DatabasebetaFinite Group Databasebeta| order | 8646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1441 |
| unambiguous semidirect product | C11⋊(C3×D131) |
| unambiguous semidirect product | C131⋊(C3×D11) |
| Fitting, socle, Hall | C3×C11×C131 ⋊ C2 |
| derived, Hall | C11×C131 ⋊ C2×C3 |
| Hall | C3×C131 ⋊ D11 |
| Sylow | C131 ⋊ C3×D11 |
| Hall | C3×C11 ⋊ D131 |
| Sylow | C11 ⋊ C3×D131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1441 |
| commutator, hypocenter | C11×C131 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C131 | C2 |
| LCS | G ▷ C11×C131 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
2166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D131, D3×D1441, D33⋊D131, … |
| maximal normal subgroup of | C3×D11×D131, D3×D1441, D33⋊D131, … |
| maximal quotient of | C3×Dic1441, C2×C3×D1441, C9×D1441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8646, 4);