Finite Group DatabasebetaFinite Group Databasebeta| order | 6314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D287 |
| unambiguous semidirect product | C7⋊(C11×D41) |
| unambiguous semidirect product | C41⋊(C11×D7) |
| Fitting, socle, Hall | C7×C11×C41 ⋊ C2 |
| derived, Hall | C7×C41 ⋊ C2×C11 |
| Hall | C11×C41 ⋊ D7 |
| Hall | C7×C11 ⋊ D41 |
| Sylow | C41 ⋊ C11×D7 |
| Sylow | C7 ⋊ C11×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D287 |
| commutator, hypocenter | C7×C41 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C41 | C2 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
1595 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D7×D41, D11×D287, D77⋊D41, … |
| maximal normal subgroup of | C11×D7×D41, D11×D287, D77⋊D41, … |
| maximal quotient of | C11×Dic287, C2×C11×D287, C3×C11×D287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6314, 6);