Finite Group DatabasebetaFinite Group Databasebeta| order | 6314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D451 |
| unambiguous semidirect product | C11⋊(C7×D41) |
| unambiguous semidirect product | C41⋊(C7×D11) |
| Fitting, socle, Hall | C7×C11×C41 ⋊ C2 |
| derived, Hall | C11×C41 ⋊ C2×C7 |
| Hall | C7×C41 ⋊ D11 |
| Hall | C7×C11 ⋊ D41 |
| Sylow | C41 ⋊ C7×D11 |
| Sylow | C11 ⋊ C7×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D451 |
| commutator, hypocenter | C11×C41 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C41 | C2 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
1589 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D11×D41, D7×D451, D77⋊D41, … |
| maximal normal subgroup of | C7×D11×D41, D7×D451, D77⋊D41, … |
| maximal quotient of | C7×Dic451, C2×C7×D451, C3×C7×D451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6314, 4);