Finite Group DatabasebetaFinite Group Databasebeta| order | 6678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D477 |
| unambiguous semidirect product | C9⋊(C7×D53) |
| unambiguous semidirect product | C53⋊(C7×D9) |
| Fitting, Hall | C7×C9×C53 ⋊ C2 |
| derived, Hall | C9×C53 ⋊ C2×C7 |
| Hall | C7×C53 ⋊ D9 |
| Hall | C7×C9 ⋊ D53 |
| Sylow | C53 ⋊ C7×D9 |
| Sylow | C9 ⋊ C7×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D477 |
| commutator, hypocenter | C9×C53 | C2×C7 |
| Frattini | C3 | C7×D159 |
| Fitting | C7×C9×C53 | C2 |
| socle | C3×C7×C53 | D3 |
| LCS | G ▷ C9×C53 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
1680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D9×D53, D7×D477, D63⋊D53, … |
| maximal normal subgroup of | C7×D9×D53, D7×D477, D63⋊D53, … |
| maximal quotient of | C7×Dic477, C2×C7×D477, C5×C7×D477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6678, 7);