Finite Group DatabasebetaFinite Group Databasebeta| order | 6678 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×C9×D53 |
| unambiguous semidirect product | C53⋊(C2×C7×C9) |
| Fitting, Hall | C7×C9×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C7×C9 |
| Hall | C9×C53 ⋊ C2×C7 |
| Hall | C7×C53 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C9 | D53 |
| commutator, hypocenter | C53 | C2×C7×C9 |
| Frattini | C3 | C3×C7×D53 |
| Fitting | C7×C9×C53 | C2 |
| socle | C3×C7×C53 | C2×C3 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C7×C9 | |
24 conjugacy classes of subgroups.
1764 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C9×#6157, C9×C7⋊#6157, C9×D7×D53, … |
| maximal normal subgroup of | C7×C9×#6157, C9×C7⋊#6157, C9×D7×D53, … |
| maximal quotient of | C7×C9×Dic53, C2×C7×C9×D53, C5×C7×C9×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6678, 3);