Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D71⋊C5 |
| unambiguous semidirect product | D71⋊(C5×C9) |
| unambiguous semidirect product | (C71⋊C5)⋊(C2×C9) |
| unambiguous semidirect product | (C9×D71)⋊C5 |
| Fitting, Hall | C9×C71 ⋊ C2×C5 |
| derived, Sylow | C71 ⋊ C2×C5×C9 |
| Hall | C9×C71⋊C5 ⋊ C2 |
| Hall | C9×D71 ⋊ C5 |
| Hall | C71⋊C5 ⋊ C2×C9 |
| Hall | D71 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D71⋊C5 |
| commutator, hypocenter | C71 | C2×C5×C9 |
| Frattini | C3 | C3×D71⋊C5 |
| Fitting | C9×C71 | C2×C5 |
| socle | C3×C71 | C2×C3×C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
153 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D71⋊C5, C2×C9×D71⋊C5, C5×C9×D71⋊C5, … |
| maximal normal subgroup of | D9×D71⋊C5, C2×C9×D71⋊C5, C5×C9×D71⋊C5 |
| maximal quotient of | C9×Dic71⋊C5, C2×C9×D71⋊C5, C9×D71⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 10);