Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D355 |
| unambiguous semidirect product | C5⋊(C9×D71) |
| unambiguous semidirect product | C71⋊(C9×D5) |
| Fitting, Hall | C5×C9×C71 ⋊ C2 |
| derived, Hall | C5×C71 ⋊ C2×C9 |
| Hall | C9×C71 ⋊ D5 |
| Sylow | C71 ⋊ C9×D5 |
| Hall | C5×C9 ⋊ D71 |
| Sylow | C5 ⋊ C9×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D355 |
| commutator, hypocenter | C5×C71 | C2×C9 |
| Frattini | C3 | C3×D355 |
| Fitting | C5×C9×C71 | C2 |
| socle | C3×C5×C71 | C2×C3 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
1611 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D5×D71, D9×D355, D45⋊D71, … |
| maximal normal subgroup of | C9×D5×D71, D9×D355, D45⋊D71, … |
| maximal quotient of | C9×Dic355, C2×C9×D355, C9×D1775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 5);