Finite Group DatabasebetaFinite Group Databasebeta| order | 6570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D657 |
| unambiguous semidirect product | C9⋊(C5×D73) |
| unambiguous semidirect product | C73⋊(C5×D9) |
| Fitting, Hall | C5×C9×C73 ⋊ C2 |
| derived, Hall | C9×C73 ⋊ C2×C5 |
| Hall | C5×C73 ⋊ D9 |
| Sylow | C73 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ D73 |
| Sylow | C9 ⋊ C5×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D657 |
| commutator, hypocenter | C9×C73 | C2×C5 |
| Frattini | C3 | C5×D219 |
| Fitting | C5×C9×C73 | C2 |
| socle | C3×C5×C73 | D3 |
| LCS | G ▷ C9×C73 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
1650 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D73, D5×D657, D45⋊D73, … |
| maximal normal subgroup of | C5×D9×D73, D5×D657, D45⋊D73, … |
| maximal quotient of | C5×Dic657, C2×C5×D657, C25×D657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6570, 7);