Finite Group DatabasebetaFinite Group Databasebeta| order | 6570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×#10620321 |
| derived, Sylow | C73 ⋊ C2×C5×C9 |
| Hall | C2×C5×C73 ⋊ C9 |
| Hall | C5×C73 ⋊ C2×C9 |
| Hall | C2×C73 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | C73⋊C3 |
| commutator, hypocenter | C73 | C2×C5×C9 |
| Frattini | C3 | C2×C5×C73⋊C3 |
| Fitting, socle | C2×C3×C5×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C3×C5 | |
24 conjugacy classes of subgroups.
810 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6570, 2);