Finite Group DatabasebetaFinite Group Databasebeta| order | 6570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D5×C73⋊C3 |
| unambiguous semidirect product | C5⋊(C2×C3×C73⋊C3) |
| unambiguous semidirect product | (D5×C73)⋊C32 |
| unambiguous semidirect product | (C3×D5×C73)⋊C3 |
| Fitting, socle | C3×C5×C73 ⋊ C2×C3 |
| derived, Hall | C5×C73 ⋊ C2×C32 |
| Hall | C3×C5×C73⋊C3 ⋊ C2 |
| Hall | D5×C73 ⋊ C32 |
| Sylow | C73 ⋊ C32×D5 |
| Sylow | C5 ⋊ C2×C3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×C73⋊C3 |
| commutator, hypocenter | C5×C73 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C73 | C2×C3 |
| LCS | G ▷ C5×C73 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6570, 20);