Finite Group DatabasebetaFinite Group Databasebeta| order | 9540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×C3⋊D3×D53 |
| unambiguous semidirect product | (C3×D53)⋊(C5×D3) |
| Fitting, socle, Hall | C32×C5×C53 ⋊ C22 |
| derived, Hall | C32×C53 ⋊ C22×C5 |
| Hall | C5×C53 ⋊ C2×C3⋊D3 |
| Sylow | C53 ⋊ C2×C5×C3⋊D3 |
| Hall | C32×C5 ⋊ C2×D53 |
| Sylow | C32 ⋊ C2×C5×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D3×D53 |
| commutator, cosocle, hypocenter | C32×C53 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C53 | C22 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups.
840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9540, 70);