Finite Group DatabasebetaFinite Group Databasebeta| order | 8460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D141 |
| unambiguous semidirect product | (C3×D5)⋊(C3×D47) |
| unambiguous semidirect product | (D5×C47)⋊(C3×D3) |
| Fitting, socle, Hall | C32×C5×C47 ⋊ C22 |
| derived | C3×C5×C47 ⋊ C22×C3 |
| Hall | C32×C47 ⋊ C2×D5 |
| Hall | C5×C47 ⋊ C2×C3×D3 |
| Sylow | C47 ⋊ C3×D3×D5 |
| Hall | C32×C5 ⋊ C2×D47 |
| Sylow | C32 ⋊ D5×D47 |
| Sylow | C5 ⋊ C2×C3×D141 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D141 |
| commutator, hypocenter | C3×C5×C47 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C47 | C22 |
| LCS | G ▷ C3×C5×C47 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
864 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8460, 50);