Finite Group DatabasebetaFinite Group Databasebeta| order | 8460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D9×D47 |
| unambiguous semidirect product | (D9×C47)⋊(C2×C5) |
| unambiguous semidirect product | (C9×D47)⋊(C2×C5) |
| unambiguous semidirect product | D423⋊(C2×C5) |
| Fitting, Hall | C5×C9×C47 ⋊ C22 |
| derived, Hall | C9×C47 ⋊ C22×C5 |
| Hall | C5×C47 ⋊ C2×D9 |
| Sylow | C47 ⋊ C2×C5×D9 |
| Hall | C5×C9 ⋊ C2×D47 |
| Sylow | C9 ⋊ C2×C5×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D9×D47 |
| commutator, hypocenter | C9×C47 | C22×C5 |
| Frattini | C3 | C5×D3×D47 |
| Fitting | C5×C9×C47 | C22 |
| socle | C3×C5×C47 | C2×D3 |
| LCS | G ▷ C9×C47 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
750 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8460, 13);