Finite Group DatabasebetaFinite Group Databasebeta| order | 8460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D45⋊D47 |
| unambiguous semidirect product | D235⋊D9 |
| unambiguous semidirect product | D423⋊D5 |
| Fitting, derived, Hall | C5×C9×C47 ⋊ C22 |
| Hall | C9×C47 ⋊ C2×D5 |
| Hall | C5×C47 ⋊ C2×D9 |
| Sylow | C47 ⋊ D5×D9 |
| Hall | C5×C9 ⋊ C2×D47 |
| Sylow | C9 ⋊ D5×D47 |
| Sylow | C5 ⋊ D9×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C47 | C22 |
| Frattini | C3 | D15⋊D47 |
| socle | C3×C5×C47 | C2×D3 |
| LCS | G ▷ C5×C9×C47 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,47,3|c^3=f^2,d^a=d^4,e^a=e^46,c^b=c^2f,d^b=d^4,f^b=f^2576 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8460, 20);