Finite Group DatabasebetaFinite Group Databasebeta| order | 8460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(C47⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C47⋊(C9⋊AGL(1,𝔽5)) |
| Fitting, derived, Hall | C5×C9×C47 ⋊ C4 |
| Hall | C9×C47 ⋊ AGL(1,𝔽5) |
| Hall | C5×C47 ⋊ Dic9 |
| Sylow | C47 ⋊ C9⋊AGL(1,𝔽5) |
| Hall | C5×C9 ⋊ Dic47 |
| Sylow | C9 ⋊ C47⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic423 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C47 | C4 |
| Frattini | C3 | C3⋊(C47⋊AGL(1,𝔽5)) |
| socle | C3×C5×C47 | Dic3 |
| LCS | G ▷ C5×C9×C47 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,47,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^2,e^a=e^46,f^a=f^2,d^b=d^4849 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8460, 15);