Finite Group DatabasebetaFinite Group Databasebeta| order | 8460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(C47⋊AGL(1,𝔽5))) |
| unambiguous semidirect product | C47⋊(C3⋊ΓL(1,𝔽16)) |
| Fitting, socle, derived, Hall | C32×C5×C47 ⋊ C4 |
| Hall | C32×C47 ⋊ AGL(1,𝔽5) |
| Hall | C5×C47 ⋊ C3⋊Dic3 |
| Sylow | C47 ⋊ C3⋊ΓL(1,𝔽16) |
| Hall | C32×C5 ⋊ Dic47 |
| Sylow | C32 ⋊ C47⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3⋊Dic141 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C47 | C4 |
| LCS | G ▷ C32×C5×C47 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,47|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^46,e^b=e^4849 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8460, 55);