Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(C31⋊AGL(1,𝔽5))) |
| unambiguous semidirect product | C31⋊(C3⋊ΓL(1,𝔽16)) |
| Fitting, socle, derived, Hall | C32×C5×C31 ⋊ C4 |
| Hall | C32×C31 ⋊ AGL(1,𝔽5) |
| Hall | C5×C31 ⋊ C3⋊Dic3 |
| Hall | C32×C5 ⋊ Dic31 |
| Sylow | C31 ⋊ C3⋊ΓL(1,𝔽16) |
| Sylow | C32 ⋊ C31⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3⋊Dic93 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C31 | C4 |
| LCS | G ▷ C32×C5×C31 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,31|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^30,e^b=e^4561 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 140);