Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(Dic31⋊C5)) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C3⋊Dic3) |
| unambiguous semidirect product | (C3⋊Dic93)⋊C5 |
| derived, Hall | C32×C31 ⋊ C4×C5 |
| Hall | C32×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C3⋊Dic93 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C3⋊Dic3 |
| Sylow | C31 ⋊ C5×C3⋊Dic3 |
| Sylow | C32 ⋊ Dic31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊(D31⋊C5)) |
| commutator, hypocenter | C32×C31 | C4×C5 |
| Fitting, socle | C2×C32×C31 | C2×C5 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3^2,31,2|a^2=f,c^a=c^2,d^a=d^2,e^a=e^30,e^b=e^16114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 64);