Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D3×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C2×C3)⋊(D3×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C2×C3⋊D3×C31)⋊C5 |
| Fitting, socle | C2×C32×C31 ⋊ C2×C5 |
| derived, Hall | C32×C31 ⋊ C22×C5 |
| Hall | C32×ΓL(1,𝔽32) ⋊ C22 |
| Hall | C2×C3⋊D3×C31 ⋊ C5 |
| Sylow | C31 ⋊ C2×C5×C3⋊D3 |
| Sylow | C32 ⋊ C22×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D3×ΓL(1,𝔽32) |
| commutator, hypocenter | C32×C31 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C31 | C2×C5 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 117);