Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D3×D15×C31 |
| unambiguous semidirect product | (C3×D3)⋊(D5×C31) |
| unambiguous semidirect product | (C5×D3)⋊(D3×C31) |
| Fitting, socle, Hall | C32×C5×C31 ⋊ C22 |
| derived, Hall | C32×C5 ⋊ C22×C31 |
| Hall | C32×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ D32 |
| Sylow | C32 ⋊ C2×D5×C31 |
| Sylow | C5 ⋊ D32×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D3×D15 |
| commutator, hypocenter | C32×C5 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C31 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C31 | |
88 conjugacy classes of subgroups.
837 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C31×D75, D3×D15×ΓL(1,𝔽32), C5×D3×D15×C31, … |
| maximal normal subgroup of | D3×D15×ΓL(1,𝔽32), C5×D3×D15×C31 |
| maximal quotient of | D3×C31×D75, C5×D3×D15×C31, D152×C31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 149);