Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D155 |
| Fitting, socle, derived, Hall | C32×C5×C31 ⋊ C22 |
| Hall | C32×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×C3⋊D3 |
| Hall | C32×C5 ⋊ C2×D31 |
| Sylow | C31 ⋊ D5×C3⋊D3 |
| Sylow | C32 ⋊ C2×D155 |
| Sylow | C5 ⋊ C3⋊D3×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C31 | C22 |
| LCS | G ▷ C32×C5×C31 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
474 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×D775, C3⋊D3×C5⋊(D31⋊C5), C5×C3⋊D3×D155, … |
| maximal normal subgroup of | C3⋊D3×C5⋊(D31⋊C5), C5×C3⋊D3×D155 |
| maximal quotient of | C3⋊D3×D775, C5×C3⋊D3×D155, C3⋊D15×D155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 144);