Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D31×D45 |
| unambiguous semidirect product | (C5×D31)⋊D9 |
| unambiguous semidirect product | (C9×D31)⋊D5 |
| Fitting, derived, Hall | C5×C9×C31 ⋊ C22 |
| Hall | C9×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D45 |
| Sylow | C9 ⋊ D5×D31 |
| Sylow | C5 ⋊ D9×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C31 | C22 |
| Frattini | C3 | D15×D31 |
| socle | C3×C5×C31 | C2×D3 |
| LCS | G ▷ C5×C9×C31 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
408 conjugacy classes — view the full character table.
| maximal subgroup of | D31×D225, D45×D31⋊C5, C5×D31×D45, … |
| maximal normal subgroup of | D45×D31⋊C5, C5×D31×D45 |
| maximal quotient of | D31×D225, C5×D31×D45, D31×C5⋊D45, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 41);