Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C9×C31 ⋊ C22×C5 |
| Hall | C9×ΓL(1,𝔽32) ⋊ C22 |
| Hall | D9×D31 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×D9 |
| Sylow | C31 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C2×D31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C31 | C22×C5 |
| Frattini | C3 | D3×D31⋊C5 |
| socle | C3×C31 | C2×C5×D3 |
| LCS | G ▷ C9×C31 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
78 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D9×D31⋊C5, D45×D31⋊C5, D9×C5⋊(D31⋊C5), … |
| maximal normal subgroup of | C5×D9×D31⋊C5 |
| maximal quotient of | D9×D31⋊C25, C5×D9×D31⋊C5, D45×D31⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 21);