Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D9×ΓL(1,𝔽32) |
| unambiguous semidirect product | C9⋊(C22×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C2×C9)⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C2×D9×C31)⋊C5 |
| Fitting | C2×C9×C31 ⋊ C2×C5 |
| derived, Hall | C9×C31 ⋊ C22×C5 |
| Hall | C9×ΓL(1,𝔽32) ⋊ C22 |
| Hall | C2×D9×C31 ⋊ C5 |
| Sylow | C31 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C22×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×ΓL(1,𝔽32) |
| commutator, hypocenter | C9×C31 | C22×C5 |
| Frattini | C3 | C2×D3×ΓL(1,𝔽32) |
| Fitting | C2×C9×C31 | C2×C5 |
| socle | C2×C3×C31 | C5×D3 |
| LCS | G ▷ C9×C31 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
132 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D9×ΓL(1,𝔽32), C2×C5×D9×ΓL(1,𝔽32), C2×D45×ΓL(1,𝔽32) |
| maximal normal subgroup of | C2×C5×D9×ΓL(1,𝔽32) |
| maximal quotient of | C2×D9×C31⋊C25, D5×D9×ΓL(1,𝔽32), C2×C5×D9×ΓL(1,𝔽32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 29);