Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3×ΓL(1,𝔽32) |
| unambiguous semidirect product | C3⋊(C3×C4×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C3×Dic3×C31)⋊C5 |
| derived | C3×C31 ⋊ C3×C4×C5 |
| Hall | C32×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C3×Dic3×C31 ⋊ C5 |
| Hall | C32×C31 ⋊ C4×C5 |
| Sylow | C31 ⋊ C3×C5×Dic3 |
| Sylow | C32 ⋊ C4×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×ΓL(1,𝔽32) |
| commutator, hypocenter | C3×C31 | C3×C4×C5 |
| Frattini | C2 | C3×D3×ΓL(1,𝔽32) |
| Fitting, socle | C2×C32×C31 | C2×C5 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C2×C3 | |
56 conjugacy classes of subgroups.
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 63);