Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D4×D5×D9 |
| Fitting | C5×D4×C9 ⋊ C22 |
| Hall | C5×C9 ⋊ C22×D4 |
| Sylow | C9 ⋊ C2×D4×D5 |
| Sylow | C5 ⋊ C2×D4×D9 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D5×D9 |
| commutator, cosocle | C2×C5×C9 | C24 |
| Frattini | C2×C3 | C22×D3×D5 |
| Fitting | C5×D4×C9 | C22 |
| socle | C2×C3×C5 | C23×D3 |
| hypercenter | D4 | D5×D9 |
| hypocenter | C5×C9 | C22×D4 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C2 ◁ D4 | |
708 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D9×AGL(1,𝔽5), D4×D5×AGL(1,ℤ/9), D9×#87886, … |
| maximal normal subgroup of | D4×D9×AGL(1,𝔽5), D4×D5×AGL(1,ℤ/9) |
| maximal quotient of | D9×#87886 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1593);