Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×D5×D12 |
| Fitting | C32×C4×C5 ⋊ C23 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C2×D4×D5 |
| Sylow | C5 ⋊ C2×D3×D12 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×D5 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C32×C4×C5 | C23 |
| hypercenter | C4 | D32×D5 |
| hypocenter | C32×C5 | C22×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D4×D5, D5×#64314, D3×AGL(1,𝔽5)×D12, … |
| maximal normal subgroup of | D32×D4×D5, D5×#64314, D3×AGL(1,𝔽5)×D12, … |
| maximal quotient of | D5×#88955 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5282);