Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D32×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×D32×D5 |
| Fitting | C32×C4×C5 ⋊ C23 |
| derived, Hall | C32×C5 ⋊ C23×C4 |
| Sylow | C32 ⋊ C22×C4×D5 |
| Sylow | C5 ⋊ C2×C4×D32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D32×D5 |
| commutator, hypocenter | C32×C5 | C23×C4 |
| Frattini | C2 | C2×D32×D5 |
| Fitting | C32×C4×C5 | C23 |
| socle, cosocle | C2×C32×C5 | C24 |
| prime radical | C2×D32×D5 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D4×D5, D5×#64312, #72230209, … |
| maximal normal subgroup of | D32×D4×D5, D5×#64312, #72230209, … |
| maximal quotient of | D32×D5×AGL(1,𝔽5), D3×D5×#624, D5×#63921 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5281);