Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×D32×D4 |
| Fitting | C32×C5×D4 ⋊ C22 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C22×C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C22×D32 |
| commutator, cosocle | C2×C32 | C24×C5 |
| Frattini | C2 | C22×C5×D32 |
| Fitting | C32×C5×D4 | C22 |
| socle | C2×C32×C5 | C24 |
| hypercenter | C5×D4 | D32 |
| hypocenter | C32 | C22×C5×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C5 ◁ C5×D4 | |
998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D4×D5, C5×#10596675, #72231747 |
| maximal normal subgroup of | D32×D4×D5, C5×#10596675, #72231747 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5640);