Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C32×D5×#41 |
| Fitting | C32×C5×#41 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×#41 |
| Sylow | C5 ⋊ C2×C32×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C4 | C22×D5 |
| commutator, cosocle | C2×C5 | C24×C32 |
| Frattini | C2 | C23×C32×D5 |
| Fitting | C32×C5×#41 | C2 |
| socle | C2×C32×C5 | C24 |
| hypercenter | C32×#41 | D5 |
| hypocenter | C5 | C2×C32×#41 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C32×C4 ◁ C32×#41 | |
984 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5770);