Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D45 |
| Fitting | C24×C5×C9 ⋊ C2 |
| derived, Hall | C5×C9 ⋊ C25 |
| Sylow | C9 ⋊ C24×D5 |
| Sylow | C5 ⋊ C24×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D45 |
| commutator, cosocle, hypocenter | C5×C9 | C25 |
| Frattini | C3 | C24×D15 |
| Fitting | C24×C5×C9 | C2 |
| socle | C24×C3×C5 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C24 | |
2244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4588);