Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | Dic5×C9⋊C8 |
| derived, Hall | C5×C9 ⋊ C4×C8 |
| Sylow | C9 ⋊ C8×Dic5 |
| Sylow | C5 ⋊ C4×C9⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D5×D9 |
| commutator, hypocenter | C5×C9 | C4×C8 |
| Frattini | C2×C3×C4 | D3×D5 |
| Fitting, cosocle | C2×C4×C5×C9 | C22 |
| socle, prime radical | C22×C3×C5 | C2×Dic3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C2×C4 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 25);