Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×C24⋊C5 |
| unambiguous semidirect product | (C24×C9)⋊C5 |
| Fitting, Hall | C24×C9 ⋊ C5 |
| derived, Sylow | C24 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C24⋊C5 |
| commutator, hypocenter | C24 | C5×C9 |
| Frattini | C3 | C3×C24⋊C5 |
| Fitting | C24×C9 | C5 |
| socle, cosocle | C24×C3 | C3×C5 |
| prime radical | C3×C24⋊C5 | C3 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C9 | |
51 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 399);