Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×C24⋊C5 |
| unambiguous semidirect product | (C24×C32)⋊C5 |
| Fitting, socle, Hall | C24×C32 ⋊ C5 |
| derived, Sylow | C24 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C24⋊C5 |
| commutator, cosocle, hypocenter | C24 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C32 | |
102 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, 821);