Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #67194 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#67194 |
| Fitting, socle | C22×C32×C5 ⋊ C8 |
| derived, Hall | C32×C5 ⋊ C22×C8 |
| Sylow | C32 ⋊ C22×#168 |
| Sylow | C5 ⋊ C22×AGL(1,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #67194 |
| commutator, hypocenter | C32×C5 | C22×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C5 | C8 |
| prime radical | C22×C5×C3⋊D3 | C4 |
| cosocle | C5×#157 | C23 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5912);