Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×C32×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C22×C32×C4) |
| Fitting, socle | C23×C32×C5 ⋊ C4 |
| derived, Sylow | C5 ⋊ C23×C32×C4 |
| Hall | C32×C5 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C32 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C23×C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32×C5 | C4 |
| prime radical | C23×C32×D5 | C2 |
| cosocle | D5 | C24×C32 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C32 | |
1416 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5940);