Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #4380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C3×C4 |
| direct product | C8×#4380 |
| Fitting | C32×C5×C8 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C8 |
| Sylow | C32 ⋊ C8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C8×#157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #4380 |
| commutator, hypocenter | C32×C5 | C4×C8 |
| Frattini | C4 | C2×#4380 |
| Fitting | C32×C5×C8 | C4 |
| socle | C2×C32×C5 | C42 |
| prime radical | C2×C3⋊D15 | C2×C4 |
| cosocle | C4×C3⋊D15 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C8 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2685);