Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C44 · Schur multiplier (H2) = C46 |
| direct product | C43×AGL(1,𝔽5) |
| Fitting | C43×C5 ⋊ C4 |
| derived, Sylow | C5 ⋊ C44 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C44 |
| Frattini | C23 | C23×AGL(1,𝔽5) |
| Fitting | C43×C5 | C4 |
| socle | C23×C5 | C23×C4 |
| prime radical, cosocle | C23×D5 | C24 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C43 | |
3966 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098151);