Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C8×AGL(1,𝔽5) |
| Fitting | C23×C5×C8 ⋊ C4 |
| derived, Sylow | C5 ⋊ C23×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C23×C4×C8 |
| Frattini | C4 | C24×AGL(1,𝔽5) |
| Fitting | C23×C5×C8 | C4 |
| socle | C24×C5 | C42 |
| prime radical | C24×D5 | C2×C4 |
| cosocle | C4×D5 | C25 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C8 | |
4638 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×AGL(1,𝔽5)×#97, C23×#11716761 |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×#97 |
| maximal quotient of | C23×#11716761 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114642);