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×C4×#170 |
| derived, Sylow | C5 ⋊ C23×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C23×C4×C8 |
| Frattini | C22 | C24×AGL(1,𝔽5) |
| Fitting | C24×C4×C5 | C4 |
| socle, prime radical | C25×C5 | C2×C4 |
| cosocle | C2×Dic5 | C25 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C24×C4 | |
4638 conjugacy classes of subgroups; only the 3000 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 3000 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1280 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114643);