Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C8 · Schur multiplier (H2) = C23×C43 |
| direct product | C42×D5⋊C8 |
| derived, Sylow | C5 ⋊ C2×C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C2×C42×C8 |
| Frattini | C23 | C23×AGL(1,𝔽5) |
| Fitting | C43×C5 | C4 |
| socle | C23×C5 | C23×C4 |
| prime radical | C23×D5 | C22×C4 |
| cosocle | C22×Dic5 | C24 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C43 | |
2046 conjugacy classes of subgroups; only the 1152 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1103366);