Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×#3573⋊C5 |
| unambiguous semidirect product | (C2×#3573)⋊C5 |
| Fitting, Sylow | C2×#3573 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | C24⋊C5 |
| commutator, hypocenter | 2−1+4 | C2×C4×C5 |
| Frattini | C4 | C22×C24⋊C5 |
| Fitting | C2×#3573 | C5 |
| socle | C22 | C4×C24⋊C5 |
| prime radical | C2×#585⋊C5 | C2 |
| cosocle | #585 | C22×C5 |
| LCS | G ▷ 2−1+4 | |
| UCS | C1 ◁ C2×C8 | |
1120 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 1120 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 256 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116339);