Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C23 |
| direct product | D8×C24⋊C5 |
| unambiguous semidirect product | (C24×D8)⋊C5 |
| Fitting, Sylow | C24×D8 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×C24⋊C5 |
| commutator, cosocle | C24×C4 | C22×C5 |
| Frattini | C4 | C22×C24⋊C5 |
| Fitting | C24×D8 | C5 |
| socle | C25 | C5×D4 |
| hypercenter | D8 | C24⋊C5 |
| hypocenter | C24 | C5×D8 |
| LCS | G ▷ C24×C4 ▷ C25 ▷ C24 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
1585 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 1585 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116341);