Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C25 |
| Fitting, Sylow | C25×D4 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C24⋊C5 |
| commutator, cosocle | C25 | C23×C5 |
| Frattini | C2 | C23×C24⋊C5 |
| Fitting | C25×D4 | C5 |
| socle | C26 | C22×C5 |
| hypercenter | C2×D4 | C24⋊C5 |
| hypocenter | C24 | C2×C5×D4 |
| LCS | G ▷ C25 ▷ C24 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
11217 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 11217 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116348);