Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×#3531⋊C5 |
| unambiguous semidirect product | (C2×#3531)⋊C5 |
| Fitting, Sylow | C2×#3531 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | C24⋊C5 |
| commutator, cosocle, hypocenter | #564 | C22×C5 |
| Frattini | C22 | C22×C24⋊C5 |
| Fitting | C2×#3531 | C5 |
| socle | C23 | C2×C24⋊C5 |
| LCS | G ▷ #564 | |
| UCS | C1 ◁ C22×C4 | |
713 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 713 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 256 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#62694⋊C5, #72209975 |
| maximal normal subgroup of | C2×#62694⋊C5, #72209975 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116326);