Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#10617447 |
| unambiguous semidirect product | D5⋊#2946 |
| Fitting | C2×C5×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C5 ⋊ C2×#2946 |
2946 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#576 |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#576 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1115006);