Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×AGL(1,𝔽5)×SD32 |
| unambiguous semidirect product | D5⋊(C4×SD32) |
| Fitting | C2×C5×SD32 ⋊ C4 |
| Sylow | C5 ⋊ C2×C4×SD32 |
742 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#509, C2×SD32×#1043 |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#509 |
| maximal quotient of | C2×SD32×#1043 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113837);