Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#10604118 |
| unambiguous semidirect product | D5⋊#2159 |
| Fitting | C2×C5×M32 ⋊ C4 |
| Sylow | C5 ⋊ C2×#2159 |
718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#509, C2×#13026054, C2×#13026049, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#509, C2×#13026054, C2×#13026049 |
| maximal quotient of | C2×#72242311 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113678);