Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×D5×#347 |
| Fitting | C2×C5×#347 ⋊ C2 |
| Sylow | C5 ⋊ C22×#347 |
782 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#347, C2×D5×AGL(1,ℤ/16), C2×#13026049, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#347, C2×D5×AGL(1,ℤ/16), C2×#13026049 |
| maximal quotient of | C2×C5⋊D5×#347 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 322220);