Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×D5⋊#568 |
| unambiguous semidirect product | D5⋊(C2×#568) |
| Sylow | C5 ⋊ C22×#568 |
11118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#568 |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#568 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116299);