Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#10617223 |
| unambiguous semidirect product | D5⋊#2358 |
| Fitting | C2×C5×#120 ⋊ C4 |
| Sylow | C5 ⋊ C2×#2358 |
5942 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D42×AGL(1,𝔽5) |
| maximal normal subgroup of | C2×D42×AGL(1,𝔽5) |
| maximal quotient of | #72221508, #72221519 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114241);