Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D5×#3068 |
| Fitting | C5×#3068 ⋊ C2 |
| Sylow | C5 ⋊ C2×#3068 |
2746 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#61110, #72221514, AGL(1,𝔽5)×#3068, … |
| maximal normal subgroup of | D5×#61110, #72221514, AGL(1,𝔽5)×#3068 |
| maximal quotient of | #72223210, #72223486, #72226564 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1036966);