Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | D5×#1393 |
| Fitting | C5×#1393 ⋊ C2 |
| Sylow | C5 ⋊ C2×#1393 |
1154 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1393, #72242767, D5×#13343 |
| maximal normal subgroup of | AGL(1,𝔽5)×#1393, #72242767, D5×#13343 |
| maximal quotient of | D5×#7307 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 84533);