Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C22×#65800 |
| unambiguous semidirect product | D5⋊(C2×#379) |
| Fitting | C26×C5 ⋊ C4 |
| Sylow | C5 ⋊ C22×#379 |
33214 conjugacy classes of subgroups; only the 2056 normal subgroups are shown.
This group has 33214 conjugacy classes of subgroups — too many to draw. Only its 2056 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(1,𝔽5)×#120, #72242753, #72242821, … |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×#120, #72242753, #72242821, … |
| maximal quotient of | #72253753, #72269815 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114114);