Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C42 |
| direct product | AGL(1,𝔽5)×#338 |
| Fitting | C5×#338 ⋊ C4 |
| Sylow | C5 ⋊ C4×#338 |
858 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1091843);