Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#10617370 |
| unambiguous semidirect product | D5⋊#2380 |
| Fitting | C2×C5×#127 ⋊ C4 |
| Sylow | C5 ⋊ C2×#2380 |
3798 conjugacy classes of subgroups; only the 824 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 824 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.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114455);