Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | SD16×C24⋊C5 |
| unambiguous semidirect product | (C24×SD16)⋊C5 |
| Fitting, Sylow | C24×SD16 ⋊ C5 |
1367 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 1367 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116342);