Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#64904 |
| unambiguous semidirect product | D5⋊(C2×#357) |
| Fitting | C22×C5×D8 ⋊ C4 |
| Sylow | C5 ⋊ C22×#357 |
1470 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 320 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113601);