Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#10604344 |
| unambiguous semidirect product | D5⋊#1441 |
| Fitting | C22×C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1441 |
3246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098333);