Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C8×Q8×AGL(1,𝔽5) |
| Fitting | C5×C8×Q8 ⋊ C4 |
| Sylow | C5 ⋊ C4×C8×Q8 |
1070 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104096);