Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×C4×Q8×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C42×Q8) |
| Fitting | C2×C4×C5×Q8 ⋊ C4 |
| Sylow | C5 ⋊ C2×C42×Q8 |
3966 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×#41×AGL(1,𝔽5) |
| maximal normal subgroup of | C2×C4×#41×AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114099);