Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| unambiguous semidirect product | D5⋊#1783 |
| Sylow | C5 ⋊ C2×#1783 |
5942 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^2,g^b=gh,i^d=i^4,i^g=i^4104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1783, #72242718, #72242730, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1783, #72242718, #72242730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104419);