Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D5⋊#2161 |
| Sylow | C5 ⋊ C2×#2161 |
642 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=eg,e^2=gh,f^2=h,g^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^2,c^b=ch,i^d=i^4,i^f=i^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113686);