Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D5⋊#2170 |
| Sylow | C5 ⋊ C2×#2170 |
662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,c^2=f,e^2=h,f^2=g,g^2=h,b^a=be,e^a=eh,i^a=i^3,e^b=eh,i^c=i^2,i^d=i^4,i^f=i^4140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113817);