Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | D5⋊#1454 |
| Sylow | C5 ⋊ C2×#1454 |
802 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,e^2=g,f^2=h,c^a=cgh,i^a=i^2,c^b=cg,i^d=i^4,i^e=i^4152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1099281);