Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D5⋊#1814 |
| Fitting | C2×C5×#131 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1814 |
1330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^2,f^c=fh,g^c=gh,i^d=i^4,i^g=i^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104599);