Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#1379 ⋊ C2 |
| Sylow | C5 ⋊ #12787 |
450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=d,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^b=i^4,e^c=eh,f^c=fh,i^c=i^4188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 85504);