Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C5×#3282 ⋊ C2 |
| Sylow | C5 ⋊ D4×#135 |
2822 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|e^2=h,f^2=h,b^a=bf,c^a=cg,d^a=dh,f^a=fh,d^b=df,f^b=fh,f^d=fh,i^d=i^4,i^e=i^4140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1044857);