Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C5×#3499 ⋊ C2 |
| Sylow | C5 ⋊ #60391 |
4666 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=h,c^2=h,f^2=h,b^a=bf,c^a=cg,f^a=fh,f^b=fh,g^b=gh,i^b=i^4,f^c=fh,e^d=eh146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1036275);