Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C5×#3585 ⋊ C2 |
| Sylow | C5 ⋊ #61107 |
2624 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|b^2=h,f^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,g^a=gh,d^b=df,f^b=fh,i^b=i^4,g^c=gh,f^d=fh134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1045829);