Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C22×C5×#127 ⋊ C2 |
| Sylow | C5 ⋊ #60798 |
2822 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|b^2=f,g^2=h,b^a=bf,c^a=cg,d^a=df,e^a=eh,g^a=gh,i^a=i^4,c^b=cf,g^c=gh164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1040992);