Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#2117 ⋊ C2 |
| Sylow | C5 ⋊ #12750 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^4,d^b=dgh,f^b=fh,g^b=gh,i^b=i^4,e^c=eh,f^c=fh128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 85308);