Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C5×2−1+4 ⋊ C4 |
| Sylow | C5 ⋊ #60093 |
4852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=g,f^2=h,g^2=h,b^a=bf,e^a=eh,f^a=fh,i^a=i^2,f^b=fh,i^b=i^4,d^c=dh,i^g=i^4116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114766);