Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C5×H(3,ℤ/4) ⋊ C4 |
| Sylow | C5 ⋊ #10699 |
842 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=g,d^2=h,g^2=h,b^a=bd,f^a=fh,e^b=eh,i^c=i^2,i^g=i^4110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1091846);