Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C2×C5×#493 ⋊ C2 |
| Sylow | C5 ⋊ #60647 |
3386 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|b^2=fh,c^2=g,f^2=h,b^a=bf,c^a=cg,f^a=fh,e^d=eh,i^e=i^4152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1039107);