Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C5×#2296 ⋊ C2 |
| Sylow | C5 ⋊ #34056 |
2358 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=h,d^2=g,e^2=f,b^a=bf,c^a=cg,d^a=df,c^b=cf,i^c=i^4,i^d=i^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 328231);