Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C16 ⋊ C2 |
| Sylow | C5 ⋊ #11465 |
454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,c^2=g,e^2=g,g^2=h,b^a=bd,d^a=df,e^b=ef,i^b=i^4248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 78790);