Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C5×#341 ⋊ C2 |
| Sylow | C5 ⋊ #20351 |
1978 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,e^2=h,f^2=h,g^2=h,b^a=be,e^a=eh,g^a=gh,d^c=dh,i^d=i^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 166990);