Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| unambiguous semidirect product | D5⋊#2992 |
| Sylow | C5 ⋊ C2×#2992 |
1938 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=g,d^2=f,g^2=h,b^a=bf,d^a=df,i^a=i^2,c^b=cf,d^b=dh,i^e=i^4,i^g=i^4116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1115533);