Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #7332 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
Polycyclic presentation:
2^8,5|a^2=c,b^2=d,c^2=e,d^2=f,e^2=h,f^2=g,g^2=h,b^a=be,d^a=dh,c^b=ch,i^b=i^4248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 56901);