Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #12591 |
390 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 227 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1280 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=d,e^2=g,g^2=h,b^a=bd,c^a=ch,i^a=i^4368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 84570);