Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #12851 |
416 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^2,f^b=fh,e^c=eh,i^f=i^498 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096784);