Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #7270 |
208 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 72 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=d,b^2=e,c^2=f,d^2=h,e^2=fg,g^2=h,b^a=bc,c^a=cf,e^a=efg,g^a=gh,i^a=i^3,c^b=cg,f^b=fh,g^b=gh,i^b=i^2,i^d=i^4,i^e=i^474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1084169);