Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #7323 |
256 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=d,b^2=e,c^2=h,d^2=f,e^2=h,b^a=bc,c^a=cf,e^a=egh,i^a=i^4,c^b=cg,d^b=dfh,g^b=gh,i^b=i^2,e^c=eh,i^e=i^474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1084317);