Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #7787 |
430 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 85 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=g,b^2=f,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,i^a=i^4,d^b=df,e^b=eg,i^b=i^4,d^c=dg,e^c=eh113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 58599);