Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #12019 |
226 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 119 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=e,b^2=d,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^4,e^b=eh212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 81200);