Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊(C4⋊C32) |
| Sylow | C5 ⋊ C2×C4⋊C32 |
230 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 118 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,e^2=f,f^2=g,g^2=h,b^a=bd,i^a=i^2,i^c=i^4,i^e=i^4224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098056);