Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D5⋊#1829 |
| Sylow | C5 ⋊ C2×#1829 |
1434 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 262 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,c^2=e,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^2,g^b=gh,f^c=fh,i^d=i^4,i^g=i^492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104681);