Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#1357 |
| Sylow | C5 ⋊ C2×#1357 |
494 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 88 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=e,d^2=g,e^2=fg,f^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,i^a=i^2,d^b=dg,e^b=efgh,f^b=fh,i^c=i^4,i^e=i^468 conjugacy classes — view the full character table.
| maximal subgroup of | #72221506, #72221540, #72221557, … |
| maximal normal subgroup of | #72221506, #72221540, #72221557, … |
| maximal quotient of | #72223213 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1095096);