Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D5⋊#1333 |
| Sylow | C5 ⋊ C2×#1333 |
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,d^2=f,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^2,d^b=dfh,e^b=eh,f^b=fh,i^c=i^4,i^e=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | #72242075, #72242079, AGL(1,𝔽5)×#1333, … |
| maximal normal subgroup of | #72242075, #72242079, AGL(1,𝔽5)×#1333 |
| maximal quotient of | #72242193, #72242212, #72253153 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1093968);