Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #12800 |
524 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 101 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=f,b^2=d,c^2=h,e^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,c^b=ch,i^b=i^4,e^c=eh,f^c=fgh,f^e=fh86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 85561);