Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #13478 |
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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=de,b^2=dg,d^2=gh,e^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,i^a=i^4,c^b=cf,f^b=fh,i^b=i^4,d^c=dg,e^c=egh,f^c=fg,g^c=gh128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 89349);