Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#1407 ⋊ C2 |
| Sylow | C5 ⋊ #13608 |
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=h,c^2=h,d^2=g,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,c^b=cg,d^b=dg,e^b=efgh,f^b=fh,d^c=dh,i^c=i^4,e^d=egh,f^e=fh53 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 89966);