Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#1382 ⋊ C2 |
| Sylow | C5 ⋊ #12996 |
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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=dfg,d^2=gh,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^4,d^c=dh,e^c=eh,f^c=fh,i^c=i^4134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 86532);