Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #12999 |
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=dfg,d^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^4,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^4,d^c=dh,f^c=fh104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 86553);