Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #12678 |
292 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 123 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=e,b^2=f,c^2=de,d^2=gh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=cg,d^a=dh,d^b=dg,e^b=egh,g^b=gh,d^c=dh,e^c=eh,i^c=i^4110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 84994);