Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #13429 |
434 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 73 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|c^2=d,d^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fgh,c^b=cf,d^b=dh,e^b=eg,e^c=eh,f^c=fh,g^c=gh,i^c=i^4,f^e=fh80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 89043);