Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #11755 |
586 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 95 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=h,d^2=g,b^a=bd,d^a=df,f^a=fh,i^a=i^4,c^b=cf,d^b=dg,e^b=efg,d^c=dh,e^d=eh113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 80034);