Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #11551 |
398 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 83 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=e,b^2=h,d^2=h,e^2=g,b^a=bd,d^a=df,f^a=fh,c^b=cg,d^b=dh,e^b=efh,i^b=i^4,e^d=eh125 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 79132);