Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #10633 |
294 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 87 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,c^2=d,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,f^a=fg,i^a=i^4,c^b=cf,d^b=dg,e^b=eg,f^b=fh,i^b=i^4,e^c=eg,f^c=fgh98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 74371);