Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #13377 |
648 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 75 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=dh,b^2=dh,b^a=bd,c^a=ce,f^a=fgh,i^a=i^4,c^b=cf,e^b=eg,i^b=i^4,g^c=gh,f^e=fh95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 88710);