Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #8114 |
942 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 160 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=f,f^2=g,b^a=bd,d^a=dg,f^a=fh,c^b=ch,d^b=dh,e^b=eg,i^b=i^2,i^f=i^492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1086859);