Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #20529 |
1170 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 312 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=f,b^2=g,f^2=h,b^a=be,c^a=ch,d^a=de,i^a=i^2,c^b=ceh,d^b=dh,i^f=i^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104157);