Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ C8×#100 |
542 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 134 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=f,c^2=e,e^2=h,f^2=g,b^a=bd,f^a=fg,i^a=i^3,d^b=dg,i^b=i^3,i^c=i^2,i^e=i^4,i^f=i^4110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1087072);