Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊C32 |
| Fitting | C2×C5×C32 ⋊ C4 |
| Sylow | C5 ⋊ #7465 |
202 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 86 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=d,b^2=e,d^2=f,f^2=g,g^2=h,b^a=bc,i^b=i^2,i^e=i^4224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1084634);