Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#493 ⋊ C4 |
| Sylow | C5 ⋊ #13261 |
566 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=dfg,c^2=eh,d^2=gh,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^3,d^b=dg,f^b=fg,g^b=gh,i^b=i^2,i^f=i^468 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2213, #72221496, #72221498, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2213, #72221496, #72221498, … |
| maximal quotient of | #72223157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1097679);