Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#443 ⋊ C4 |
| Sylow | C5 ⋊ #12821 |
430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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=dh,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^a=i^2,e^c=eg,g^c=gh,i^f=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2213, #72221506, #72221509, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2213, #72221506, #72221509, … |
| maximal quotient of | #72223129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096727);