Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#360 ⋊ C4 |
| Sylow | C5 ⋊ #12650 |
438 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 102 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=e,b^2=f,c^2=e,d^2=g,e^2=h,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,i^a=i^3,c^b=cg,e^b=eh,i^b=i^3,d^c=dh,f^c=fh,i^c=i^2,i^e=i^4,i^f=i^462 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×AGL(1,ℤ/16), #72220788, #72221516, … |
| maximal normal subgroup of | AGL(1,𝔽5)×AGL(1,ℤ/16), #72221516, C2×#13025928, … |
| maximal quotient of | #72220788, #72242084, C2×#13025928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096196);