Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C5×#492 ⋊ C4 |
| Sylow | C5 ⋊ #9829 |
610 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 116 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=f,b^2=dfg,c^2=eg,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^3,c^b=cg,i^b=i^2,i^f=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | #72221440, #72221443, AGL(1,𝔽5)×#1715, … |
| maximal normal subgroup of | #72221440, #72221443, AGL(1,𝔽5)×#1715 |
| maximal quotient of | #72223265 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1091598);