Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D5⋊#365 |
| Fitting | C5×M32 ⋊ C4 |
| Sylow | C5 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 64 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:
2^7,5|a^2=e,b^2=d,d^2=f,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,e^b=eg,h^c=h^4,h^e=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#365, #13026049, #13026698, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#365, #13026049, #13026698, … |
| maximal quotient of | D5⋊#1368, #13025044, #13025047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6198);