Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #2165 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^2,e^b=eg,e^c=eg,h^c=h^4,h^e=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #13013757, #13013760, #13013762, … |
| maximal normal subgroup of | #13013757, #13013760, #13013762, … |
| maximal quotient of | #13025652, #13025714, #13025971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6834);