Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #2183 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2,h^c=h^2,h^e=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13025202, #13025204, #13025210, … |
| maximal normal subgroup of | #13025202, #13025204, #13025210, … |
| maximal quotient of | #13025986, #13025991, #13027052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6530);