Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1839 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^2,h^f=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13013216, #13013227, #13014688, … |
| maximal normal subgroup of | #13013216, #13013227, #13014688, … |
| maximal quotient of | #13018767, #13018773, #13021895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6270);