Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #1780 |
612 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^2,c^b=cg,h^b=h^4,h^c=h^4,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13014014, #13017844, #13017849, … |
| maximal normal subgroup of | #13014014, #13017844, #13017849, … |
| maximal quotient of | #13017425, #13017428, #13017431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7065);