Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1965 |
396 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=df,c^2=e,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,d^b=dg,f^b=fg,h^b=h^3,h^f=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #13017868, #13017869, #13017874, … |
| maximal normal subgroup of | #13017868, #13017869, #13017874, … |
| maximal quotient of | #13020932, #13020933, #13020934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7035);