Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1822 |
272 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 66 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=g,c^2=d,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,h^b=h^4,f^c=fg,h^f=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #13013732, #13018047, #13018048, … |
| maximal normal subgroup of | #13013732, #13018047, #13018048, … |
| maximal quotient of | #13018499, #13018501, #13018502, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6329);