Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C5 ⋊ #1744 |
296 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^2,h^e=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013206, #13013235, #13013245, … |
| maximal normal subgroup of | #13013206, #13013235, #13013245, … |
| maximal quotient of | #13016661, #13016663, #13016667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6255);