Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2965 |
412 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,h^a=h^2,h^b=h^4,h^c=h^2,h^d=h^4,h^f=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13016932, #13016938, #13016944, … |
| maximal normal subgroup of | #13016932, #13016938, #13016944, … |
| maximal quotient of | #13033656, #13033663, C4×#65704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19278);