Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #3407 |
360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 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=e,e^2=f,f^2=g,d^a=dg,h^a=h^2,c^b=cg,h^b=h^4,h^e=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13025780, #13025781, #13026668, … |
| maximal normal subgroup of | #13025780, #13025781, #13026668, … |
| maximal quotient of | #13043112, #13043113, #13043121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19486);