Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1374 |
160 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 90 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=d,b^2=e,d^2=f,f^2=g,b^a=bc,h^a=h^2,h^d=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013393, #13013394, #13013425, … |
| maximal normal subgroup of | #13013393, #13013394, #13013425, … |
| maximal quotient of | #13013464, #13013478, #13013488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 780);