Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #3387 |
326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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=eg,c^2=g,d^2=eg,f^2=g,b^a=beg,c^a=cf,f^a=fg,h^a=h^4,c^b=cg,d^b=deg,h^b=h^4,f^c=fg,h^c=h^473 conjugacy classes — view the full character table.
| maximal subgroup of | #12088854, #12088856, #12088869, … |
| maximal normal subgroup of | #12088854, #12088856, #12088869, … |
| maximal quotient of | #12115952, #12115963, #12117616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15719);