Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #3039 |
480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^4,f^c=fg76 conjugacy classes — view the full character table.
| maximal subgroup of | #12137608, #12137610, #12137611, … |
| maximal normal subgroup of | #12137608, #12137610, #12137611, … |
| maximal quotient of | #12083218, #12083222, #12083227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17780);