Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2980 |
394 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 144 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,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^2,c^b=ce,d^b=dg,h^b=h^4,d^c=dg,h^d=h^4,h^f=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #13019050, #13019051, #13019052, … |
| maximal normal subgroup of | #13019050, #13019051, #13019052, … |
| maximal quotient of | #13033902, #13033903, #13033934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19399);