Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2967 |
362 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 148 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,c^2=f,d^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^2,c^b=cg,h^b=h^4,h^c=h^2,h^d=h^4,h^f=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #13020236, #13020238, #13020240, … |
| maximal normal subgroup of | #13020236, #13020238, #13020240, … |
| maximal quotient of | #13033671, #13033681, #13033738, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19395);