Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2992 |
356 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 146 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,d^2=e,f^2=g,b^a=be,d^a=de,h^a=h^2,c^b=ce,d^b=dg,h^c=h^4,h^f=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #13020252, #13020254, #13020256, … |
| maximal normal subgroup of | #13020252, #13020254, #13020256, … |
| maximal quotient of | #13033957, #13034008, #13034040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19401);