Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1830 |
236 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,f^b=fg,e^c=eg,h^f=h^449 conjugacy classes — view the full character table.
| maximal subgroup of | #13026230, #13026231, #13026232, … |
| maximal normal subgroup of | #13026230, #13026231, #13026232, … |
| maximal quotient of | #13018597, #13018598, #13018599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6469);