Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#117 ⋊ C4 |
| Sylow | C5 ⋊ #1828 |
296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 296 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) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=d,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,f^b=fg,h^b=h^4,e^c=eg,h^f=h^449 conjugacy classes — view the full character table.
| maximal subgroup of | #13026222, #13026223, #13026224, … |
| maximal normal subgroup of | #13026222, #13026223, #13026224, … |
| maximal quotient of | #13018596, #13018597, #13018598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6467);