Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ #1728 |
480 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 480 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) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,e^2=g,b^a=bd,c^a=cg,h^b=h^2,h^f=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13013637, #13013643, #13021745, … |
| maximal normal subgroup of | #13013637, #13013643, #13021745, … |
| maximal quotient of | #13015271, #13015272, #13015275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6835);