Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ #1753 |
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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=e,b^2=f,c^2=e,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 | C2×#10604757, #13033300, #13033305, … |
| maximal normal subgroup of | C2×#10604757, #13033300, #13033305, … |
| maximal quotient of | #13016710, #13016712, #13016714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6839);