Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C5×Q16 ⋊ C4 |
| Sylow | C5 ⋊ #1979 |
276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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=dfg,c^2=eg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,d^b=dg,f^b=fg,h^b=h^3,h^f=h^446 conjugacy classes — view the full character table.
| maximal subgroup of | #13026866, #13026867, #13026871, … |
| maximal normal subgroup of | #13026866, #13026867, #13026871, … |
| maximal quotient of | #13020999, #13021000, #13021001, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6934);