Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C5 ⋊ #1883 |
370 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 370 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) = 40 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,d^b=dg,f^b=fg,h^b=h^3,e^c=eg,h^f=h^443 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10604863, #13034939, #13034940, … |
| maximal normal subgroup of | C2×#10604863, #13034939, #13034940, … |
| maximal quotient of | #13019160, #13019161, #13019162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6945);