Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×M32 ⋊ C4 |
| Sylow | C5 ⋊ #2110 |
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,c^b=cg,d^b=dg,h^b=h^2,h^c=h^4,h^e=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13025419, #13025775, #13025782, … |
| maximal normal subgroup of | #13025419, #13025775, #13025782, … |
| maximal quotient of | #13023000, #13023003, #13023005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6197);