Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#108 ⋊ C4 |
| Sylow | C5 ⋊ #1953 |
184 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 66 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=f,c^2=e,d^2=g,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,h^b=h^3,h^c=h^4,h^f=h^446 conjugacy classes — view the full character table.
| maximal subgroup of | #13026714, #13026715, #13026720, … |
| maximal normal subgroup of | #13026714, #13026715, #13026720, … |
| maximal quotient of | #13020834, #13020835, #13020836, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6174);