Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2164 |
138 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,h^a=h^2,c^b=cg,h^c=h^4,h^e=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#2164, C2×#10604747, #13043443, … |
| maximal normal subgroup of | D5⋊#2164, C2×#10604747, #13043443, … |
| maximal quotient of | #13025636, #13025678, #13025945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6829);