Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#356 |
| Sylow | C5 ⋊ C2×#356 |
240 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=g,d^2=g,e^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,d^b=dg,e^b=efg,h^c=h^4,e^d=eg,h^e=h^440 conjugacy classes — view the full character table.
| maximal subgroup of | #13014423, #13014455, #13014483, … |
| maximal normal subgroup of | #13014423, #13014455, #13014483, … |
| maximal quotient of | D5⋊#1319, D5⋊#1325, #13023288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6724);