Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D5⋊#407 |
| Sylow | C5 ⋊ C2×#407 |
1008 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=be,c^a=cg,h^a=h^2,h^d=h^4,h^f=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13015533, #13015539, #13015545, … |
| maximal normal subgroup of | #13015533, #13015539, #13015545, … |
| maximal quotient of | D5⋊#1462, D5⋊#1463, D5⋊#1464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19547);