Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D5⋊#413 |
| Sylow | C5 ⋊ C2×#413 |
756 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^2,f^b=fg,h^d=h^4,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13021737, #13021738, #13021745, … |
| maximal normal subgroup of | #13021737, #13021738, #13021745, … |
| maximal quotient of | D5⋊#1458, D5⋊#1459, #13029197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19634);