Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | D5⋊#568 |
| Sylow | C5 ⋊ C2×#568 |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,d^a=dg,h^a=h^2,c^b=cg,h^e=h^4,h^f=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13021732, #13021737, #13021746, … |
| maximal normal subgroup of | #13021732, #13021737, #13021746, … |
| maximal quotient of | #13044391, #13044400, C4×#66256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21491);