Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D5⋊#408 |
| Sylow | C5 ⋊ C2×#408 |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=be,h^a=h^2,c^b=cg,h^d=h^4,h^f=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13021749, #13021751, #13021766, … |
| maximal normal subgroup of | #13021749, #13021751, #13021766, … |
| maximal quotient of | D5⋊#1468, D5⋊#1469, D5⋊#1470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19622);