Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| unambiguous semidirect product | D5⋊#431 |
| Sylow | C5 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^2,h^d=h^4,h^f=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #13015290, #13015292, #13015293, … |
| maximal normal subgroup of | #13015290, #13015292, #13015293, … |
| maximal quotient of | #13033215, C4×D5⋊(C22⋊C8), C4×D5⋊(C4⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19115);