Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ C8×#41 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^a=h^2,h^c=h^3,h^d=h^4,h^f=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #13016908, #13016914, #13016920, … |
| maximal normal subgroup of | #13016908, #13016914, #13016920, … |
| maximal quotient of | #13033650, #13033652, C4×D4×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19235);