Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ D4×M16 |
544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^2,h^b=h^4,d^c=dg,h^c=h^3,h^d=h^4,h^f=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13019021, #13019023, #13019029, … |
| maximal normal subgroup of | #13019021, #13019023, #13019029, … |
| maximal quotient of | #13032701, #13032707, #13032715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19234);