Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2925 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^2,d^b=dg,h^b=h^4,d^c=dg,h^f=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13031085, #13031088, #13031092, … |
| maximal normal subgroup of | #13031085, #13031088, #13031092, … |
| maximal quotient of | #13033239, #13033275, #13033493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19226);