Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #3046 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^4,f^c=fg88 conjugacy classes — view the full character table.
| maximal subgroup of | #12137371, #12137376, #12137386, … |
| maximal normal subgroup of | #12137371, #12137376, #12137386, … |
| maximal quotient of | #12084764, #12084775, #12084786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17715);