Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1372 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=ceg,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,h^b=h^4,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13014329, #13014330, #13014337, … |
| maximal normal subgroup of | #13014329, #13014330, #13014337, … |
| maximal quotient of | #13013392, #13013518, #13014363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 729);