Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #2166 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^2,c^b=cg,e^b=eg,h^b=h^4,e^c=eg,h^c=h^4,h^e=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #13013801, #13013804, #13024302, … |
| maximal normal subgroup of | #13013801, #13013804, #13024302, … |
| maximal quotient of | #13025655, #13025717, #13025978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 5957);