Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×Q32 ⋊ C4 |
| Sylow | C5 ⋊ #2179 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^2,d^b=df,f^b=fg,h^b=h^4,h^c=h^2,h^e=h^443 conjugacy classes — view the full character table.
| maximal subgroup of | #13027865, #13027866, #13027869, … |
| maximal normal subgroup of | #13027865, #13027866, #13027869, … |
| maximal quotient of | #13025183, #13025186, #13025191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6219);