Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2179 |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|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^30,d^b=df,f^b=fg,h^b=h^52,h^c=h^30,h^e=h^52175 conjugacy classes — view the full character table.
| maximal subgroup of | #28312657, #28312658, #28312661, … |
| maximal normal subgroup of | #28312657, #28312658, #28312661, … |
| maximal quotient of | #28309975, #28309978, #28309983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20913);