Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C53×#500 ⋊ C2 |
| Sylow | C53 ⋊ #2243 |
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^52,c^b=cg,h^b=h^52,h^c=h^52598 conjugacy classes — view the full character table.
| maximal subgroup of | #27297926, #27297927, #27297933, … |
| maximal normal subgroup of | #27297926, #27297927, #27297933, … |
| maximal quotient of | #27300479, #27302021, #27302028, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6749);