Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#340 ⋊ C2 |
| Sylow | C53 ⋊ #1823 |
344 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=f,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^52,e^c=eg766 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1823, C2×#20274800, #27383883, … |
| maximal normal subgroup of | D53×#1823, C2×#20274800, #27383883, … |
| maximal quotient of | #27277438, #27277451, #27277464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4595);