Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16811487 |
| Sylow | C53 ⋊ C2×#335 |
200 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
472 conjugacy classes — view the full character table.
| maximal subgroup of | #28298701, #28298722, #28298746, … |
| maximal normal subgroup of | #28298701, #28298722, #28298746, … |
| maximal quotient of | C2×#20289545, C4×#16811487, #28303028, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20056);