Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16811519 |
| Sylow | C53 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
460 conjugacy classes — view the full character table.
| maximal subgroup of | #28298430, #28298431, #28298433, … |
| maximal normal subgroup of | #28298430, #28298431, #28298433, … |
| maximal quotient of | C2×#20289635, #28307874, C2×#20289651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20743);