Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16811610 |
| Sylow | C53 ⋊ C2×#413 |
756 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306536, #28306540, #28306566, … |
| maximal normal subgroup of | #28306536, #28306540, #28306566, … |
| maximal quotient of | C2×#20289947, C2×#20289949, C2×#20289951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21119);