Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16811535 |
| unambiguous semidirect product | D53⋊#357 |
| Fitting | C2×D8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#357 |
272 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
226 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16811535, #357×#6157, #28310668, … |
| maximal normal subgroup of | C4×#16811535, #357×#6157, #28310668, … |
| maximal quotient of | C2×#20289669, D53⋊#1331, C2×#20289670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20815);