Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#13133286 |
| unambiguous semidirect product | D53⋊(C2×#107) |
| Fitting | C22×C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C22×#107 |
600 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 258 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 | #28306887, #28306888, #28306889, … |
| maximal normal subgroup of | #28306887, #28306888, #28306889, … |
| maximal quotient of | C22×#16811486, C2×D53⋊#335, C22×#16811487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21160);