Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#16811570 |
| unambiguous semidirect product | D53⋊#385 |
| Fitting | C2×C22⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#385 |
1232 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #28307042, #28307057, #28307364, … |
| maximal normal subgroup of | #28307042, #28307057, #28307364, … |
| maximal quotient of | C2×#20289888, C2×#20289895, C4×#16811570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20960);