Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D8×#88324 |
| Sylow | C53 ⋊ C8×D8 |
196 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 196 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.
238 conjugacy classes — view the full character table.
| maximal subgroup of | D16×#88324, #28309965, SD32×#88324, … |
| maximal normal subgroup of | D16×#88324, #28309965, SD32×#88324, … |
| maximal quotient of | #102×#88324, #107×#88324, #28303670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20089);