Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | SD16×#88322 |
| Sylow | C53 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
784 conjugacy classes — view the full character table.
| maximal subgroup of | C8×SD16×D53, C2×SD16×#88322, C8×#13133238, … |
| maximal normal subgroup of | C8×SD16×D53, C2×SD16×#88322, C8×#13133238, … |
| maximal quotient of | #102×#88322, #103×#88322, #106×#88322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3311);