Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#13133163 |
| Sylow | C53 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27295823, C8×#13133163, #27295835, … |
| maximal normal subgroup of | #27295823, C8×#13133163, #27295835, … |
| maximal quotient of | C8×#13133163, #27296006, #27296008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6367);