Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16810990 |
| Sylow | C53 ⋊ C2×#491 |
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
760 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16810990, #27392171, #27392190, … |
| maximal normal subgroup of | C4×#16810990, #27392171, #27392190, … |
| maximal quotient of | C2×#20274847, C2×#20275402, C2×#20275403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14848);