Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16810433 |
| Sylow | C53 ⋊ C2×#360 |
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16810433, #360×Dic53, #27299383, … |
| maximal normal subgroup of | C4×#16810433, #360×Dic53, #27299383, … |
| maximal quotient of | C2×#20272682, C2×#20272685, #27293863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6242);