Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#16810445 |
| Sylow | C53 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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 | #27299475, C4×#16810445, #27299513, … |
| maximal normal subgroup of | #27299475, C4×#16810445, #27299513, … |
| maximal quotient of | C2×#20272780, #27295649, #27295723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6278);