Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD32×Dic53 |
| Sylow | C53 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
616 conjugacy classes — view the full character table.
| maximal subgroup of | C4×SD32×D53, C2×SD32×Dic53, C4×#16811054, … |
| maximal normal subgroup of | C4×SD32×D53, C2×SD32×Dic53, C4×#16811054, … |
| maximal quotient of | SD32×#88322, #27295995, #27296002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6363);