Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD32×#6157 |
| Fitting | SD32×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
187 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD32×#6157, #508×#6157, #509×#6157, … |
| maximal normal subgroup of | C2×SD32×#6157, #508×#6157, #509×#6157, … |
| maximal quotient of | SD32×#88324, #28309968, #28309969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20904);