Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q32×#6157 |
| Fitting | Q32×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 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 | SD64×#6157, Q64×#6157, #28312646, … |
| maximal normal subgroup of | SD64×#6157, Q64×#6157, #28312646, … |
| maximal quotient of | Q32×#88324, #28309972, #28309973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20905);