Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#13133280 |
| Fitting | C4×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×#103 |
332 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
316 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#13133280, #28301753, #28301758, … |
| maximal normal subgroup of | C8×#13133280, #28301753, #28301758, … |
| maximal quotient of | C4×Q8⋊#88324, C4×#16811473, #28301643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20278);