Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#16811505 |
| Fitting | C22×C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
460 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16811505, #28306415, #28306420, … |
| maximal normal subgroup of | C4×#16811505, #28306415, #28306420, … |
| maximal quotient of | C2×#20289555, #28300359, #28300363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20219);