Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#16811551 |
| Sylow | C53 ⋊ C2×#368 |
144 conjugacy classes of subgroups.
460 conjugacy classes — view the full character table.
| maximal subgroup of | #28299181, #28299182, #28299200, … |
| maximal normal subgroup of | #28299181, #28299182, #28299200, … |
| maximal quotient of | C2×#20289746, C2×#20289749, #28309862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20863);