Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #103×Dic53 |
| Sylow | C53 ⋊ C4×#103 |
332 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#103×D53, C2×#103×Dic53, C4×#16810618, … |
| maximal normal subgroup of | C4×#103×D53, C2×#103×Dic53, C4×#16810618, … |
| maximal quotient of | Q8⋊C8×Dic53, #27274721, #27274726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4332);