Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#13133163 |
| Sylow | C53 ⋊ C22×Q32 |
360 conjugacy classes of subgroups.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27301167, #27301168, #27301170, … |
| maximal normal subgroup of | #27301167, #27301168, #27301170, … |
| maximal quotient of | C22×#16810426, C22×#16810427, C22×#16810448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17622);