Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | SD16×C22⋊D53 |
| Fitting | C22×SD16×C53 ⋊ C2 |
| Sylow | C53 ⋊ D4×SD16 |
546 conjugacy classes of subgroups.
763 conjugacy classes — view the full character table.
| maximal subgroup of | D4×SD16×D53, C2×SD16×C22⋊D53, #28259381, … |
| maximal normal subgroup of | D4×SD16×D53, C2×SD16×C22⋊D53, #28259381, … |
| maximal quotient of | #27373555, #27373560, #27373570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16200);