Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | #421×D53 |
| Fitting | C53×#421 ⋊ C2 |
| Sylow | C53 ⋊ C2×#421 |
772 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1794, #27383417, D53×#1795, … |
| maximal normal subgroup of | D53×#1794, #27383417, D53×#1795, … |
| maximal quotient of | D53×#1478, D53×#1479, D53×#1477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13049);