Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | #416×D53 |
| Fitting | C53×#416 ⋊ C2 |
| Sylow | C53 ⋊ C2×#416 |
792 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1764, D53×#1765, #27381952, … |
| maximal normal subgroup of | D53×#1764, D53×#1765, #27381952, … |
| maximal quotient of | D53×#1476, D53×#1488, #27350500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13002);