Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16811634 |
| unambiguous semidirect product | D53⋊#428 |
| Fitting | C2×M16×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#428 |
536 conjugacy classes of subgroups.
304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306988, #28306989, #28306997, … |
| maximal normal subgroup of | #28306988, #28306989, #28306997, … |
| maximal quotient of | C2×#20290266, D53⋊#1565, C2×#20290267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21162);