Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16811573 |
| unambiguous semidirect product | D53⋊#388 |
| Fitting | C2×C22⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#388 |
928 conjugacy classes of subgroups.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #28301551, C4×#16811573, #388×#6157, … |
| maximal normal subgroup of | #28301551, C4×#16811573, #388×#6157, … |
| maximal quotient of | C2×#20289890, C2×#20289895, C2×#20289896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20963);