Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16811633 |
| unambiguous semidirect product | D53⋊#427 |
| Fitting | C22×C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#427 |
512 conjugacy classes of subgroups.
472 conjugacy classes — view the full character table.
| maximal subgroup of | #28306879, #28306880, #28306883, … |
| maximal normal subgroup of | #28306879, #28306880, #28306883, … |
| maximal quotient of | C2×#20290262, D53⋊#1564, C2×#20290263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21161);