Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16811613 |
| unambiguous semidirect product | D53⋊#416 |
| Fitting | C2×#41×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#416 |
792 conjugacy classes of subgroups.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #28306638, #28306639, #28306647, … |
| maximal normal subgroup of | #28306638, #28306639, #28306647, … |
| maximal quotient of | C2×#20290006, D53⋊#1476, C2×#20290007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21126);