Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×D53⋊#108 |
| unambiguous semidirect product | D53⋊(C2×#108) |
| Sylow | C53 ⋊ C22×#108 |
480 conjugacy classes of subgroups.
472 conjugacy classes — view the full character table.
| maximal subgroup of | #28306879, #28306883, #28306892, … |
| maximal normal subgroup of | #28306879, #28306883, #28306892, … |
| maximal quotient of | C2×D53⋊#334, C2×D53⋊#335, C2×#20290262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21167);