Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q32×Dic53 |
| Sylow | C53 ⋊ C4×Q32 |
150 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | #27304668, SD64×Dic53, #27304675, … |
| maximal normal subgroup of | #27304668, SD64×Dic53, #27304675, … |
| maximal quotient of | Q32×#88322, #27296009, #27296083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6369);