Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | AGL(1,ℤ/8)×Dic53 |
| Sylow | C53 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | #453×Dic53, #27389969, #454×Dic53, … |
| maximal normal subgroup of | #453×Dic53, #27389969, #454×Dic53, … |
| maximal quotient of | AGL(1,ℤ/8)×#88322, #27353677, #27353700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13320);