Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #137×Dic53 |
| Sylow | C53 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | #455×Dic53, #27389980, #456×Dic53, … |
| maximal normal subgroup of | #455×Dic53, #27389980, #456×Dic53, … |
| maximal quotient of | #137×#88322, #27353688, #27353711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13331);