Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810761 |
| Sylow | C53 ⋊ C2×#448 |
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
766 conjugacy classes — view the full character table.
| maximal subgroup of | #27279213, #27279215, #27280557, … |
| maximal normal subgroup of | #27279213, #27279215, #27280557, … |
| maximal quotient of | C2×#20273637, C2×#20273705, C2×#20273654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13697);