Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810781 |
| Sylow | C53 ⋊ C2×#451 |
740 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 740 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.
1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27279221, #27279223, #27280531, … |
| maximal normal subgroup of | #27279221, #27279223, #27280531, … |
| maximal quotient of | C2×#20273674, C2×#20273742, C2×#20273691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13706);