Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810773 |
| Fitting | C2×C22⋊Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#450 |
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 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 | #27279234, #27279236, #27280508, … |
| maximal normal subgroup of | #27279234, #27279236, #27280508, … |
| maximal quotient of | C2×#20273666, C2×#20273734, C2×#20273683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13691);