Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#16810756 |
| Fitting | C2×#121×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 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 | #27279227, #27279229, #27280536, … |
| maximal normal subgroup of | #27279227, #27279229, #27280536, … |
| maximal quotient of | C2×#20273632, C2×#20273700, C2×#20273649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13685);