Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#16810347 |
| Sylow | C53 ⋊ C2×#323 |
456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271050, #27271051, #27271211, … |
| maximal normal subgroup of | #27271050, #27271051, #27271211, … |
| maximal quotient of | C2×#20272536, C2×#20272541, #27272044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2817);