Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#16810388 |
| Sylow | C53 ⋊ C2×#341 |
392 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271238, #27271240, #27271244, … |
| maximal normal subgroup of | #27271238, #27271240, #27271244, … |
| maximal quotient of | C2×#20272550, #27273551, #27273558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4234);