Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#13133162 |
| Fitting | C22×C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×SD32 |
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27301155, #27301157, #27301162, … |
| maximal normal subgroup of | #27301155, #27301157, #27301162, … |
| maximal quotient of | C22×#16810425, C22×#16810428, C22×#16810451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17620);