Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#13133160 |
| Fitting | C22×Q16×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.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27301154, #27301156, #27301160, … |
| maximal normal subgroup of | #27301154, #27301156, #27301160, … |
| maximal quotient of | C22×#16810423, C22×#16810427, C22×#16810450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17618);