Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#13133162 |
| Fitting | C4×C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 | #27295818, C8×#13133162, #27295830, … |
| maximal normal subgroup of | #27295818, C8×#13133162, #27295830, … |
| maximal quotient of | C8×#13133162, #27295996, #27296003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6364);