Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #106×#6157 |
| Fitting | #106×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×#106 |
280 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
238 conjugacy classes — view the full character table.
| maximal subgroup of | #360×#6157, #365×#6157, C2×#106×#6157, … |
| maximal normal subgroup of | #360×#6157, #365×#6157, C2×#106×#6157, … |
| maximal quotient of | #334×#6157, #28302090, #28302103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20321);