Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16810409 |
| Fitting | C2×#99×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
598 conjugacy classes — view the full character table.
| maximal subgroup of | #27299223, C4×#16810409, #27299238, … |
| maximal normal subgroup of | #27299223, C4×#16810409, #27299238, … |
| maximal quotient of | C2×#20272642, C2×#20272662, #27293340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6141);