Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | #99×Dic53 |
| Sylow | C53 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
616 conjugacy classes — view the full character table.
| maximal subgroup of | #27299223, AΣL(1,𝔽16)×Dic53, #27299228, … |
| maximal normal subgroup of | #27299223, AΣL(1,𝔽16)×Dic53, #27299228, … |
| maximal quotient of | #323×Dic53, #324×Dic53, #27274604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4300);