Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #352×D53 |
| Fitting | C53×#352 ⋊ C2 |
| Sylow | C53 ⋊ C2×#352 |
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
364 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#352×D53, D53×#2120, D53×#2121, … |
| maximal normal subgroup of | C2×#352×D53, D53×#2120, D53×#2121, … |
| maximal quotient of | D53×#1317, D53×#1326, #27293344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6144);