Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | #349×D53 |
| Fitting | C53×#349 ⋊ C2 |
| Sylow | C53 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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 | D53×#1320, #27293212, D53×#1321, … |
| maximal normal subgroup of | D53×#1320, #27293212, D53×#1321, … |
| maximal quotient of | D53×#1314, #27293152, D53×#1322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6126);