Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | #341×D53 |
| Fitting | C53×#341 ⋊ C2 |
| Sylow | C53 ⋊ C2×#341 |
392 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1349, D53×#1350, #27294343, … |
| maximal normal subgroup of | D53×#1349, D53×#1350, #27294343, … |
| maximal quotient of | D53×#1277, #27273549, #27273556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4232);