Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #331×D53 |
| Fitting | C53×#331 ⋊ C2 |
| Sylow | C53 ⋊ C2×#331 |
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
532 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1402, C2×#331×D53, D53×#1540, … |
| maximal normal subgroup of | D53×#1402, C2×#331×D53, D53×#1540, … |
| maximal quotient of | D53×#1270, #27272065, #27272367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3149);