Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810940 |
| Fitting | C2×#102×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#481 |
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
766 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16810940, #27391226, #27391293, … |
| maximal normal subgroup of | C4×#16810940, #27391226, #27391293, … |
| maximal quotient of | C2×#20274804, C2×#20274909, C2×#20275029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14408);