Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810791 |
| Fitting | C2×H(5,𝔽2)×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#453 |
844 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
916 conjugacy classes — view the full character table.
| maximal subgroup of | #27301391, #27301401, #27303049, … |
| maximal normal subgroup of | #27301391, #27301401, #27303049, … |
| maximal quotient of | C2×#20273633, C2×#20273638, C2×#20273735, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13834);