Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #104×Dic53 |
| Sylow | C53 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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 | C4×#104×D53, C2×#104×Dic53, #27381814, … |
| maximal normal subgroup of | C4×#104×D53, C2×#104×Dic53, #27381814, … |
| maximal quotient of | D4⋊C8×Dic53, Q8⋊C8×Dic53, #27274706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4317);