Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | SD16×Dic106 |
| Sylow | C53 ⋊ Q8×SD16 |
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
763 conjugacy classes — view the full character table.
| maximal subgroup of | #27373585, #27373594, #27373645, … |
| maximal normal subgroup of | #27373585, #27373594, #27373645, … |
| maximal quotient of | #102×Dic106, #103×Dic106, SD16×#11719919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17368);