Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#16811469 |
| Sylow | C53 ⋊ C2×#324 |
328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
460 conjugacy classes — view the full character table.
| maximal subgroup of | #28298627, #28298629, #28301528, … |
| maximal normal subgroup of | #28298627, #28298629, #28301528, … |
| maximal quotient of | C2×#20289534, #28299427, #28299457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19740);