Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16811529 |
| Fitting | C22×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#354 |
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
286 conjugacy classes — view the full character table.
| maximal subgroup of | #28299205, #28299206, #28299237, … |
| maximal normal subgroup of | #28299205, #28299206, #28299237, … |
| maximal quotient of | C2×#20289645, C2×#20289656, #28308075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20778);