Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16810415 |
| Fitting | C2×#99×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
598 conjugacy classes — view the full character table.
| maximal subgroup of | #27299253, C4×#16810415, #27299265, … |
| maximal normal subgroup of | #27299253, C4×#16810415, #27299265, … |
| maximal quotient of | C2×#20272646, C2×#20272660, #27293360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6167);