Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16810429 |
| Fitting | C2×#108×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#359 |
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27299315, C4×#16810429, #27299320, … |
| maximal normal subgroup of | #27299315, C4×#16810429, #27299320, … |
| maximal quotient of | C2×#20272675, C2×#20272678, #27293830, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6233);