Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16810440 |
| Sylow | C53 ⋊ C2×#362 |
216 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 216 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.
1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299349, C4×#16810440, #27299370, … |
| maximal normal subgroup of | #27299349, C4×#16810440, #27299370, … |
| maximal quotient of | C2×#20272686, #27293872, #27294103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6255);