Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810390 |
| Sylow | C53 ⋊ C2×#342 |
680 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271211, #27271213, #342×Dic53, … |
| maximal normal subgroup of | #27271211, #27271213, #342×Dic53, … |
| maximal quotient of | C2×#20272558, #27273686, #27273692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4240);