Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#16810364 |
| Sylow | C53 ⋊ C2×#330 |
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 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.
1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27275009, C4×#16810364, #27275017, … |
| maximal normal subgroup of | #27275009, C4×#16810364, #27275017, … |
| maximal quotient of | C2×#20272537, C2×#20272539, #27272063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3093);