Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #101×#6157 |
| Fitting | #101×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×#101 |
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
187 conjugacy classes — view the full character table.
| maximal subgroup of | #355×#6157, #356×#6157, #28310642, … |
| maximal normal subgroup of | #355×#6157, #356×#6157, #28310642, … |
| maximal quotient of | #324×#6157, #28301541, #28301546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20264);