Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16811629 |
| Sylow | C53 ⋊ C2×#424 |
512 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #28307047, #28307061, #28307365, … |
| maximal normal subgroup of | #28307047, #28307061, #28307365, … |
| maximal quotient of | C2×#20290282, C2×#20290284, C2×#20290286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21149);