Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D53⋊#100 |
| unambiguous semidirect product | D53⋊(C2×#100) |
| Sylow | C53 ⋊ C22×#100 |
992 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306515, #28306516, #28306545, … |
| maximal normal subgroup of | #28306515, #28306516, #28306545, … |
| maximal quotient of | C2×D53⋊#323, D53⋊#1460, C2×#20289955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21114);