Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#11719910 |
| Sylow | C53 ⋊ D4⋊C16 |
110 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=d,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^30,c^b=ce,h^d=h^52316 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4⋊#11719910, D53⋊(D4⋊C16), #28308450, … |
| maximal normal subgroup of | C2×D4⋊#11719910, D53⋊(D4⋊C16), #28308450, … |
| maximal quotient of | #28298120, #28298122, #28298124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19460);