Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊#88324 |
| Sylow | C53 ⋊ SD16⋊C8 |
176 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 72 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=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^30,d^b=df,h^c=h^30,h^e=h^52226 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16⋊#88324, D53⋊(SD16⋊C8), #28316376, … |
| maximal normal subgroup of | C2×SD16⋊#88324, D53⋊(SD16⋊C8), #28316376, … |
| maximal quotient of | #28301755, #28301759, #28302131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20099);