Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D53⋊#359 |
| Sylow | C53 ⋊ C2×#359 |
224 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 64 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,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^30,d^b=df,f^b=fg,h^c=h^52,h^e=h^52226 conjugacy classes — view the full character table.
| maximal subgroup of | #359×#6157, #28310677, #28310678, … |
| maximal normal subgroup of | #359×#6157, #28310677, #28310678, … |
| maximal quotient of | D53⋊#1331, D53⋊#1332, #28308477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20822);