Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D53⋊#323 |
| Sylow | C53 ⋊ C2×#323 |
456 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 84 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,e^2=g,b^a=bd,d^a=df,h^a=h^30,e^b=ef,h^c=h^52,h^e=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28298417, #28298624, #323×#6157, … |
| maximal normal subgroup of | #28298417, #28298624, #323×#6157, … |
| maximal quotient of | D53⋊#1270, D53⋊#1272, #28299422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19736);